Citation
Searching the solar neighborhood for protoplanetary debris disks

Material Information

Title:
Searching the solar neighborhood for protoplanetary debris disks a survey of Vega-like sources and a discussion of new disk examples
Creator:
Fisher, Robert Scott
Publication Date:
Language:
English
Physical Description:
x, 178 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Crates ( jstor )
Diameters ( jstor )
Flux density ( jstor )
Grain size ( jstor )
Hertzsprung Russell diagrams ( jstor )
Signals ( jstor )
Silicates ( jstor )
Stellar evolution ( jstor )
Telescopes ( jstor )
Wavelengths ( jstor )
Astronomy thesis, Ph. D ( lcsh )
Circumstellar matter ( lcsh )
Dissertations, Academic -- Astronomy -- UF ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 2001.
Bibliography:
Includes bibliographical references (leaves 172-177).
General Note:
Printout.
General Note:
Vita.
Statement of Responsibility:
by Robert Scott Fisher.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
027697059 ( ALEPH )
48198422 ( OCLC )

Downloads

This item has the following downloads:


Full Text










SEARCHING THE SOLAR NEIGHBORHOOD FOR PROTOPLANETARY DEBRIS
DISKS: A SURVEY OF VEGA-LIKE SOURCES AND A DISCUSSION OF NEW
DISK EXAMPLES

















By

ROBERT SCOTT FISHER


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2001

































Copyright 2001

by

Robert Scott Fisher

































This work is dedicated to my fellow inhabitants of 317, 135, 8, 2613, 139, and 1072A.















ACKNOWLEDGMENTS

I would first like to acknowledge my advisor Dr. Charles Telesco for his role in

this work and for his valuable friendship. In the time spanning the work for this

dissertation I have learned from him in many ways. In the office, the lab, or the control

room, I have always enjoyed our discussions. It seems like not so long ago that we met

for the first time in a small office on the second floor and talked about the idea of this

project... Not long after that came the infamous 'run of 100 ms.' Then we were off to

Chile where we learned that the polar axis of a telescope points to the South pole in the

southern hemisphere, and that cake is not always what it seems. We had nights of El Niio

there, and nights of high stakes science. Then we went to Keck and learned what D4

really means. At Keck we first used the unit 'pJy' and also learned that the PicTel can

sometimes be a good thing. Now we are at Gemini. OSCIR is still getting time on the sky

and T-ReCS is coming soon. I look forward to the planned collaboration with Charlie,

and I look forward to our continued friendship.

I would also like to thank Dr. Robert Pifia for his guidance and his friendship.

Bringing OSCIR into operation and spending time with Robert running the system are

some of my best memories of this work. I admire his ability to diagnose a problem, and I

will always relish coming into his office to 'check this out.' I hope that I somehow

contributed to the many talks about the OSCIR interface and the acquisition system. I

would like to thank Kevin Hanna for his development of the OSCIR electronics system,

and Jeff Julian for his design and fabrication of critical OSCIR components. One of the









main reasons that OSCIR has been a premier instrument for the last 6 years is the talent

these two possess. I would especially like to recognize Kevin for his unquestionable

perseverance and dedication to getting OSCIR operational. I thank him for the nights he

and Robert put in at HP and Tololo.

I also would like to thank my friends James Radomski and Jim De Buizer. I sat

here and tried to think of which of their qualities I wanted to mention, but basically I

thank them for the whole deal and for being my friends. We all know the secret of row

90, and I can think of no better way to spend a Saturday afternoon than in The Swamp

with the two of them and Brent.

My family has also played an important role in this work. I thank Brent, Jeanette,

and Wik for keeping me grounded and keeping me company. There has always been an

inner strength to our family-unit, and that has helped me in ways both obvious and subtle.

Thanks to them I never missed a flight, and I never forgot the HASP. To my extended

family in St. Augustine and in Pennsylvania I also send my thanks for their support since

day one.

The last people I want to recognize are Ann, Audrey, Debra, Glenda, and Tracey

in the main office. We all know that without them the department would not run, but no

one seems to thank them for it. So thanks.



This work was supported in part by a NASA Graduate Student Research Fellowship and

funding from the National Science Foundation
















TABLE OF CONTENTS

page

ACKNOW LED GM ENTS............................................................................................ iv

ABSTRACT ....................................................................................................................... ix

CHAPTERS

1 INTRODUCTION ..................................................................................................... 1

Star Form ation and Disk Creation.................................. ............... .......................... 4
Evolutionary Status of Vega-like Disks.................................................. .............. 8
Outline of the Project .............................................................................................. 11

2 OBSERVATIONS AND DATA REDUCTION..................................... ........... 13

Source Lists ................................................................................................................... 14
Instrum entation........................................................................................................ 17
Observational Strategy ............................................................................................ 20
Nightly Variation of the PSF...................................................... ........................... 21
Data Reduction Steps .............................................................................................. 23
Rem oval of Contam inated Data ................................................ ........................ 23
Cross-Correlation of Im ages .................................................... ......................... 25
Skyfit ................................................................................................................... 25
Calibration/Airm ass Correction ................................... .........................................26
Flat-field Correction ........................................................................................... 29
Photom etry .......................................................................................................... 29
Color Correction.................................................................................................. 30
Resolved or Unresolved: The Question ................................ .............. ....... ..... 34

3 SURVEY DISCUSSION ........................................................................................ 37

Disk Sizes...................................................................................................................... 38
Photosphere Rem oval..............................................................................................41
Grain M odels........................................................................................................... 47
Color Tem peratures and Optical Depths............................................ ............... 54
Scale Size Com parison........................................................................................ 59
A Proposed Evolutionary Sequence ............................................... ....................... 64
SED Evolution........................ ............................................................................. 64









Class IIIa: The near-IR N ine ........................................................................ 68
Class IIIb: ZAM S Sources .............................................................. ......... ...........70
Class IIIc: Post ZAM S Sources .......................................................................... ...71
Survey Sources in the HR D iagram ......................................... ................................. 73

4 THE FACE-ON DISK OF H D 169142................................................................... 79

M id-Infrared Observations at Keck...................................................... .................. 83
HD 169142 Source Size ........................................................................................ 85
M odeling of Characteristic Grain Param eters............................................ ......... 87
M odel Results.......................................................................................................90
Grain Sizes and Tem peratures................................................................................... 91
Discussion and Conclusions.......................................................... 99
Disk Orientation ..................................................................................................... 99
Evolutionary Status ................................................................................................ 101
Conclusions ............................................................... .................................................. 106

5 KECK IM AGIN G OF HD 141569 ............................................................................. 108

Observations................................................................................................................ 110
Source Size.................................................................................................................. 113
Dust Tem perature and Grain Size ............................................................................... 117
Com prison to N ICM OS Im ages ................................................................................ 119
Conclusions About the Disk of HD 141569................................................................ 122

6 SAO 26804: A QUESTION OF CLASSIFICATION ............................................... 124

The Detection and Non-detection of the SA O 26804 Disk......................................... 125
Previous Observations ............................................................................................. 125
New Keck Im aging w ith OSCIR ........................................................................... 127
First-Ascent Giant or M ain-Sequence Dw arf? ......................................................... 131
Luminosity Class V: A Main-Sequence Dwarf................................. 132
Lithium Abundance................................................................................................. 134
Position in the H-R Diagram ................................................................................... 136
Sum m ary and Conclusions.......................................................................................... 139

7 INSTRUMENTATION ACTIVITIES: THE OSCIR SYSTEM................................ 140

System Overview ........................................................................................................ 141
The Dew ar............................................................................................................... 144
Optics .................................................................................................................. 147
Entrance W indow and Filters ............................................................................ 150
Detector ............................................................................................................... 154
VM E Crate .............................................................................................................. 158
Control Com puter.................................................................................................... 162
Sum m ary of Activities ................................................................................................ 164










APPENDIX

M ID-IR ASTRONOMY: A SHORT COURSE.............................................................. 165
Extracting the Source Signal ....................................................................................... 167
The Standard Chop-Nod Technique.............................................................................. 168

LIST OF REFERENCES ................................................................................................ 172

BIOGRAPHICAL SKETCH..................................................................................... 178















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

SEARCHING THE SOLAR NEIGHBORHOOD FOR PROTOPLANETARY DEBRIS
DISKS: A SURVEY OF VEGA-LIKE SOURCES AND A DISCUSSION OF NEW
DISK EXAMPLES


By

Robert Scott Fisher

August 2001


Chairman: Charles M. Telesco
Major Department: Astronomy

Theory suggests that planets form in the dusty circumstellar disks associated with

young stars. Many classes of stars exhibit excess infrared emission that is attributed to the

dust grains in these disks. In this dissertation we present mid-IR (10 and 18 gm) imaging

observations of a sample of almost forty Vega-like stars. These are stars that have mostly

finished their pre-main-sequence evolution and are now close to, or already on the main

sequence. Our imaging shows that most of these sources are unresolved at arcsecond

resolution at 10 and 18 9Lm. We did however make the first detection of extended mid-IR

emission for two stars; HD 141569 and HD 169142. We use our observations to

investigate the properties of the mid-IR-emitting dust grains in these two resolved disks,

and the unresolved disks of 22 of the survey sources using radiative equilibrium models.

The results of our modeling show that the mid-IR emission from these disks traces the









position of grains that are 1 to 10 ltm in diameter in the disks of these stars. The mid-IR-

emitting grains orbit the stars at distances of tens of AU, similar to the size of the Solar

system, and therefore trace the region of assumed planetary formation in these disks.

Additionally, we place the survey stars into the H-R diagram, and use the characteristics

of their infrared excess in conjunction with their positions to suggest a proposed

evolutionary sequence for them. Finally, discuss the development, characterization, and

support of the OSCIR camera system that was a fundamental aspect of the work

presented in this dissertation.














CHAPTER 1
INTRODUCTION

This dissertation focuses on the study of circumstellar disks around main-

sequence stars. The most fundamental question one can ask is, why is the study of disks

important? There are two facets to the answer to that question. The first deals with star

formation and the evolution of stellar objects during the initial stages of their lives.

Current theories of star formation like that of Andre (1994) suggest that the formation of

a circumstellar disk is necessary for the successful formation of a low or intermediate

mass (M < -5 M.) star. In this context, circumstellar disks are just one of a myriad of

supporting players in the process of star formation, but an important one. The disks

dissipate angular momentum from the system while bi-polar outflows remove excess gas

and dust from the close stellar environment in the first few million years of its life. With

the relative explosion of observations of circumstellar disks in the last 10 years, they now

seem ubiquitous. Also important is the fact that planetary systems form from these disks.

With the recent discovery of numerous exo-solar planets and planetary systems (Marcy

and Butler 1996), understanding the formation and evolution of circumstellar disks is

more important than ever. The research presented in this dissertation relates more to the

second facet presented above. Our research is centered on the study of circumstellar disks

around stars that are either in the very last stages of their pre-main-sequence (PMS)

formation, or have already moved onto (or past) the zero-age-main-sequence (ZAMS) in

the H-R diagram. These disks are the so-called "Vega-like," or debris disks.





















0.10



0.01 -



10 100 1000
Wavelength [pm]


Figure 1-1: The spectral energy distribution (SED) of Vega. Solid line is a model
atmosphere. Dotted line is a modified blackbody fit to the data with T=73 K and
Q(X) a X'1' Flux estimates from ISOPHOT and IRAS. Submillimeter fluxes from
Zuckerman and Becklin (1993). Figure from Heinrichsen et al. (1998)



The IRAS satellite discovered the "Vega phenomenon" in 1984 when it was

performing what was thought to be routine calibration observations of the photometric

standard star, Vega. The surprising result returned by IRAS was that at all X> 12 gIm

Vega exhibited levels of emission that were several times higher than what was predicted

by model stellar atmosphere calculations. In Figure 1-1 we plot the SED of Vega to show

the shape and extent of this excess emission. This excess emission was attributed to

emission from dust grains in the vicinity of the star, presumably in the form of a disk.

Three more examples of this phenomenon were quickly discovered: a PsA, P Pictoris,

and E Eri; and together with Vega they became the archetypes for this class of object

(Aumann et al. 1984). Smith and Terrile (1984) proved the disk hypothesis with their









coronagraphic image of 3 Pictoris, which showed a nearly edge-on disk (i > 800) around

the star with dimensions of 100s of AU. The publication of this image jumpstarted the

field and the study of Vega-like disks has become one of the most heavily researched

aspects in modem astronomy; since 1984 there have been almost 1700 papers published

with the name "Beta Pictoris" in the title.

Since planets are thought to form in the dusty environments around stars, there

seems to be a growing consensus that the Vega phenomenon is intimately connected with

the occurrence of planetary systems. Indeed, we live inside our own Vega-like disk, the

so-called Zodiacal "cloud" disk around the Sun. Many of the characteristics of the Vega-

like disks are similar to our own dust disk, including the fact that the lifetime of dust in

orbit around the archetypes is much shorter than the estimated age of the central stars.

This means that the dust must be replenished in some manner, which hints at the

existence of hidden planetary companions in the disks that could supply the system with

fresh dust much like comets and asteroidal collisions do in the Solar system. In the last

few years evidence has been accumulating for the existence of exo-solar planets in some

Vega-like disks. High-resolution STIS images have revealed a warp in the disk of P

Pictoris (Heap et al. 1997), and subsequent near-IR (2 um) observations confirm that

warp exists and suggest that a planet with a -30 inclination could cause it (Mouillet et al.

1997). In the mid-IR (5 to 30 gLm) the disk of HR 4796A has been imaged at -0.3"

resolution by Telesco et al. (2000), Jayawardhana et al. (1998), and Koerner et al. (1998)

showing evidence for an inner hole of approximately Solar system dimensions.

Our motivation for this dissertation is to characterize a number of these Vega-like

disks in the mid-IR. To this end we used a modern mid-infrared camera system with large









aperture telescopes to conduct a survey of nearly 40 Vega-like stars in the mid-IR (10 and

18 gpm). In the following chapters we discuss our survey results, and place the observed

Vega-like sources into an evolutionary sequence. We also discuss two new disk examples

that we resolved in the mid-IR for the first time.

In the remainder of this chapter we summarize the current paradigm of low and

intermediate mass star formation and see that the formation of a circumstellar disk is

most likely a requisite step in the process. We then contrast the disks we see around

Vega-like stars with those around stars in earlier stages of formation, like the Herbig

Ae/Be stars. We end the chapter with a statement of the dissertation project and list what

we hope to add to the current status of Vega-like disk research.




Star Formation and Disk Creation

The formation of stars is the main way that material is removed from the

interstellar medium. Star formation is also one of the main topics of study in modem

infrared astronomy. The very first stage of star formation takes place in the cores of giant

molecular clouds (GMCs). The evidence that star formation occurs in these clouds is

strong. First and foremost, direct observation easily correlates regions of star formation

with dark clouds in the sky, for example in the constellations of Taurus and Ophiuchus.

Since the newly formed stars are by definition young, we believe that they have not yet

had sufficient time to move away from their birthplaces. Additional evidence comes in

the form of the correlation between the youngest stars known and the presence of

molecular CO emission (Churchwell 1991). In fact, Churchwell (1991) shows that there

is no place in the galaxy where active star formation is occurring where there is not









significant CO emission. Since CO is a major constituent of molecular clouds, it seems

very reasonable to think that stars form out of the material in these GMCs. The earliest

stage of the formation of a star is the fragmentation and collapse of part of a GMC. The

passing of a galactic spiral density wave, or a close encounter with a nearby star may

trigger the collapse. Whatever the trigger, the process of star formation is underway when

a fragment of approximately 104 AU "breaks-off' from the main cloud and starts its

collapse. The luminosity associated with these "protostars" is at first derived from the

gravitational energy associated with this collapse. At some point in this process there is

enough luminosity associated with the protostar that it can be observed directly. We

begin our more detailed discussion of star formation at this point following the work of

Lada (1987) and Andre et al. (1993).

In Figure 1-2 we show the different stages in the evolutionary sequence of young

stellar objects. On the right side of the figure there is a model spectral-energy-distribution

(SED) of the source. The middle panels show a sketch of the system, and the left side

lists relevant masses and timescales for each Class. A Class 0 source is the earliest

observable stage of star formation. Class 0 sources are only visible in the millimeter

regime or through the detection of CO spectrally. The dust shells surrounding these

sources are still so dense they are optically thick to even mid and far-IR radiation.

Because collimated CO outflows are often associated with Class 0 sources, it is believed

that a centralized core has formed by this stage and that matter from the surrounding shell

is actively accreting onto it. At this stage the shell is likely still more massive than the

protostar at its core.









i lumd 0101 0.1 1

I-' O iiM O4.V I C I1
'Cld Bladc Bo0y : O
Age s









1 2 10 100
SCASS ~ :

""I I Me

mdMd
p-**yrf






























perhaps 2 tm. There are still collimated outflows of molecular gas, for example CO,
1 2 10 M00


AVS 1'yri




LInl



Figure 1-2: Schematic of low and intermediate mass star formation by Lada (1987) and
Andre et al. (1994).



The flow of matter onto the protostar continues unabated past the transition into

the Class I phase, which occurs on timescales of _105 yr. At this point the formation of

the protostar is almost complete, and it is now detectable through the infrared, down to

perhaps 2 gim. There are still collimated outflows of molecular gas, for example CO,

associated with Class I objects indicating that the inner regions of the shell are still being









accreted onto the protostar. The amount of material around the star is still large, upwards

of 0.1 Me. Class I objects are also normally associated with extended millimeter

continuum emission. Some form of disk has likely formed around the protostar at this

stage.

By the time the system becomes a Class II source the millimeter continuum has

become much more compact, and there is rarely any evidence for outflows associated

with the source. The age of the system is now ~ 106 yr and the mass of the optically thick

disks associated with these sources is close to the minimum mass Solar nebula, -0.01

Me. At this stage the SED of the source is beginning to resemble that of a Herbig Ae/Be

star with strong excess emission detected down to 2 .Lm or less. This is relevant to our

work since it is believed that the Herbig Ae/Be stars are the progenitors of the Vega-like

stars that we study in this dissertation. Indeed, some of the SEDs of our survey sources

resemble those of the Class II objects shown in Figure 1-2, although most of our sources

are clearly Class III, or later.

The Class III stars have thin disks associated with them and their SEDs are

approaching those of normal stars. Depending on the mass of the star, Class III is reached

in the few x 106 yr timescale. In this stage there is little evidence for active accretion onto

the star and absorption lines are often seen in the spectra of these sources. The mass of

the disks around Class III stars is low: around 0.003 Me; much less than that in Class II

or earlier. It is around Class III sources that you find Vega-like disks. This connection

between a Class III and a Vega-like source is beautifully illustrated by comparing the

SED of the Class III source in Figure 1-2 with the SED of Vega in Figure 1-1.









Evolutionary Status of Vega-like Disks

As seen in the last section the Vega-like sources most resemble stars in the last

stages of star formation. To more clearly define what a "Vega-like' system is we use the

definition suggested by Lagrange et al. (2000). In their review they suggest the following

criteria for defining a Vega-like system

Ldus/L* << 1
M(dust+gas) << 0.01 M
Dust dynamics not controlled by gas ; Mgas << 10 Mdust
grain destruction times less than age of star

The first criteria is set to make sure that a massive protostellar disk is not present around

the star. Criteria 2 guarantees that the circumstellar material is optically thin. Criteria 3

makes sure that the dust is separated from any remnant gas left in the system and that the

motion of the dust grains are Keplerian modified by radiative processes. This should

exclude systems where dust is condensing in winds and jets. Criteria 4 that is crucial to

the definition because it ensures that the dust around the source is not primordial. That is,

the grains have been processed within the disk. It implies that the dust grains must be

somehow replenished from larger objects. This is important since it implies that larger

grains are present, and also hints at the existence of even larger, planetesimal sized bodies

capable of sending the smaller bodies into collision-producing orbits (Lagrange et al.

2000).

There is also some issue with the name "main-sequence" being an integral part of

the definition of a Vega-like system. The definition of Lagrange et al. (2000) above

defines the class in terms of the physical state of the circumstellar matter, not the exact

evolutionary state of the central star. The star itself may or may not have reached the










Table 1-1: Resolved Vega-like Disks

Source D ) Spectral Age
Name Type (yr)

EEri 3.2 K2V (5-10)x108
a PsA 7.7 A3V 1-3x108
a Lyr 7.8 AOV 3x108
pPictoris 19.3 A5V 1-2xl07
HR 4796A 67.0 A5V (8+3)x106
HD 141569 99.0 B9V 1xl07
HD 169142 145.0 A5V (3-5)x 106
BC+31643 330.0 B5V 106-107
SEstimates from this dissertation
SOSCIR estimate, see Telesco et al. (2000)


Disk Radius at Given Wavelength (AU)
0.5 Lm 2 gm 10-20 pm 60 pm 850 .m

S 60
S 80 160
S 100 125
800 120 150 250 250
70 70 -
400 100 --
90t
> 1000
> 1000 -----


main sequence by the time its disk meets the above criteria. This is relevant to this

dissertation since we have investigated a number of stars that seem to be transitioning

from Class II to Class III. While the stars may not yet have reached the ZAMS, they

clearly exhibit characteristics reminiscent of main-sequence stars. Lagrange et al. (2000)

coined the term 'old pre-main-sequence' stars (OPMS) to describe these sources. They

are an interesting class of object since they represent the transition between the pre-main-

sequence stars of the star forming regions, and the main-sequence stars in the solar

neighborhood.

Because the Vega-like disks are optically thin, tenuous structures, they are very

difficult to detect. In the 17 years since Smith and Terrile (1984) published their

watershed image of P Pictoris only seven other Vega-like disks have been directly

imaged. In Table 1-1 we list the Vega-like disks that have been resolved at any

wavelength. This is however, rapidly changing. New instruments coupled with large

aperture telescopes are giving us the opportunity to detect more of these disks than ever

before. This is made evident by the fact that 12 of the 14 size estimates in Table 1-1 have









been published in the last 4 years. In particular the latest generation of near and mid-IR

instruments allows us to investigate this class of object as never before. The sub-

arcsecond angular resolution achieved by the 8 to 10 m class telescopes lets us see down

to a few AU from the stars in the closer of the sample sources, and the sensitivities of the

latest generation mid-IR cameras give us the chance to detect fainter extended emission

from these disks than ever before. This is one of the motivating factors behind this

dissertation, to use the latest generation of infrared camera systems on the largest aperture

telescopes to investigate the class of Vega-like source as a whole.

This work is unique in one important way. Investigating these disks in the mid-IR

directly probes the region where planetary systems form in them. This work is

complementary to research done in the near-IR, sub-mm, and mm regimes. At the longer

wavelengths we are detecting the coldest dust in the systems, which has temperatures in

the tens of Kelvin range. This cold dust also orbits hundreds of AU from the stars, much

farther away than any known planetary companions. At the shorter wavelengths, the near-

IR, we detect two different kinds of radiation. Some sources exhibit thermal emission

from hot dust (T = 1 to 2000 K) very close (1 to 3 AU) to the stars (e.g., HD 169142;

Chapter 4). Others like HD 141569 (Weinberger et al. 1999) and P Pictoris (Kalas &

Jewitt 1995) are associated with near-IR radiation that is scattered from the dust in their

disks. This scattered radiation is seen out to hundreds of AU in these two cases and is

likely being scattered off the dust grains that are responsible for the far-IR/sub-mm/mm

emission detected around these systems. The mid-IR forms a bridge between these two

regimes. It can be said that the long wavelength emission comes from the "Kupier belts"

and perhaps "Oort clouds" of the Vega-like sources, while the near-IR emission comes









from the very inner parts of their disks. In this scheme the mid-IR emission would come

from the Zodiacal dust of the Vega-like systems, most likely tracing the region where

planets are forming, exactly where they formed in our own Solar System. For this reason

these disks are important to study, for by answering questions about them as a class, we

may well be able to answer outstanding questions about the formation and evolution of

our own Earth. In the next section we outline the work presented here.




Outline of the Project

This dissertation is centered on mid-IR (10 and 18 pLm) imaging of a large sample

of Vega-like stars. We undertook this project with the hoping to characterize a number of

disks at these wavelengths, and we succeeded by making the first detection of extended

mid-IR emission around two stars, HD 141569 and HD 169142. We did not detect any

extension around the remainder of the survey sample.

In Chapter 2 we discuss our sample, our observations of the survey sources, and

the data reduction steps we used. Chapter 3 presents our conclusions about the survey as

a whole and we place our sample sources into what may be an evolutionary sequence. In

Chapter 4 we discuss the newly discovered disk around the star HD 169142, and

investigate the properties of the dust in that disk through radiative equilibrium models.

We present similar results for HD 141569 in Chapter 5. For HD 141569 we derive grain

size estimates for the mid-IR-emitting grains, and compare our mid-IR images of this

disk to near-IR images from HST. In Chapter 6 we present observations that "de"-resolve

the source SAO 26804, a star previously thought to be associated with a Vega-like disk.

We show that it is likely that SAO 26804 is a luminosity Class III star and not on the






12


main sequence. Chapter 7 discusses the OSCIR instrument and its role in this

dissertation. We close with an Appendix on mid-IR observing and discuss the specialized

techniques used in that wavelength regime.














CHAPTER 2
OBSERVATIONS AND DATA REDUCTION

We have used front-line infrared instrumentation and large aperture telescopes to

survey approximately 40 Vega-like sources in the northern and southern sky. Most of the

survey was conducted at the Blanco 4-meter telescope at the Cerro Tololo Inter-American

Observatory (CTIO). Parts of the survey were also conducted at the NASA Infrared

Telescope Facility (IRTF) and the W. M. Keck Observatory (Keck). The project centered

on imaging each of the survey sources at 10 and 18 p.m using the Observatory

Spectrometer and Camera for the Infrared (OSCIR). The OSCIR system is discussed in

detail in Chapter 7. For most of the sources our images are the first mid-IR observations

of them since those of the IRAS satellite. A literature search for other mid-IR

observations of our survey sources returned only two further studies. Fajardo-Acosta,

Telesco, and Knacke (1993) imaged five of the sources at -4" resolution, and Sylvester et

al. (1996) presented mid-IR spectra of a dozen of the sources on our list. A small number

of our sources have questionable classification, and have been included in studies of

Herbig Ae/Be stars also. In particular, the studies of van den Ancker et al. (1998) and van

den Ancker (2001) contain members of our sample. Although the stars in our survey have

been studied in other wavelength regimes, our mid-IR imaging here represents the

highest resolution mapping of these sources to date. Our observations typically have sub-

arcsecond resolution limits with some as low as 0.3". At the average distance of our

survey stars (77 pc) at these resolutions we are tracing emission from dust that is tens of

AUs from the star, a region where planetary systems are born and evolve. We cannot yet









directly detect any planets around these stars. However, we can detect the effects of

hidden planets on the disks they inhabit. An example of this idea is the inner holes

predicted by the SEDs of some of the sources. An inner hole with a diameter of

approximately 50 AU was predicted in the disk of HR 4796A by Jura et al. (1998) and

was then directly imaged by Jayawardhana et al. (1998), Koerner et al. (1998) and

Telesco et al. (2000). Observing our survey sources in two mid-IR passbands also gives

us the opportunity to investigate the physical properties of the mid-IR-emitting grains in

these disks. Our 10 and 18 gm observations let us estimate the temperature of the grains;

and investigate their composition, size and distance from the stars. We also comment on

the dynamical properties of the grains and discuss the roles of Poynting-Robertson drag

and radiation expulsion on the evolution of the grains. In the next sections we discuss or

sample stars and describe how we reduced the data.




Source Lists

Our primary source list is that of Walker and Wolstencroft (1988) [hereafter

WW]. One of the first searches of the IRAS database after the discovery of the four

archetypes, WW is one of the primary lists of Vega-like sources used today. WW present

a list of 34 sources that have characteristics similar to Vega and the other archetypes.

Their selection criteria are shown below.

1. Sources must be associated with bright visual sources (SAO stars), but not
with a well-known emission-line star.
2. Sources must have a 60 gm/100 gm flux density ratio similar to that of the
prototypes. The range of the accepted ratios corresponds to black body
temperatures of the dust from 60 to 150 K.
3. Sources must show evidence for extension in one of more of the IRAS bands
in the IRAS Working Survey Database.








The 34 sources that met these criteria were separated by WW into four categories: the

prototypes, section A, section B, and those associated with objects in the Gliese catalog.

The prototypes are exactly that: a Lyra, a PsA, E Eri, and P Pictoris. Section A contained

the best candidates for disks similar to the prototypes. Sources were relegated to Section

B if there was evidence for mass-loss or emission characteristics in their spectra. The

sources associated with the Gliese catalog were separated from the others since they were

not stringently required to meet Criteria #3, however, most of them were flagged as

extended in the IRAS database. All of the sources in the Gliese category are also on the

Vega-like list of Aumann (1985). WW calculated temperatures for the dust using the

IRAS 25 and 60 ltm fluxes to fit the dust emission with a blackbody curve. By using

published B and V magnitudes to model the photosphere, WW plotted the SEDs of the

sources. Their plots give us a first look at the amount of excess associated with each

source, and we used them to help prioritize the sequence in which we observed the stars.

Our secondary lists are those of Sylvester et al. (1996) and Mannings and Barlow

(1998). The Sylvester et al. (1996) list was particularly useful since their selection

process was similar to what we had in mind for this project. They included objects on

their list that maximized their chances of determining disk and grain parameters. Their

sources are therefore bright in the infrared, relatively close to the Sun, and have large IR

excesses associated with them. Their list contains a total of 24 sources, of which we

observed 20 during our survey. The Sylvester et al. (1996) list does have some overlap

with the WW list, with a total of 12 stars common to both. A useful facet of the Sylvester

et al. (1996) research is that they presented mid-IR spectra for 11 of their sources taken

with CGS3 on UKIRT. We used these spectra to help prioritize our observations, and to

compare to our results on the disks of HD 141569 (Chapter 5) and HD 169142 (Chapter









4). The better defined SEDs of the star/disk systems in Sylvester et al. (1996) were also

very useful in our source selection.

The third list we used to select our survey stars from is that of Mannings &

Barlow (1998). Their method of source identification was based on the cross-correlation

of the Michigan Catalog of Two-Dimensional Spectral Types with the IRAS Faint Source

Survey Catalog. The Mannings and Barlow list contains some 60 new Vega-like sources

not contained on either the Sylvester et al. (1996) or WW list. Our primary use of the

Mannings and Barlow sample was to search for Vega-like stars at Southern declinations.

In the decade between the publication of the Walker and Wolstencroft (1988)

paper and the Mannings and Barlow (1998) list, significant work was done on the

spectral classification of the Vega-like stars. In 1988 some of the sources on the WW list

are listed as luminosity Class I, III or IV, and a few had no luminosity classification at all.

Mannings and Barlow (1998) note that today only about half of the sources on the WW

list sources are known to be on the main sequence. At first glance this seems to have a

negative effect on the completeness of our survey; however, this is not detrimental to our

purposes. An important part of our research is to place these sources into an overall

evolutionary sequence. To start to piece together that sequence we need to see these

sources in all stages of their evolution. This includes the time immediately before, and the

time just after they are on the main sequence. It is therefore not unreasonable to make

observations of PMS objects and post-main-sequence objects that meet the criteria of the

Vega-like surveys to fill in the gaps in this evolutionary sequence we are trying to

construct. As we see in Chapter 3, it is the fact that we made observations of sources with

questionable classifications, and varying amounts of IR excess that allows us to put

together such a sequence for our survey stars.









The sources we observed for our survey are listed in Table 2-1. In total we

observed 36 sources at both 10 and 18 gm. Three other sources were only observed in

one filter because of poor observing conditions. In Table 2-1 we present which list the

objects came from and see that in total we observed 25 sources from Walker and

Wolstencroft (1988); 9 unique sources from Sylvester et al. (1996); and 4 sources from

Mannings and Barlow. One star used as part of the survey, HR 4796A (HD 109573), was

not present on any of our source lists. We also list the equatorial coordinates (J2000), and

distance to each source as listed in the Hipparcos database. Only 5 of our sample stars do

not have a Hipparcos measured parallax, and therefore distance. Values of (B-V) for each

star from the Tycho catalogs are also listed. Using these newly measured distances for the

sources allowed us to calculate absolute magnitudes for the stars, a requirement in setting

up our evolutionary sequence presented in Chapter 3.




Instrumentation

We used the OSCIR camera system exclusively for the observations in this

dissertation. OSCIR is a mid-IR camera/spectrometer system built and operated by the

University of Florida Infrared Astrophysics Group. The camera is built around a 128 x

128 pixel Si:As blocked-impurity-band (BIB) detector from Rockwell/Boeing. Chapter 7

more fully discusses the role of OSCIR in this dissertation. As noted previously we

collected data for this research on the IRTF, CTIO 4m, and Keck II telescopes. Because

of the different apertures of the telescopes some important characteristics of OSCIR

changed as we moved from site to site. Table 2-2 lists the parameters and their values on

each telescope. The survey was conducted using the standard "chop/nod" technique with

chop frequencies of a few Hz and chop throws in the range of 10" to 30." Appendix A









Table 2-1: Survey source data.
Spectral Distance RAa DECa
Source Name Class ()a (2000) ( M (B-V) Ref.
Class (pc)a (2000) (2000)


HD 432
HD 8538
HD 9672
HD 16908
HD 17848
HD 20010
HD 22049
HD 27290
HD 34282
HD 34700
HD 35187
HD 38678
HD 39060
HD 49662
HD 74956
HD 98800
HD 101584
HD 102647
HD 104237
HD 109573
HD 123160
HD 135344
HD 139614
HD 139664
HD 141569
HD 142165
HD 142666
HD 143006
HD 144432
HD 155826
HD 158643
HD 163296
HD 169142
HD 172167
HD 188037
HD 207129
HD 216956
HD 218396
HD 233517'


F2IV
A5IV
AIV
B3V
A2V
F8IV
K2V
FOV
AOV
GO
A2V
A2V
A5V
B7IV
A1V
K2V
FOI
A3V
AO
AOV
G5V
AOV
A7V
F5V
B9V
B5V
A8V
G6
A9V
F7V
AOV
A1V
A5V
AOV
A2
GOV
A3V
A5V
K2


17
30
61
113
51
14
3
20
164
1162
150
22
19
186
24
47
813
11
116
67
16
40
157+
18
99
127
114+
94
253
31
131
122
145
8
229*
16
25
40


000910.6
012548.9
01 3437.7
024327.1
024901.7
03 1204.5
03 32 55.8
041601.5
05 16 00.4
05 1941.4
052401.1
05 46 57.3
05 47 17.0
06 48 57.7
08 44 42.2
112205.2
114058.8
11 49 03.5
120005.0
123601.0
1406 12.8
15 1548.4
154046.3
1541 11.3
154957.7
15 53 53.9
155640.0
145052.7
160657.9
14 50 52.7
17 31 24.9
175621.2
18 24 29.7
183656.3
195230.0
21 45 01.1
22 54 53.5
23 07 28.7
08 22 46.7


+59 08 59.2
+60 14 07.0
-15 4034.8
+27 42 25.7
-62 38 23.5
-28 59 45.7
-09 27 29.4
-512911.9
-09 48 35.4
+05 38 42.7
+24 57 37.5
-1449 19.0
-51 0403.5
-150841.0
-544231.7
-24 46 39.7
-55 34 25.8
-55 34 25.8
-78 11 34.5
-3952 10.1
-114957.8
-37 09 16.2
-42 29 53.5
-44 39 40.3
-03 55 16.3
-2431 59.3
-22 01 40.0
-22 57 15.2
-27 43 09.8
-38 35 38.0
-23 57 45.5
-21 5721.8
-29 46 49.3
+384701.2
+22 27 14.2
-4731 55.8
-29 53 15.7
+21 0803.3
-34 27 06.0


1.2
0.2
1.7
-0.6
1.7
3.1
6.2
2.7
3.8
-1.2
1.9
1.9
2.4
-1.0
0.0
5.5
-2.6
1.9
1.3
1.6
7.6
5.6
3.0
3.4
2.1
-0.1
3.5
5.3
1.2
3.5
-0.8
1.4
1.9
0.0
1.2
4.6
1.7
3.0


0.38
0.16
0.07
-0.12
0.10
0.54
0.88
0.31
0.30
0.57
0.28
0.10
0.17
-0.10
0.04
1.15
0.37
0.09
0.24
0.00
1.50
0.53
0.25
0.41
0.10
-0.01
0.55
0.75
0.75
0.58
0.02
0.09
0.29
0.00
0.90
0.60
0.15
0.46
1.20


WW
WW
WW
Sy196
MB
WW
WW
WW
Sy196
WW
WW
MB
WW
Sy196
WW
WW
WW
WW
WW

Sy196
WW
Syl96
WW
WW
MB
Sy196
WW
Syl96
WW
Sy196
MB
WW
WW
WW
WW
WW
Sy196
WW


SSpectral classifications from Mannings & Barlow (1999).
a Data taken directly from the Hipparcos and/or Tycho catalogs.
t Ambiguous distance and absolute magnitude, see Chapter 6
+ Distance from Walker & Wolstencroft (1988) or Sylvester et al. (1996)









Table 2-2: OSCIR/Telescope Characteristics
OSCIR
OSCIR OSCIR Chop
e Aperture Focal Field of Chop Freq.
Platescale ie Throw hop Freq.
rech (m) Ratio View (Hz)
) Ratio (arcsec) Vie (arcsec)
(arcsec)
IRTF 3 F/35 0.223 29 30 3-5
CTIO 4 F/30 0.184 23 25 5
Keck 10 F/40 0.062 8 10 3



gives a thorough explanation of these standard mid-IR observing techniques and more

fully describes why these observational parameters were chosen.

During the planning stages of the survey we decided to observe all of the sources

in a consistent manner, with follow-up observations made when warranted. For the

survey observations, we made deep N (Xo= 10.8 Jim, AX = 5.2 gpm) and IHW18 (Xo= 18.2

gim, AX = 1.7 pm) integration with exposure times ranging from 10 to 20 minutes of

chopped-integration (5 to 10 minutes on-source) in each filter. Due to the inherent

inefficiencies of chop/nod observing the elapsed time during an observation is

approximately a factor of three longer than the on-source time. We felt that this exposure

time allowed us to efficiently use the allocated telescope time while giving us a good

chance to detect any extended emission associated with the survey sources. Given these

integration times the possibility exists of faint extended emission around some

of the survey stars that we did not detect. However, to keep our dataset consistent we

observed all of the sources in a coherent manner. Next we describe our observational

technique used for the survey observations.









Observational Strategy

Observations for this work were made over a period of three years at the above

mentioned telescopes. We followed a set observing strategy for each of the observations

made. When observing a science source we also made a series of observations in support

of the actual data on the Vega-like source itself. The sequence of observations made is as

follows

1. Observation of photometric flux calibrator
2. Observation of a nearby point-spread-function (PSF) star
3. Observation of the science source
4. Observation of the PSF star

There was normally no need to observe a 'pointing' star for these observations as all of

our science sources are visually bright and easily detected with a 3 m class telescope. We

attempted to start each Vega-like sequence with observations of a photometric standard at

both 10.8 and 18.2 mrn, however, due to time constraints this was not always possible.

Since we were trying to determine if the science sources were resolved or not, the

observations of the PSF star were as critical as those of the science source. As illustrated

in Figure 2-3 our determination of whether or not a science source was resolved is based

in part on our comparison of scans through the science source and PSF star. To make as

accurate a comparison as possible, during the data reduction process we always used the

PSF observation that was taken closest in time to the science source observation. The

data was reduced in this way to combat the temporal changes observed in the PSF of the

various telescopes. In the next section we give an example of these changes. The PSF

stars were chosen to be bright, nearby stars with no excess associated with them. By

selecting K or M class stars with mv < 5 we could normally find a suitable star to use

within 100 of the science object. In some cases the PSF stars were up to 150 away. Our









chopped integration times for the PSF stars were 2 to 4 minutes (1 to 2 minutes on-

source).


Nightly Variation of the PSF

During the planning stages of this work we attempted to form a viable

observational program that took into account some of the obstacles we knew we would

face. One of the problems we foresaw was the overall stability of the PSF of the

telescope-camera system. Many factors including slumping of the telescope structure,

changes in the ambient temperature in the dome, and issues with the mirror support

systems, can contribute to the instability of the PSF of the system. On modem telescopes

like Keck and Gemini, active control of the mirror surface mostly compensates for these

effects. However, even with these systems in operation some changes in the PSF are

evident. To illustrate this point we present Figure 2-1, which is a plot of scans through all

of the PSF measurements taken with OSCIR on the night of 04 May 1999. On this

particular night of observing at Keck II we obtained five measurements of the PSF at 10.8

gtm, and three at 18.2 plm. Inspection of the figure shows the magnitude of PSF changes

for the night clearly. Although it is somewhat difficult to distinguish the lines, the

sequence of 10.8 p.m measurements goes from the narrowest scan, made early in the

evening, to the broadest, made close to dawn. The 18.2 p.m PSF scans follow the same

trend. This implies that the PSF of the telescope became markedly worse as the night

went on, illustrating the reason why we used the PSF taken as closely as possible in time

to our science observations.

Note however that even though there is significant difference in the shape of the

PSFs within each filter throughout the night, the FWHM of the PSF is relatively

unaffected by these differences. From best to worst case the FWHM of the PSF changed











10.8 micron PSF measurements 18.2 micron PSF mcasurmcnts



0.6
l
0.4 81





Offset (arcseconds) Offset secondsd)

Figure 2-1: Nightly variation of the point-spread-function (PSF) at 10.8 gm (left) and
18.2 lm (right). Plotted are scans through the five PSF measurements at 10.8 gm and the
three measurements at 18.2 gm on the night of 04 May 1999, with OSCIR on Keck II.
The earliest measurements of the night are the narrowest, later measurements were
progressively broader.



by 0.15" at 10 lm and 0.11" at 18 gm. Similar analysis done for other nights show that


these values are slightly higher than normal. For most nights the FWHM of the PSF was

stable to within -0. 1" at Keck, and that is from the best to worst case on a night. The

variations between sequential PSF measurements were lower than this, implying that the


changes to the PSF were gradual, akin to a slow drift that occurred over the course of

hours. This is encouraging since the PSF measurements we used to compare to our

science sources were normally taken within 30 minutes of the end of the science source

observation. Along with the PSF star measurements we also observed infrared standard

stars to absolutely calibrate our data. In the next section we discuss our data reduction

steps, including that calibration.









Data Reduction Steps

Over the course of making our survey observations we acquired a large amount of

data. Including the PSF and standard star observations approximately 12 GB of data was

amassed for this project. The sheer amount of data alone made the data reduction arduous

and time consuming. The reason that the amount of raw data is so large is because the

OSCIR data is saved in specialized 6-dimensional FITS files. This unusual data structure

is required due to the chop/nod method of observing in the mid-IR (see Appendix A).

Briefly, the OSCIR detector is readout approximately every 10 ms during normal

observations. The data from the readouts is saved in buffers in a VME control crate on

the back of the telescope. Once every 2 seconds the buffers are sent down a fiber optic

cable connecting the VME crate and the control computer. Once the data is sent to the

control computer it is written to disk in one of these 6d FITS files. The advantage of this

is that the observer has access to the entire data stream of the observation after the fact.

While this produces data files in the 20 to 50 MB range, having access to the data in 2

second quanta is an invaluable asset during the data reduction. All of the data reduction

for this dissertation was done in IDL, using the "f6tools" to access the OSCIR 6d FITS

files, and the "wtools" to reduce the data in a GUI environment.



Removal of Contaminated Data

One of the advantages of having access to the entire data stream is evidenced in

the very first step of any OSCIR data reduction, the removal of contaminated data sets.

The advantage is that we can remove data in 2 second increments without changing the

overall quality of the data as a whole. The main reason that portions of the data stream

must be removed is due to fluctuations in the background. As explained in Appendix A,














44.5 -


44.0 -


S43.5


43.0


425 -


42.0
0 100 200 300 400
Frame Number

Figure 2-2: Background at 10.8 pm during an observation of HD 141569 at Keck II.
Here we plot %well (a measure of how close to saturation the OSCIR detector is) vs.
frame number for an observation of HD 141569 at Keck II. During the reduction process
frame numbers 145 to 200 were removed due to the large background change.



accurate removal of the background is paramount in mid-IR observations. Using the

routine 'f6bstat' we produced plots for each survey star observation like the one shown in

Figure 2-2 above. In this figure we plot '%well' as a function of frame number for an

observation of the science source HD 141569 at Keck II. The quantity '%well' is a

measure of the background seen by the OSCIR detector during each of its 10 ms

integration. Experience has shown that an acceptable background variation is < 0.5%

change in '%well'. In this case we therefore remove the frames between number 145 to

200 because of the large change in well during those readouts. This large change in

'%well' was most likely due to a faint band of cirrus clouds moving through the field of









view of OSCIR. Once any contaminated frames are removed from the data we move onto

the next step of the reduction, which is the creation of a single image from the individual

frames in the 6d FITS file.



Cross-Correlation of Images

Once any contaminated frames are removed from the data, we have a series of so-

called 'sig' frames to work with. These are the final products of a complete nod-cycle, a

single 128 x 128 image that has the background from the sky and telescope fully

removed. For our survey mode observations we typically had 10 to 15 of these 'sig'

frames to work with for each filter.

For sources that are not bright enough to be seen in each individual 'sig' frame,

we performed what is called a "straight-stack". A straight-stack is the direct sum of all of

the sig frames in an observation, no shift-and-add processing done to the data. Most of

our sources were relatively bright in the mid-IR and were detected in the individual sig

frames. For these sources we developed and used two IDL routines that use a chi-squared

minimization kernel to cross correlate the images to find the best offsets between them

before stacking them into a single image. We find that this helps remove any tracking

errors or other systematic drifts in the data. Once the sig images are straight-stacked or

cross-correlated we move to the next step of the reduction sequence, ensuring that the sky

is zero-mean before we calibrate the image.



Skyfit

The skyfit routine is used to ensure that the off-source portions of the final image

are zero-mean. Due to imprecise background removal during some of our observations








the final image from a 6d FITS file may have a non-zero mean sky. To correct for this we

use the skyfit routine written by Drs. Jim De Buizer and Robert Pifia. This routine allows

you to mask any portion of the array, for example around your source, and then it fits the

remaining, unmasked, background with a 2 dimensional polynomial surface of specified

order typically 3,3 to 'flatten' the sky. This routine was used on all of our survey data

with good success. Once we have a zero-mean sky image, we are ready to calibrate.



Calibration/Airmass Correction

Our science observations were absolutely calibrated by observing infrared

standard stars as part of our observational sequence. In Table 2-2 we list the fifteen

primary standards that we observed during the survey. We also present their assumed flux

densities at 10.8 and 18.2 gm. For most of the standard stars we have model atmospheres

from Cohen et al. (1999). The flux densities for these stars were calculated by integrating

the models for the star through the passband of the OSCIR filters. We used the following

relation to calculate the bandpass averaged flux density standard star flux density Fx.




Fv (x) -(Tfilter() -Tatran (k)) dX

1x
Fk :=--^-c---2----

2- (Tfilter(k) 'Tatran ()) dX



where Tfilter and Tatan are the transmission curves of the OSCIR filter and the atmosphere

respectively. XI and X2 are the wavelengths where the transmission of the filter drops to

zero, and c is the speed of light. On average we observed standards at both 10 and 18 p.m









3 or 4 times per night during the survey observations. Each of these data was reduced and

a calibration ('cal') value that converts the instrumental units of ADU/sec into the

physical units of mJy was calculated. The 'cal' value was then applied to the reduced

science data to create maps in mJy/pixel.

We comment here on the uncertainties associated with the photometric calibration

since they are the dominant uncertainties we dealt with for the survey observations. The

effects of atmospheric transmission always dominate the photometric uncertainties in

mid-IR. As Figure A-l shows (see appendix A), the mid-IR atmospheric windows at 10

and 20 pim are riddled with atmospheric absorption features from water vapor, C02, and

03. A variation in the column density of these species has a dramatic effect on the

transparency of the atmosphere in the mid-IR. Indeed, it is these variations of the sky

background that requires the use of chopping in the mid-IR.

Van der Bliek et al. (1996) measure short term variations in the atmospheric

transmission of -10% for the 10 tim window, and upwards of 15% in the 20 gim window.

Looking at the calibration data directly related to our survey, which consists of > 60

individual stellar observations, we find that the overall uncertainty in the absolute

calibration is 10% at both 10.8 and 18.2 gm. The discrepancy with the van der Bliek et

al. (1996) long wavelength conclusion is most likely related to the fact that our 18.2 gLm

filter has a bandpass on only AX = 1.7 gm; relatively narrow when compared to the

broadband 20 lim filters discussed in their paper. We adopt 10% uncertainties for all of

our measured OSCIR flux densities.

The airmass corrections in the mid-IR are generally small. Under good sky

conditions, a rule-of-thumb measure for the airmass correction in the N-band (10.8 glm) is

- 0.02 mag/airmass. Even so, we attempted to perform airmass corrections for all of our









Table 2-2: Standard Star Flux Densities
Flux Density (Jy)

Standard 10.8 glm 18.2 gjm
Star (N-Band) (IHW18)
aLyrt 37.8 11.9
a CMa 130.7 41.1
a CrB 5.0 1.8
a Boot 682.7 219.1
a Hyat 125.2 41.5
a Taut 600.6 200.1
pAndt 245.9 83.9
pGemt 115.5 37.0
SGru 906.0 323.1
0Pegt 352.1 122.2
yAqlt 77.2 25.6
yCru 833.9 286.7
yRet 72.6 28.7
Vel 194.6 69.4
t UMat 99.1 33.9

t Values are bandpass-averaged flux densities
calculated by integrating Kurucz models of each star
through the OSCIR filter bands also taking into account
the detector QE, and atmospheric transmission. All
other values come from the CTIO standard list.


survey data by using the observations of the photometric calibrators over a range of

airmass. At times this was impossible due to insufficient standard star observations, or

obviously contaminated standard data where there was no trend at all evident in the cal

values. When there was sufficient data of good quality available we used a linear

regression of log(cal) vs. airmass to correct the science observations for airmass. These

corrections rarely made a more than 5% change in the flux estimate for a survey source,

well within the 10% photometric errors assigned to our OSCIR photometry.









Flat-field Correction

Figure 7-6 shows an image of the OSCIR detector under uniform illumination in

the N-band (10.8 gm). There are approximately 10 hot pixels distributed across the array

that have significantly different response than the others. There are also about 10 dead

pixels. Overall the uniformity of the detector is very good, however there is a small

amount of vignetting in the lower right corer of the array. The response of the array is

generally very flat though, the flat-filed varies < 5% across the array. All of the structure

seen in Figure 7-6 is 'fixed-pattern' and is removed during the chop-nod process.

Because of the flat response of the array, no flat filed corrections were applied to the

survey data.



Photometry

The last step in the reduction was to conduct aperture photometry on the science

sources to estimate their brightness at 10.8 and 18.2 gm. We used two methods to

perform the photometry on the survey stars. The first is an automated routine, which

estimates the sky background, and automatically grows an aperture around a point source

until the increase in flux obtained is less then or equal to the measured noise in the

background contained within the annulus bounded by the last two apertures. This routine

works very well for strongly detected sources and was used for the photometry for 75%

of the survey data. We also used this routine when we manually reduced standard star

data, or obtained flux estimates for PSF stars. For faint sources we used a manual

aperture for the photometry. For consistency, all manual apertures used had a radius r =

2". The measurement errors associated with the photometry (i.e. opix(Npix)112) were

always dominated by the 10% photometric error for all survey sources. Our observed








color corrected OSCIR flux density estimates for the survey sources are presented in

Table 3-1. In Chapter 3 we also discuss the removal of the stellar photosphere from those

values to calculate a values for the excess emission from the circumstellar dust.



Color Correction

Flux density estimates for objects observed through wide bandpass infrared filters

need to have a correction applied to them called a 'color correction'. This is particularly

true of the OSCIR N-band filter that has a bandpass of 5.2 pm. The color correction must

be applied since the spectral shapes of the flux calibration star and science object are

different through the bandpass of the filter. Because stellar temperatures are high (> 5000

K), the SED of a calibration star peaks well short of the mid-IR and its SED is on the

Raleigh-Jeans tail through the OSCIR filters. For our science sources though, this is not

be the case. For our science targets we are observing dust that has a temperature in the

hundreds of Kelvin. Because of this the SED of the science source may be peaking, or

has not yet peaked, in the mid-IR which means that its spectral shape through the

passband of the OSCIR filters is different than that of the calibration star. This is an issue

because we prefer to discuss monochromatic flux densities in the mid-IR, and since the

calibration star and science objects have different SEDs through the filter, any

monochromatic flux density given is dependent on the spectral shape of the source

through the passband. Since we also make the assumption that the SEDs of our science

objects follow a modified blackbody function (Fv = (1 e ). By(T)) through the

passband. The color correction term is applied to scale that function to give us the correct

in-band flux for the science source.








We outline the procedure for this correction below starting with the definition of the

effective wavelength of the N-band filter (Lef). Since the OSCIR detector is a photon

counter for these purposes ~ff is defined in terms of the photon with the average energy

in the bandpass.

The color correction factor assumes that the ratio of instrumental counts for the

calibration star (ADUS) to that of the program object (ADUP) is equal to the ratio of

number of photons detected from the calibration star (Ny) to the program source (NyP).

This equality is shown below in equation 1.



ADUL N 7
U (1)
ADUI Ny



the number of photons a source will generate through a bandpass is



N := Q sys-dv (2)




Where Fv is the flux density of the source with temperature T and optical depth tv

and is defined as


F,:= (-e /n-Bv(T) (3)

We also define the 'quantum efficiency' of the system as


Q sys:= T filte )T atran(X) QE(X)









where this relation takes into account the QE of the OSCIR detector, the atmospheric

transmission, and the transmission of the OSCIR filter. Substituting (3) into (2) gives



N :=l-e )-B V(T) (4)
:= Qsys hv

If we are given a monochromatic flux density of the source at some frequency, Fvo using

equation (3) and solving for 0 we can define the following relation


Fro
-( )vo( (5)
(Ie- VO)-B v(T)


substituting equation (5) into (4) gives



FVO (1-e -.Bv(T)
N:= Qsys e-) ) dv (6)
(1 e Bvo(T) hv



which is an expression for the number of photons produced by a source with flux density

Fv through the passband of the filter. Recalling equation (1)


ADIf N P
ADUP N y


we can use equation (6) to relate the number of photons received from the program

source (Np) to the counts measured from the program source (ADUP) and the number of

counts measured from the calibration star (ADUS). First solving (1) for (N/) and then

substituting in expressions for the number of photons received from the star and program

source from (6) gives









F F (I-e -B; AD FO B )
SQ s -- B dv A:=D Q Sys ) dv (7)
S- e- SYS hv BADLB ) sys hv



the absence of the (1 e~) terms on the right hand side of equation (7) is due to the fact

that the calibration star is assumed to be a simple blackbody. We can now solve (7) for

the flux density of the program object at vo, (FvoP)



Bv(T) i
y BV (Ts) hv
F vo := ADU vo J
\ADUS (8)
(1 e- T) -B VT
Q sys ----- dv
1 e o YvoS ( e B (TV) v


In equation (8) we have equated the flux density of the program source at the

monochromatic frequency vo to three known quantities, ADUP, FvoS, and ADUS. The first

term on the right hand side of (8) is the measured instrumental counts of the program

source. The second term is simply the ratio of the given flux density of the calibration

star at vo the measured instrumental counts for the calibration star. This is the "cal" value

mentioned in the calibration section. The third term is the color correction term. It is this

factor that is applied to the data to account for the different spectral shapes of the

calibration star and program object through the bandpass of the filters.

To color correct our fluxes we used a program written for MATHCAD. Using our

raw 10 and 18 pLm flux density estimates as a starting point the code iterates to

simultaneously solve for T, T, and color correction. All of our flux density estimates









presented in this dissertation are color corrected. For the sample as a whole the mean

color correction for our broad band 10.8 gm flux density estimates was approximately

13%. The 18 gm estimates had a mean correction of -3%. The 18 gim value is lower due

to the much narrower passband of the 18 gim filter. Color corrections for 10.8 gim (N-

band) fluxes on the order of 15 to 20% are consistent with the work of Hanner et al.

(1984).




Resolved or Unresolved: The Question

Perhaps the most fundamental question we attempted to answer in this

dissertation is, are our sample Vega-like sources resolved? For the most part, the answer

to that question is no. We find that -90% of our survey sources are unresolved at both

10.8 and 18.2 gm. However, in this section we only discuss how we answered the

question of resolution. The full results of the survey are presented in Chapter 3.

Our primary method of determining whether or not a survey source was extended

was close inspection of the reduced data by eye. We found early on in the reduction of

the survey data that the eye is the best detector for faint extended emission near bright

stellar sources. This is especially true when the data is reduced with the latest generation

of data reduction software. The ability to scale and color data in a point-and-click

environment is a very powerful tool at our disposal and we used it to the fullest extent we

could during this project. For each of our survey sources we carefully studied the data as

closely as possible by eye to look for hints of extended emission near the science sources.

Visual comparison of the science sources and PSF stars was also performed for each

survey source.






35



ar 1.0
a b





0.8 i 0.8
S0.6 0.6

S0.4-



S/ d



0 0.2 O 2 -, 0 2:
.. yr. / .....




I t] .- : I :, -




Are~-)ds AnrAsewnds

Figure 2-3: Scans of a resolved (a & c) and unresolved source (b & d). (a and c) Scans of
HD 151469 and PSF star at 10.8 pm and 18.2 ptm respectively. HD 141569 is the solid
line, the PSF star is dashed. The dotted line is a Gaussian fit to the data. (b and d) Scan of
HD 16908 at 10.8 pm (b) and 18.2 p.m (d). 18.2 ptm data for HD 16908 and PSF star have
a 2-pixel (0.12" FWHM) Gaussian smooth applied to boost the signal to noise of the HD
16908 detection.



Another way we investigated the data to try to answer the question of resolution

was through scans (i.e. line-cuts) through the science objects and corresponding PSF

stars. We find the best way to visualize the data in this form is through plots like Figure

2-3. In Figure 2-3 we show scans that are representative of a resolved and unresolved

source. The resolved source (panel a & c) is HD 141569 which we observed at Keck II

in 1999 May. This source is discussed in detail in Chapter 5. We contrast HD 141569

with a representative unresolved source, HD 16908. Also observed at Keck, the HD

16908 data has the same resolution as the HD 141569 observations.
OAnohrwyw netgtdtedt otyt wrteqeto frslto
wa3hog cn ie iect)truh h cec bet n orsodn S
stars. We ind the best way to visualize the da4ta nti omi hog lt ieFgr
2-.IZ iue23w hwsasta r ersnaieo eovdadursle









One immediately sees the differences in the two sets of panels. HD 141569 is

clearly broader than the PSF star at both 10.8 and 18.2 pm while the HD 16908 and PSF

star scans lie on top of each other. It is the extended emission of HD 141569 that causes

this broadening of its scan with respect to the PSF star. Close inspection of panel (a)

shows that there is significant extended emission from HD 141569 detected out to a

radius of ~1". At 18.2 plm the noise in the source scan prevents a determination of the

exact extent of the extended emission, however, even with the relatively low signal-to-

noise of the HD 141569 18.2 pLm data the difference in width of it and the PSF star is

easily distinguishable in panel (c). Images of HD 141569 also exhibit a 'fuzziness' that is

not present when observing a true point source. This effect is difficult to describe, but it is

very evident when looking at the data on a monitor.

The scans of HD 16908 are representative of the unresolved sources in the survey.

There is virtually no difference in the FWHM measurements of HD 16908 and the PSF

star at either 10.8 or 18.2 gpm. There is also no evidence for faint extended emission at the

lowest levels of panels (b) and (d). Using these scans in conjunction with an in depth

inspection by eye, we can confidently conclude that HD 16908 is unresolved at this

angular scale at both 10.8 and 18.2 pm. In the next chapter we move onto the discussion

of our survey data.














CHAPTER 3
SURVEY DISCUSSION

In this chapter we discuss our survey data. We do not give further details on the

mechanics of making the survey, rather we discuss our overall interpretations of the data.

In the first sections of this chapter we present size limits on the disks of the unresolved

sources, and give our derived grain parameters for their dust. We then compare the

unresolved survey sources to p Pictoris and HR 4796A, and show that if the survey stars

were at the distance of 0 Pictoris (19 pc) about 50% would still have been unresolved in

our observations. This comparison allows us to answer the question of whether the

unresolved sources are unusual as compared to archetypal disk examples, and gives us an

idea of how the unresolved sources fit into the Vega-like class.

In the later sections we discuss trends seen in the data and show how they can be

used to form a probable evolutionary sequence for Vega-like stars. By breaking the

survey sources into three classes and using the H-R diagram, we can graphically see how

these stars may be evolving. We bring in evidence that supports such a sequence in the

form of the SEDs of the star/disk system and relate the evolution of those SEDs to the

evolution of the disks around the stars. Using one of the sub-classes as a pivot point, we

see how one group of stars is likely still moving onto the ZAMS, while the majority of

them have already made it there and are now moving across the main-sequence in the

middle stages of their lives. In general we have incorporated ideas that are already well

represented in the literature into our survey discussion while adding our own ideas to the









overall evolutionary scheme. We start the chapter with the presentation of our disk size

estimates and a discussion of their implications.




Disk Sizes

Perhaps the most fundamental piece of information we can gain from our

observations are size estimates for the mid-IR-emitting region of the disk around each of

the survey stars. Once we have these estimates we can then compare them to the disks of

the archetypal Vega-like stars to piece together a more complete picture of the scale sizes

of this type of disk. As was mentioned in Chapter 1, the majority of our survey sources

are unresolved at both 10 and 18 jim. In fact, we observe 34 out of 38 sources as

unresolved within the uncertainties associated with our observations. Only HR 4796A,

HD 169142 (Chapter 4), HD 141569 (Chapter 5), and possibly 49 Ceti were resolved

during the survey.

Since over 88% of the sources are unresolved we can only place upper limits on

the size of their disks in the mid-IR. We do this by using the observed FWHM of the

emission as the limiting size of the mid-IR-emitting region of the disk. Using this limiting

size in conjunction with distance estimates to the stars allows us to translate the size into

physical units. Since most of our Vega-like sample stars are have distances < 200 pc, and

are bright in the visible, most of them were observed with the Hipparcos satellite. Indeed,

we have Hipparcos measured parallaxes, and therefore distances, for all but 5 of the stars

in our sample. As we will see later in the chapter the fact that we have accurate distances

for most of the stars is one of the main reasons that we can put these stars into an









evolutionary sequence. For now we use the distance estimates to help us place limits on

the size of disks associated with the unresolved sources in the sample.

Our limiting disk sizes are listed in the last column of Table 3-1. For each star in

the survey we present the observed upper limit on the diameter of its disk. Although

using the observed FWHM to limit the disk size is the least constraining method, for the

majority of the sources these limits are the tightest existing constraints on the size of their

disks in the mid-IR. For sources that are resolved we list approximate limits on the sizes

of their mid-IR-emitting regions (denoted with '=' in the limiting size column). Our size

estimates for these disks are only approximate since there may be faint extended emission

from the disk that we did not detect in our survey-mode observations. An observational

program centered on deep mid-IR imaging of these systems will more accurately define

the limits of emission for these four disks. Many of the sources have not been observed in

the mid-IR since IRAS, and those that have been observed were mostly observed with

single element detectors or at low spatial resolution. Walker and Heinrichsen (2000)

observed nine of the sample with ISO, but only at 60 and 90 pLm and at relatively low

spatial resolution. The only other observations of a significant number of the survey stars

is that of Sylvester et al. (1996), in which mid-IR spectra of 12 of the sources were

presented, but no imaging.

Table 3-1 also lists our color corrected observed flux densities of the survey

sources at 10.8 and 18.2 pm. The flux densities presented in Table 3-1 are the sum of the

photospheric emission of the star and the thermal emission from the circumstellar dust.

We present these values here in this manner so that they can be directly compared to

other observations. For our analysis of the dust properties we remove the stellar









Table 3-1: Observed Properties of the Survey Sources

IRAS IRAS IRAS IRAS
Source F10.8pm F18.2 pm IRAS IRAS IRAS IRS Limiting
Name (Jy) (Jy) 12m 25tm 6m 100m Size (AU)
(Jy) (Jy) (Jy) (Jy)

HD 432 13.5 3.59 11.7 2.87 1.00 <12.7 16
HD 8538 5.69 1.42 4.96 1.14 0.35 <6.09 27
HD 9672 0.36 0.14 0.33 0.38 2.02 1.88 =150
HD 16908 0.45 0.09 0.38 0.41L 0.36 <1.87 31
HD 17848 0.25 0.23L 0.46 0.25L <0.40 <1.00 51
HD 20010 3.09 0.77 2.85 0.74 0.23 <1.00 14
HD 22049 10.5 3.50 9.52 2.65 1.59 1.87 3
HD 27290 1.34 0.24 1.20 0.37 0.28 <1.00 20
HD 34282 0.63 0.32 0.70 1.63 10.8 10.7 173
HD 34700 0.48 1.40 0.57 4.42 14.1 9.38 900
HD 35187 3.86 6.02 5.39 11.5 7.95 5.00 200
HD 38678 1.80 0.63 2.12 1.15 <0.53 <1.00 35
HD 49662 0.19 0.13L 0.43 1.62 4.60 5.68 180
HD 74956 8.08 3.54 8.21 1.99 0.42 <8.76 40
HD 98800 1.58 5.09 1.98 9.44 7.28 4.46 4
HD 101584 96.5 113.0 92.6 138 179 99.1 800
HD 102647 7.45 2.70 5.26 1.75 1.02 <1.00 10
HD 104237 17.8 8.50 22.5 22.7 13.5 9.21 115
HD 109573 0.19 0.91 0.45 1.39 7.36 3.81 =200
HD 123160 0.66 0.14 0.60 0.38 3.11 4.41 10
HD 135344 1.58 2.69 1.57 6.91 25.6 25.7 60
HD 139614 4.26 8.05 4.11 18.14 19.3 13.9 68
HD 139664 1.11 0.61L 1.42 0.69 0.59 <1.00 15
HD 141569 0.29 0.65 0.53 1.82 5.54 3.48 =200
HD 142165 0.32 0.06L 0.25L 0.34 <2.77 <11.6 40
HD 142666 10.5 9.10 8.67 11.5 7.23 5.46 35
HD 143006 1.02 1.92 0.87 3.06 6.57 4.82 50
HD 144432 9.85 6.83 7.62 9.23 5.77 3.29 105
HD 155826 3.49 4.05 4.12 5.30 8.63 <260 20
HD 158643 20.0 11.8 15.6 10.1 1.06 <5.97 65
HD 163296 26.3 17.4 18.2 20.9 28.2 <40.6 60
HD 169142 2.72 8.14 2.95 18.4 29.5 23.4 =175
HD 172167 36.4 12.0 41.5 11.3 9.01 7.54 4
HD 188037 295 146 227 113 11.0 12.3 70
HD 207129 1.08 0.39 0.90 0.20 0.23 <1.00 12
HD 216956 17.1 4.62 18.5 4.79 9.11 11.1 21
HD 218396 0.37 0.08 0.40 0.24 0.41 <2.59 15
HD 233517 0.48 2.02 0.48 3.43 7.60 5.10 --

We adopt 10% errors on the OSCIR photometry at 10.8 and 18.2 Alm.
Denotes source with near-IR excess as listed by Sylvester et al. (1996)
L in flux column denotes upper limit used in temperature and optical depth calculation








contribution from the observed flux density. This procedure and our results are discussed

in the next section. For the few sources that we did not detect at either 10.8 or 18.2 Aim,

we list a 3c upper limit in the appropriate column in Table 3-1. These limits were

calculated using an aperture with radius = 1.22.-(/D). Table 3-1 also lists the IRAS 60

and 100 jim flux density estimates from the IRAS Point Source Catalog v2.0 in for each

source. At these longer wavelengths these is negligible contribution to the flux from the

star, it is comprised entirely of thermal emission from the circumstellar dust. All of the

sources in our sample have significant excess emission at these long wavelengths, and the

IRAS fluxes are included to give a more complete picture of the magnitude of the

excesses associated with each star. In Table 3-1 we also mark the nine systems that

exhibit near-IR excess. As we will see, these nine systems form one of the three sub-

classes we define when discussing our proposed evolutionary sequence for the survey

sources. In the next section we explain the procedure for removing the stellar contribution

to the flux density estimates presented in Table 3-1. This is necessary since this

procedure directly bears on which sources we could accurately model.




Photosphere Removal

As mentioned above the flux density estimates presented in Table 3-1 contain

both emission from the photosphere of the star and the thermal emission from the grains

in its disk. Since we are trying to investigate the properties of the dust, we must separate

these two contributions so we know as accurately as possible how much radiation the

grains themselves emit at 10.8 and 18.2 Lm. While this procedure is straightforward, the

uncertainties associated with both the predictions of the photospheric emission and our









observed flux density estimates have consequences on the final results. The procedure we

used to calculate the photospheric contribution of each star to our observed flux density

estimate is outlined below.



1. Use a published value or spectral type of the star to find the effective
temperature of its photosphere (Teff).
2. Model the SED of the stellar photosphere as a blackbody function with
temperature Teff, and normalize the blackbody function to observed 2.2 pm
(K-band) values.
3. Use the blackbody function to predict the fluxes emitted at 10.8 and 18.2 gm
for each Teff. Then form the ratios (F1o0.8s mF2.2 pm) and (F18.2 jm/F2.2 gtm) as a
function of Teff.
4. Multiply the observed 2.2 pm flux value by the correct ratios to predict the
photospheric flux at 10.8 and 18.2 pm.
5. Subtract the predicted flux estimates from our observed estimates, which
leaves only the contribution of the dust, defined as the excess emission.


Two questions immediately come to mind concerning this procedure: (1) is it legitimate

to use the ratios (FIo.8 im/F2.2 lpm) and (F18.2 pm/F2.2 pm) in the calculation and (2) is the

assumption the photosphere behaves as a blackbody accurate enough? In short, the

answer to both is yes. As illustrated in Figure 3-1 in the mid-IR we are working on the

Raleigh-Jeans tail of the blackbody distribution for even the coolest stars in our sample

(-5000 K), and the stellar photospheres follow the well-known v-2 falloff in this regime.

Close inspection of the 5000 K curve in Figure 3-1 shows there is s slight deviation from

Raleigh-Jeans falloff at 2.2 p.m, but this is a relatively small discrepancy, and only

applies to one of our survey sources. We address the second question by plotting three

quantities in Figure 3-2, the near and mid-IR portion a blackbody function with T =

10000 K, a model atmosphere for Vega from Cohen (1995), and flux density estimates

for Vega from OSCIR observations. All three curves have been normalized to unity at 2.2







43






.0 '1900MI K
100
:5004 K


01

001 -






1 10-5


1 10 -


1 10 -

S10 01 1 10 100 110
Waveengh (mrons)

Figure 3-1: Blackbody plots for temperatures that bracket the effective temperatures
(Teff) of the stars in our Vega-like sample. Our spectral types of our sample stars range
from a B3V (19000 K) to K2V (5010 K). The mean Teff of the sample is 8500 K. The
vertical dotted lines denote 2.2, 10.8, and 18.2 gm (from left to right).




gm. For the OSCIR observations we have also plotted error bars that mark the 10%


uncertainty in their values. Both the model atmosphere and the blackbody line lie well


within the photometric uncertainties associated with our OSCIR observations. The close


correlation of all three plots in Figure 3-2 illustrates that for the relatively hot


temperatures of the intermediate mass stars in our sample the approximation of the stellar


photospheric emission as a blackbody function is robust.


We used this method to remove the stellar contribution from our observed flux


estimates for all of the stars in our sample. For star/disk systems where the mid-IR flux


comes primarily from the dust emission the procedure is sound. However, for a subset of







44





...---- 'olen Dat* a
SCIR Data
XXX BB appox.









001










WUy&,,t1, (ncrron)

Figure 3-2: Comparison of OSCIR data, 10000 K blackbody function, and model
atmosphere data for Vega. Error bars on OSCIR data are 10% and represent the
uncertainly in our measured flux values.



seventeen of the survey stars this procedure returns negative excesses at either 10.8 or

18.2 pm clearly not a legitimate result. We believe that these non-physical results are

primarily due to the 10% uncertainties in our OSCIR flux estimates. Since the

determination of the magnitude of the excess is directly related to our observed mid-IR

flux estimates, any uncertainty in those estimates translates directly into uncertainties in

our estimates of the excesses. For these seventeen sources the amount of their mid-IR

excess is within our observational uncertainties, and we therefore cannot calculate the

amount of excess they exhibit. Because of this, we are forced to remove these seventeen

stars from our analysis of the disk grain properties.









Clearly this has a dramatic effect on the results of our survey. Because of this

issue we have only modeled the grains associated with 22 of the observed systems, or

56% of our sample. However, we use the fact that some stars exhibit little or no excess in

the mid-IR in the discussion of our proposed evolutionary sequence presented later in this

chapter. Indeed, these sources with little or no mid-IR excess form one of the three sub-

classes we divide our survey into and represent the last stage of our proposed sequence.

We do have robust estimates for the 10.8 and 18.2 gtm excesses of the remaining

22 survey sources and we present them in Table 3-2. Listed by HD number, we present

our excess estimates in units of flux density, and as a percentage of our observed flux

estimate. A literature search and use of the SIMBAD database gave the spectral types for

each of the sources in the table. We also list the effective (Teff) we used for each star in

our calculations of the excess. The majority of these values were taken from Allen

(2000), while others were taken from the literature, in particular Dunkin, Barlow, and

Ryan (1997b).

One important conclusion that we can infer from Table 3-2 is that although our

sample is biased toward stars of A-type, within the sample there is no apparent

correlation between spectral type and amount of mid-IR excess. This is supported by the

literature where it has been found that at least 15% of nearby field stars of all spectral

types between A to K have circumstellar dust systems like those associated with our

sample (Lagrange, Backman, & Artymowicz 2000). We also see that percentage wise

there is varying amounts of 10.8 glm excess associated with our sample stars. The

excesses of twelve stars in Table 3-2 accounts for more than 95% of the observed 10.8im

flux, seven of the stars have intermediate values of 10.8 tim excess (between 10 to









Table 3-2: Excess Characteristics of the Survey Sources
10.8 gLm % Excess 18.2 tm % Excess
Source Name Sp. Type Tff Excess 8 Excess
(10.8 pLm) (18.2 I.m)
(Jy) (Jy)
HD 9672 A1V 9150 0.003 1.3 0.05 38.4
HD 34282 AOV 9480 0.49 98.6 0.31 99.2
HD 34700 GO 5930 0.37 88.8 1.34 98.8
HD 35187 A2V 8810 3.08 98.2 5.78 99.7
HD 38678 A2V 8810 0.13 7.2 0.05 7.7
HD 39060 A5V 8160 1.22 42.7 4.05 88.0
HD 98800 K2V 5010 1.12 79.8 4.82 98.0
HD 101584 FOI 7700 75.94 98.4 108.58 99.6
HD 104237 AO 9480 13.43 95.3 7.98 97.3
HD 109573 AOV 9480 0.03 1.6 0.84 93.1
HD 135344 AOV 9480 1.25 96.6 2.58 99.4
HD 139614 A7V 7930 3.50 99.0 7.76 99.8
HD 141569 B9Ve 10000 0.25 77.2 0.62 96.1
HD 142666 A8V 7630 8.26 99.3 8.75 99.8
HD 143006 G6 5620 0.82 97.4 1.84 99.6
HD 144432 A9V 7300 7.68 99.2 6.56 99.7
HD 155826 F7V 6240 2.10 75.7 3.67 94.1
HD 158643 AOV 9480 15.29 97.1 11.19 98.6
HD 163296 A1V 9150 20.19 97.5 16.60 99.0
HD 169142 A5Ve 8400 2.28 98.1 7.19 99.8
HD 188037 A2* 8810 167.94 72.2 95.47 80.8
HD 233517t K2III 4420 0.32 72.6 1.90 97.7
HD 233517t K2V 4900 0.32 72.6 1.90 97.7
SIn sp. Type column denotes multiple star system
t Ambiguous classification, see Chapter 6


95%), and three stars have little 10.8 gpm excess (< 10%). Coupled with the seventeen

sources that have no measurable excess and are not listed in Table 3-2 there are twenty

stars that exhibit <10% excess at 10.8 pim. This is our first look at the three sub-classes

we break the survey into with regards to our proposed evolutionary sequence. As we will








see, the amount of the 10.8 lnm excess exhibited by a star/disk pair is a good indicator of

the evolutionary state of the system.

Now that we have our best estimate at the values for the emission from the dust

around the stars in the survey we can proceed with our investigation of the properties of

that dust. In the following sections we discuss our modeling of these mid-IR-emitting

grains and present the results of that modeling.




Grain Models

In this section we discuss the properties of the radiative equilibrium models we

used to analyze our mid-IR data. The core of the model code used was developed by

members of the University of Florida Dust Dynamics Group. In particular, the version of

the code used in our analysis was written by Dr. Mark Wyatt. We begin this section with

a high-level overview of the operation of the modeling code, then present results for one

of the survey sources, HD 141569. Using the HD 141569 results as an example, we

describe the model output and show how it relates directly to the physical parameters of

the grains we are studying.

Before we discuss the operation of the modeling code, we need to address what

assumptions were made about the grains. The most fundamental assumption made is in

regards to the composition of the dust. For the models presented in this dissertation we

assume that the disk particles are comprised of the astronomical silicates of Draine and

Lee (1984) and Laor and Draine (1993). There is evidence for particles with this

composition in both interplanetary dust particles gathered high in the Earth's atmosphere

(Leinert and Griin 1990), and in disks similar to those studied here. Sylvester et al. (1996)









presented mid-IR spectra of 13 sources in our survey and definitively detected silicates in

seven of them. Other significant detections of silicate materials in Vega-like disks are

those in the archetypal Vega-like source P Pictoris (Telesco and Knacke 1991), and in the

source 51 Oph (Fajardo-Acosta, Telesco, & Knacke 1993).

We also make the assumptions that the model particles have a density p = 2.5 g

cm", and that they are spherical. We make the assumption about the density since

'astronomical silicates' is not a physical material and its measured density is undefined.

The value of 2.5 g cm-3 is used since it is representative of interplanetary dust particles

(Gustafson 1994). With regards to the assumption about the shape of the grains, one must

first realize that the methods for calculating the optical constants for grains are limited.

Rigorous solutions for light scattering from particles are only available for spherical

grains, using Mie theory, and infinite cylinders, as described in Bohren & Huffman

(1983). New solutions for more complicated aggregate particles have recently become

available (Xu & Gustafson 1999), but these methods are computationally intensive, and

beyond the scope of the modeling presented here. Recent advances in the work on the

composition and structure of particles in circumstellar disks has shown that these

assumptions likely oversimplify the grains (e.g. Gustafson 1994), however, this sort of

analysis provides a good starting point for more detailed models which incorporate more

complex grain structures. In a following section we discuss the limitations of our models,

and touch on how different compositions and/or grain morphology changes our results.

Using the optical constants for astronomical silicates from Laor and Draine

(1993) our radiative equilibrium models use Mie theory to calculate the absorption

coefficients (Qabs) of different sized particles at different distances from the central star.









Once we know how efficiently a particle of a given size (diameter, D) emits and absorbs

radiation we can work out what its temperature will be at any distance from the star (r) by

iteratively solving the equation from Gustafson (1994):

T(D,r) = [T* / r(D,r)]1/4 X Tbb (1)

Where T- is the absorption efficiency of the grain averaged over the stellar

spectrum (which has been approximated by a blackbody with temperature T.) and

T(D,r) is the same quantity averaged over a blackbody spectrum of temperature T.

Tbb is the equilibrium temperature of the grain in degrees Kelvin if it were a blackbody

and is given by:

Tbb = 278 x r-/2 x (L*/L)1/4 (2)

where r is the distance of the grain from the star in AU and L. is the stars luminosity in

units of L = 3.9 x 1033 erg sec'.

We can also calculate the thermal emission from the dust received at the Earth at

a given wavelength. In the optically thin case, which we assume for our survey sources,

this can be written as:

Fv(X, D, r) = Qabs(,, D) x Q(D) x Bv[X, T(D, r)] (3)

where Qabs(A, D) is the grains efficiency as a function of wavelength and diameter, Q(D)

is the solid angle subtended by the grain at the Earth, and Bv[A, T(D, r)] is the Planck

function for the temperature of the grain. Using the luminosity and effective temperature

of the stars along with the assumed optical properties of the grains, our models use

equations (1) and (2) to calculate temperatures for grains of different sizes at varying

distances from the stars.









300

I II 11l
250


200 10 AU






1 00 -
50 \ -- ...... 30 n -



5 0- ...... -. ..... -
0.01 0.1 1 10 100 1000
Particle diameter, /m

Figure 3-3: Model temperature calculations for spherical Mie particles 10 to 50 AU
from HD 141569. The shape to the temperature curves is due to the changes in the values
of the grain emission and absorption efficiencies. The shading marks the three regions
described in the text.


To show an example of our model temperature calculations in Figure 3-3 we plot

the calculated temperature against grain diameter for particles between 10 to 50 AU from

the star HD 141569, a source that we resolved at Keck II (see Chapter 5). We see that

grains at these distances reach temperatures of 150 to 250 K. This is the temperature

range we derive for the majority of the survey sources that have well defined excess

values, and is one of the conclusions of our work. That is, the mid-IR excess emission

from Vega-like sources traces material that is at temperatures between 150 to 300 K.

Once we have calculated the temperature of the grains as a function of distance

from the star and diameter T(D,r) we can use equation (3) in conjunction with the grain












3 1+


40 AU, \ --"5o


*o^:______V r7' 30:4_
Part'ci d omneter ur Poat'cle d3 o etr ira

Figure 3-4: Plots of emitted flux density per unit solid angle at 10.8 g.m (left) and
18.2 plm (right) for grains 10 to 50 AU HD 141569. Regions shaded as described in text.



efficiencies to calculate the amount of emission from a grain as a function of wavelength,

Fv(X, D, r). In Figure 3-4 we plot the emitted flux density per unit solid angle (i.e.

specificintensity) at 10.8 and 18.2 gm for grains near HD 141569. This is the quantity

Qabs(A, D) x By[X, T(D, r)]

from the right hand side of equation (3) and has units of Jy/ster. This is the first point in

the modeling process where we have output that is in terms of physical units which is

important since we need to compare our model output to our observations.

To make the direct comparison between our models and observations we form the

ratio of the two plots shown in Figure 3-4 by dividing the 10.8 gm curves by the

corresponding 18.2 gm ones. The resulting flux-ratio plot is shown in Figure 3-5. The

plotted curves represent the flux ratio predicted for a particle of a given size at a given

distance from the star. The horizontal line plotted in Figure 3-5 marks the observed flux

ratio of the excess emission associated with HD 141569. It is where this horizontal line

intersects the model curves that returns a particle size at a given distance from the star






52




I 1.00 ---------. \
00


10 A

S0.10 20 AU
S\ \ \\". .
30 AU-

40 AU

0.01 50 AU



0.01 0.1 1 10 100 1000
Particle diameter, p/m

Figure 3-5: Flux density ratio plot for HD 141569. The curved lines represent the flux
density ratio emitted by model grains between 10 to 50 AU from HD 141569. The
horizontal line marks our observed (10.8 pm/18.2 p.m) flux ratio. The intersection of the
model curves and horizontal line returns grain sizes at the given distance from the star
that are consistent with our observations.


that is consistent with our observed flux ratio. Note that there is a double-valued solution

for grains at 30 AU from the star. For most of the survey source model results we see this

behavior where two different values of the diameter for a particle at a given distance give

the same flux ratio. This results from the fact that the temperature of the particle depends

on the particle size, which in turn depends on the ratio of the absorption and emission

efficiencies. Since we cannot distinguish between the two values, we use the largest

consistent size to place an upper limit on the diameter of the mid-IR-emitting grains in

the disks.









It is the interaction of the absorption and emission efficiencies of the grain that

causes the shape of the curves in Figures 3-3, 3-4, and 3-5. This 'S' shape is

characteristic of our models, and is seen to some extent in all of the results for the survey

sources. This is because it is ultimately the absorption and emission efficiencies that

determine the equilibrium temperature of the grain with respect to the radiation field. The

temperature of the grains then determines the amount of emission at a given wavelength

(Figure 3-4), and the ratio of the emission at two wavelengths is how we connect the

models to the observations (Figure 3-5). Therefore, the effects of the varying efficiencies

are seen directly in all of the various model outputs. This is not surprising since these are

radiative equilibrium models, which means that the interaction of the grains with

radiation is the most fundamental physical process with which we are dealing.

To discuss the reasons behind this characteristic 'S' shape of the curves we will

use Figure 3-3 as an example. We divide the figure into the regions represented by the

three shades of gray where each of the regions defines a regime where certain interactions

between the grain efficiencies are determining the shape of the model output curves. At

the leftmost side of the plot the grains have a diameter of 0.01 p.m, similar to the

wavelength of UV radiation. At this point the small grains do not effectively absorb the

stellar radiation and have relatively low temperatures. As you move from the leftmost

side of the plot through region I to larger grain sizes, both the absorption and emission

efficiencies increase; however, the absorption efficiency increases more quickly than the

emission efficiency and we see a rise in grain temperature. At the boundary of regions I

& II the absorption efficiency reaches a maximum resulting in the maximum grain

temperature for a given distance from the star. As we move through region II toward









region III the absorption efficiency of the grains stays relatively constant but the emission

efficiency increases which results in cooler temperatures for the grains. Near the

boundary of regions II & III the grain temperatures actually dip below the blackbody

temperature for grains at a given distance from the star. This seemingly incongruous

result stems from the fact that for grains with D=20 iim their emission efficiency can go

up as high as 2 due to emission in silicate resonances and they become super efficient

emitters (Wyatt et al. 1999). In region III we move out of the regime where they grains

are super emitters and their temperature climbs back up toward the blackbody

temperature for grains at that distance from the star. The same overall shape can be seen

in the curves in Figures 3-4 and 3-5. We have shaded these figures similarly to illustrate

the three regions. The effects of the changing efficiencies are especially evident in Figure

3-4 since there we are looking at the quantity Qabs(k, D) x Bv[X, T(D, r)] and the

variations in Qabs directly change the shape of the plots.



Color Temperatures and Optical Depths

We can also use equation (3) to calculate a value for the mid-IR optical depth of

the material around the survey sources. If we use our size limits in Table 3-1 to calculate

a value for the solid angle (Q(D)) subtended by the entire mid-IR-emitting region, and

note that Qabsc t v through the relation:

T= Xt(D/2)2 Qabs X nd L (4)

where rt(D/2)2 is the cross sectional area of a grain with diameter D, nd is the number

density of the grains along the line of sight, and L is the line-of-sight path length we can

then solve for a consistent T, t pair. Using our observations at the two different









wavelengths (10.8 and 18.2 im) and equation (3) we then have two equations and two

unknowns for the temperature and T for the mid-IR-emitting dust:

Fi0.81m= x Ltio x By[10.8 um, T] (5)

and

F18.2 m= x 8.2 x Bv[18.2 im, T] (6)

We can then solve these equations iteratively for the color temperature of the dust, T, and

the corresponding depth of the dust, T. To absolutely scale the optical depth we use X =

9.7 gm as our reference wavelength. The resulting color temperatures and optical depths

are listed in Table 3-3. There is good agreement between this method of temperature

calculation and the grain temperatures returned by the modeling code. If we calculate the

average grain temperatures returned by the models for each source, and compare that

temperature to the calculated color temperature for the same source the mean difference

between the two methods is < 30 K for the survey as a whole.

We next investigate the dynamical properties of the thermally emitting grains

using our models. A particles radiation pressure efficiency (Qpr) can be calculated from

its optical constants using Mie theory. Qpr is related to its absorption and scattering

efficiencies through the relation

Qpr = Qabs + Qsca (1 )

where the term accounts for the fact that radiation is scattered asymmetrically

from the particles (Wyatt et al 1999). Once we have Qpr calculated we can consider the

ratio of the radiation forces acting on the particle to the gravitational forces as a function

of particle diameter. This ratio, called B is given by the relation below











10


-4-\




01 j


0.01
0.01 0.1 1 10 100 1000
Particle diameter, imr

Figure 3-6: The quantity 3 as a function of grain diameter for particles near HD 141569.
Horizontal line marks a value of 1. Particles with p > 1 will be removed from the system
on hyperbolic orbits in < 104 yr.



(D) = (C/pD) T* (L./L,) (M*/Me) (7)

where C = 1.15.10-3 kg m-2, p is the particle density, D is the particle diameter, and

T. = J Qpr(D,X) Fx dX / J FX dX

is the particle's radiation pressure efficiency averaged over the stellar spectrum with

assumed temperature T. (Wyatt et al. 1999). By calculating p as a function of particle

diameter, we can determine what sized particles will be removed from the system through

radiation expulsion. Particles with 0 > 1 will be removed from the system by radiation

expulsion on very short timescales. On average, the time for removal for the survey stars

is <104 yr. Figure 3-6 shows p(D) for HD 141569. The horizontal line marks p = 1. Using

Figure 3-6 we see that for HD 141569 all particles smaller than D = 5 L.m have P > 1 and

will be removed from the system quickly. We can therefore make the claim that grains









with D < 5 Clm are likely not primordial, and have been replenished by some mechanism.

The determination of whether or not the mid-IR-emitting grains in the survey disks is an

important conclusion of the modeling since the presence of "second-generation" dust in

these disks places them firmly in the Vega-like class (Lagrange et al. 2000). Plots similar

to Figure 3-6 for all the modeled survey sources allow us to set a limit on the minimum

size of grains that would not be removed from the system through radiation expulsion.

These "p-Limiting" sizes are given in the last column of Table 3-3. To reiterate, all grains

smaller than the 'p Limiting' size (i.e. the blow-out size) will be removed from the

system by radiation expulsion.

Another dynamical property we investigate is the lifetime of the disk particles

with respect to Poynting-Robertson drag (P-R drag). Once we have calculated p(D) we

use the following relation to calculate the P-R drag lifetimes of the grains as a function of

diameter.

tpR(D) = 400(M./M.)(r2/p(D))

where r is the distance of the grain from the star in AU. Using the upper limits for grain

diameter and distance from the star, we calculate a maximum P-R drag lifetime for the

mid-IR-emitting grains in each disk. This maximum value represents the longest time

any mid- IR-emitting grains would survive in the disk before spiraling into the star. If the

grains are smaller than our upper limit, or closer to the star, their P-R drag lifetimes

would be less than this value. We list the calculated maximum values for the survey stars

in Table 3-3. The longest P-R drag lifetime in the survey is 3.106 yr, for grains near HD

9672. Although it is not certain, we suspect that all of the survey sources are older than

this value. It therefore seems likely that the mid-IR-emitting grains in these disks









Table 3-3: Derived Grain Parameters
MidR Grain Grain
Mid-IR
e Cr size Distance Max. [-Limiting
Source Color
Name Tmid-IR upper Upper P-R Drag size
(K) limit Limit Lifetime (yr) (PLm)
S(m) (AU)

HD 9672 107 6.30E-03 7.00 111.0 3.0E+06 6.0
HD 34282 375 3.80E-05 10.00 10.0 3.0E+04 9.0
HD 34700 165 5.60E-03 8.00 9.0 9.0E+05 0.9
HD 35187 211 9.90E-02 5.00 31.0 3.0E+05 6.0
HD 38678 588 2.80E-06 4.00 5.0 5.0E+03 5.0
HD 39060 171 6.80E-02 4.00 31.0 5.0E+05 3.5
HD 98800* 157 1.84E-01 2.50 5.0 2.0E+05 ---
HD 101584 237 5.50E-02 7.00 630.0 1.0E+05 >100
HD 104237 390 1.40E-03 8.00 7.0 2.0E+04 9.0
HD 109573 100 5.80E-03 10.00 78.0 1.0E+06 9.0
HD 135344 203 7.50E-03 15.00 43.0 5.0E+05 9.0
HD 139614 197 4.10E-02 2.50 15.0 2.0E+05 3.5
HD 141569 187 2.33E-03 4.00 30.0 2.4E+04 5.0
HD 142666 274 3.40E-02 1.50 6.0 2.0E+04 3.0
HD 143006 196 6.10E-03 10.00 4.0 5.0E+05 4.5
HD 144432 307 1.00E-02 7.00 4.0 1.0E+04 2.5
HD 155826 213 8.80E-03 3.00 7.0 1.0E+05 1.5
HD 158643 338 1.70E-02 2.00 13.0 5.0E+04 9.0
HD 163296 315 1.10E-02 3.00 13.0 5.0E+04 6.0
HD 169142 174 9.60E-02 4.00 30.0 4.0E+05 3.0
HD 188037 410 1.27E-01 6.00 5.0 9.0E+03 5.0
HD 233517 142 6.50E-02 10.00 81.0 1.0E+06 30.0
Mean
values: 232 K 0.042 6 tm 25 AU 4.4E+05 yr 6.0 pm
3 < 1 for all grain sizes


are not primordial material and have been replenished in some way. One method of

replenishment is through the collisions of larger bodies in the disks. Replenishment of

material in this manner is apparently occurring in the archetypal Vega-like disks of both

p Pictoris (Artymowicz 1997), and HR 4796A (Wyatt et al. 1999; Telesco et al. 2000).









The last row of Table 3-3 contains the mean values of each of the quantities listed

in the table. We calculate these numbers simply to give an idea of the properties of these

disks in the broadest sense. Certainly these values are only useful as benchmarks for the

survey sources, however, it is interesting to compare them with values from other Vega-

like disks. In particular the mean upper limit to the mid-IR-emitting grains size is very

consistent with the grain sizes in other Vega-like disks. Similar modeling of the HR

4796A disk by Wyatt et al. (1999) and Telesco et al. (2000) shows that the grains in that

disk are approximately 2 gtm in diameter. Mid-IR aperture photometry of p Pictoris

implies there are 1 to 3 ptm grains in that archetypal disk (Telesco et al. 1988; Telesco &

Knacke 1991; Aitken et al. 1993). Vega itself is also reported to have 1 to 10 gim grains

as the dominant population in its disk (Van der Bliek, Prusti, & Walters 1994).

The fact that our estimated grain sizes for the 22 survey sources we studied have mid-IR-

emitting grains that are similar in size to the archetypes is one of the main conclusions of

our work. In fact, the mid-IR emission detected around this class of source is tracing this

size range of grains in their disks. This is more or less expected since this is thermal

emission from the dust we are detecting and the dust grains emit most effectively when

their size is comparable to the wavelength of the radiation they are emitting. In the next

section we continue with our comparison of the survey sources to some of the archetypes.



Scale Size Comparison

An obvious question to ask is, would the unresolved sources be resolved if they

were at the distances of p Pictoris or HR 4796A? The average distance of the modeled









Table 3-4: Comparison of Unresolved sources to Archetypal Disks

Predicted Size of
Size at Size at Size of
Source Name angular DHR4796A D Pic at HR
size 4796A at
(arcec) (arcsec) (arcsec) Dsource Dso
(arcsec) Dsource

HD 9672 3.64 3.31 11.68 3.11 3.30
HD 34282 0.12 0.30 1.05 1.16 1.23
HD 34700 0.02 0.27 0.95 0.16 0.17
HD 35187 0.41 0.93 3.26 1.27 1.34
HD 38678 0.45 0.15 0.53 8.64 9.14
HD 39060 3.26 0.93 3.26 10.00 10.58
HD 98800 0.21 0.15 0.53 4.04 4.28
HD 101584' 1.55 18.81 66.32 0.23 0.25
HD 104237 0.12 0.21 0.74 1.64 1.73
HD 109573 2.33 2.33 8.21 2.84 3.00
HD 135344 2.15 1.28 4.53 4.75 5.03
HD 139614 0.19 0.45 1.58 1.21 1.28
HD 141569 0.61 0.90 3.16 1.92 2.03
HD 142666 0.11 0.18 0.63 1.67 1.76
HD 143006 0.09 0.12 0.42 2.02 2.14
HD 144432 0.03 0.12 0.42 0.75 0.79
HD 155826 0.45 0.21 0.74 6.13 6.48
HD 158643 0.20 0.39 1.37 1.45 1.53
HD 163296 0.21 0.39 1.37 1.56 1.65
HD 169142 0.41 0.90 3.16 1.31 1.39
HD 188037 0.04 0.15 0.53 0.83 0.88
HD 233517t 0.27 2.42 8.53 0.32 0.34
SLikely not a main-sequence star




survey sources is 95 pc, while P Pictoris is at 19 pc, and HR 4796A is at 67 pc. To

answer this question we 'moved' the unresolved sources to the distances to those

archetypes and calculated what their model predicted size would be. In this analysis we

assume that the maximum extent of the mid-IR-emitting grains from the stars is given by

the upper limits returned by our models, which are listed in Table 3-3. Using these values

in conjunction with the distance estimates for the stars given in Table 2-1 we can









calculate a predicted angular size for each of the disks. We then scaled those predicted

sizes to what they would be at the distances of 0 Pictoris and HR 4796A. These predicted

and scaled sizes are listed in Table 3-4. Assuming that we are using an 8 to 10 m class

telescope to make the observations, by analogy with HD 169142 (Chapter 4), we set the

threshold of detection at an angular size 0.7". While this limit is somewhat arbitrary, our

experience with the survey data has shown that this is about the limit at which a face-on

disk source can be distinguished from PSF measurements. This represents a worst-case

scenario though since edge-on disks may be detectable at smaller angular scales.

What we see is that for the most part the predicted disk sizes at the real distances

of the stars are in the tenths of arcsecond range, below the current limit of detectability.

This changes somewhat when we move the survey stars to the distance of the archetypes.

At the distance of 3 Pictoris, the closer of the two, we predict that we could have resolved

twelve, or 54% of the disks. This seems to imply that it is only an observational limitation

that prevents us from resolving them. This is clearly a very rough way to estimate the

detectability of these sources. However, it does give us a starting point for the planning of

more in-depth observational programs.

Conversely, Table 3-4 shows that if we move the two archetypes to the distances

of the survey sources, we would be able to resolve both the disks of both P Pictoris and

HR 4796 at effectively all the distances of the survey stars. This implies that the disks of

the unresolved sources have a smaller scale size then the archetypes. While the cause of

this scale size discrepancy is still not fully understood one idea that may explain it deals

with the size of the mid-IR-emitting grains in the disks. If the grains in the P Pictoris and

HR 4796 disk are smaller then those in the disks of the unresolved sources, they will be









detected farther from the stars since smaller grains in equilibrium with a radiation field

are hotter than larger ones at a given distance from the star. If the grains in the unresolved

disks are larger then those in the archetypes, even by a factor of a few in diameter, they

will have to orbit their parent stars within a few AU for a late A-type star to emit strongly

in the mid-IR. This idea is supported by the results presented in Table 3-3 where we see

the model results imply that the grains around most of the unresolved sources orbit within

-20 AU of their stars and have diameters of -6 p.m. Compared to the -2 to 3 p.m

diameter grain in the 3 Pictoris and HR 4796 disks, the larger grains size may account for

the unresolved nature of some of the survey sources. The idea that the mid-IR-emitting

grains in the disks of the unresolved sources are larger also has implications for the

evolutionary status of those disks, and therefore the stars. Since it is believed that the

grains in these disks grow through aggregation, disks with larger grains in them are likely

older than those with small grains. In a later section of this chapter we investigate the

evolutionary status of these sources in detail, and propose an evolutionary sequence for

our survey sources.

Here we touch on two limitations of our modeling that are related to the basic

assumptions we made about the composition and morphology of the grains. Obviously,

the dust grains may not be simple Mie spheres. For example, the zodiacal particles in our

solar system seem to have a much more complex "bird's nest" structure. The "bird's

nest" like appearance of these grains occurs because the grain itself is actually an

aggregate of tens or hundreds of smaller particles that have stuck together through

collisions (Gustafson 1994). As noted, we have assumed that the observed grains are

solid and spherical. However, if the grains are actually aggregates and complex in









appearance ("fluffy"), our overall conclusions about particle lifetimes are not

significantly changed. Gustafson (1994) points out that Mie calculations for

homogeneous spheres consistently underestimate the value of 3 for aggregated dust

models by a factor of two. For our survey sources, this means that even larger particles

would have P > 1, and would be expelled from the star/disk systems in a short time. Since

the P-R drag lifetime of a particle is proportional to P-' (Wyatt et al. 1999), the larger

value of p for a grain of a given size would drive its P-R drag lifetime down, implying

that the grain would spiral in to the star in a shorter time. We therefore see that if the

grains in the disks of the survey sources are porous or fluffy, it does not change our

overall conclusion that most of them are second-generation grains, perhaps collision

fragments.

The modeling presented here has shown that the mid-IR-emitting grains in the

disks of the survey sources are on the order of a few microns in diameter, similar to the

grains in the archetypal disks of 3 Pictoris, Vega, and HR 4796. It has shown that these

grains orbit at distances of tens to a hundred AU from the central stars, and have

temperatures in the range of 150 to 250 K. Considerations of the dynamical properties of

the grains like their P-R drag lifetime and the parameter 3 imply that these grains are

likely not primordial, and have been replenished by some mechanism. We also present

rough calculations which show that about half of the disks could possibly resolved at the

distance of 3 Pictoris, but that the dust lies too close to the other half of the sources to be

seen even at this relatively close distance of 19 pc. The main conclusion that we draw

from our models is that the mid-IR properties of the survey sources are, in fact, similar to

those of the archetypes. The fact that the mid-IR-emitting grains in the survey disks are









probably replenished places them firmly into the debris disk class, and the similarity in

their grain sizes, temperatures, and distances from the central stars to those of the

archetypes implies that they are at a similar evolutionary state. In the following sections

we expand on this idea of source evolution and present an evolutionary sequence for the

survey stars.




A Proposed Evolutionary Sequence

In this section we present an evolutionary sequence we have constructed for our

survey sources using the properties of their mid-IR excesses in conjunction with the

characteristics of the stars. The idea that the Herbig Ae/Be stars are the progenitors of the

Vega-like stars is well represented in the literature (cf. Lagrange et al. 2000; van den

Ancker et al. 1998). Trends seen in the characteristics of properties of disks also support

such an evolution. For example, Holland et al. (1998) sees a strong trend of decreasing

disk mass with age. Their Figure 2 clearly shows that the mass of the dust associated with

Herbig Ae/Be stars is orders of magnitudes greater than that in the tenuous disks in our

sample (Holland et al. 1998). More relevant to the discussion of our evolutionary

sequence is the trend seen in the evolution of the spectral energy distributions (SED) of

sources with associated circumstellar dust. Below we discuss how this idea is directly

related to our survey sources.



SED Evolution

For a graphical representation of what SED evolution looks like we reintroduce

the scheme of Andre (1994) in Figure 3-7. This figure shows how the SED of a star/disk






65







2 II I09
V cc

M Body

1 2 10 100










12 10 100
A un




Dbt>k
SStI kr
1 2 10d t .






1 2 10 100
) (WW'

Figure 3-7: SED evolution of a star/disk system moving onto the ZAMS. Most of our
survey sources fall into Class III, but a small number of them exhibit some characteristics
of a Class II source. Using our survey sources we refine the Class III group here by sub-
dividing it into three smaller parts.



system evolves during the first few Myr of its existence. The most important trend to

notice in regards to our proposed additions to this sequence is how the overall amount of

excess emission decreases as the system evolves. That is, as the system evolves, less of

the overall infrared luminosity comes from the circumstellar dust, and the SED of the

system approaches that of the star itself, a simple blackbody curve. By the time the









source can be classified as Class III in this scheme the dust associated with the star has

become optically thin and only contributes a fraction of the overall system luminosity.

The low optical depths we derived for them in Table 3-3 support the idea that the dust

around our survey stars is optically thin. As we will see, a subset of our survey stars have

SEDs that have characteristics of an object transitioning from Class II to Class III.

However, the majority of our survey stars can be classified as true Class III objects.

To introduce our survey sources into the context of this sequence we present

Figure 3-8. In this figure we show three examples of SEDs of sources in our survey. In

the top panel we show the SED of HD 143006. Note the strong near-IR excess associated

with this source. We suggest that the presence of such an excess can be taken as a sign of

relative youth within the survey sources. This excess comes from dust that is close to the

star, within a couple AU in the case of HD 143006. The fact that there is dust so close to

the star implies that the processing of the inner disk has yet to commence. Indeed, the last

stages of active accretion may still be occurring in this system. Nine of our survey

sources exhibit excess emission in the near-IR, and these nine star/disk systems form the

first of three sub-groups we break our survey sources into. We name this sub-class "Class

IIIa" since the SED of these sources is similar to that of a source that has just evolved

into Class III in the Andre (1994) scheme. The middle panel of Figure 3-8 shows the

SED of HD 141569, a source that falls into our second sub-class (named Class IIIb).

Along with HD 141569, the other three members of this group represent an intermediate

stage of evolution within our survey. The four sources in Class IIIb exhibit no near-IR

excess, however they all have well defined excesses in the mid-IR. Processing of the

inner disk regions is most likely still ongoing in these sources. Interestingly, three out of









le-12 "

le-14

le-16

le-18

1 10 100 1000
Wavelength (rm)



le-12

le-14- N
le-16
le-18

1 10 100 1000
Wavelength (pm)


le-12

le-14

le-16-

le-18

1 10 100 1000
Wavelength (ptm)

Figure 3-8: SED evolution within our survey. (top) SED of HD 143006. Note the strong
near-IR excess associated with this source. (middle) SED of HD 141569. This source
represents an intermediate evolutionary step. There is no near-IR excess associate with
this star. (bottom) SED of HD 142764, a source that represents the last stage of evolution
within our survey. No near-IR or mid-IR excess is associated with this star.








the four sources in Class IIIb have been resolved in the mid-IR. The bottom panel of

Figure 3-8 shows the SED of HD 142764, a source representative of the last of the three

sub-groups, Class IIIc. HD 142764 and the other sources in this group exhibit no excess

emission in the near-IR, and little or none in the mid-IR either, indicative of them being

the most evolved. By the time a star/disk system evolved to this point, processing of the

inner portions of the disk has taken place, and a central hole has formed leading to the

paucity of excess IR emission. In the next section we discuss the three sub-classes in

more detail, and show how each group is tied together by common characteristics.



Class liIa: The near-IR Nine

The first sub-class we discuss is the group the represents the earliest stage in the

evolutionary sequence. Class Ilia contains nine of our survey sources that have a

common trait in that they all exhibit significant near-IR excess. Because of this the SEDs

of these sources all resemble that of HD 143006 (Figure 3-8 top), which exhibits a strong

near-IR excess as seen in Figure 3-8. Listed in Sylvester et al. (1996) we see that the nine

sources have an average of 0.6 mag of excess at 1.7 glm, and 1.1 mag of excess at 2.2 p.m.

Sylvester et al. (1996) also calculated blackbody fits to the near-IR excesses of the

sources and found that grain temperatures in the range of 1500 to 2000 K fit the excess

well. In our own analysis of these sources we find that the Class Ilia stars exhibit 7 out of

the top 10 highest mid-IR optical depths (see Table 3-3). The fact that these stars have

near-IR excess, and relatively high optical depths makes them similar to Herbig Ae/Be

stars, and they are therefore most likely young. Indeed, at least 3 of the 9 Class IIIa stars

show hydrogen emission lines in their spectra (Sylvester et al. 1996), another sign of










SOE-IO


the r i \ F) '- .()
\ %
-I O-2--------------------\-^^^------






I O E16S






Figure 3-9: SED of HD 169142 with ( )4/3 plotted for comparison. The diamonds are

fluxes. The solid line is a blackbody function with Teff = 8400 K. The dashed line follows
the relation F(X) a ()-4/3.



youth as compared to the other survey sources. Since it seems these sources are the

youngest in our survey, we use these sources as the starting point in our evolutionary

sequence.

One of the main distinctions between Class II and Class III sources is whether

their disk is optically thick or thin. Class II sources have optically thick disks, while those

associated with Class III stars are optically thin. As noted by Hillenbrand et al. (1992)

one of the most powerful diagnostics of a circumstellar disk is its SED in the near-IR

(1 pm < X < 2.2 plm). Objects with flat, optically thick disks have SEDs that follow a

4/3 falloff wavelength. This fact gives us a criterion we can employ to place our survey

sources into the correct class. We know that any optically thick disks will follow that









functional relationship, and would belong in Class II. A steeper than X-4/3 falloff in

indicitave of emission from an optically thin disk, and warrant a Class III designation of

any source whose SED follows this trend. To answer the question of whether the sources

we designate as Class liIa are actually Class II sources we present Figure 3-9. In this

figure we plot the SED of one of the Class liIa sources, HD 169142. Its SED is

representative of all nine of the Class Ilia sources showing a strong near-IR excess

beginning at approximately X = 1.4 lim. HD 169142 is an A5 V star with a Teff = 8400 K

(Dunkin, Barlow, & Ryan 1997) and we plot a blackbody function with this temperature

as a model photosphere in the figure. Also plotted is a dashed line designating a X-4/3

falloff with wavelength. Inspection of the figure shows that in the near-IR regime, which

is bracketed by the two vertical lines, the SED of HD 169142 has a much steeper falloff

than :-413. This implies that HD 169142 and the other eight sources with similar SEDs are

likely to have optically thin disks, and should rightfully be classified as Class liIa objects.



Class IIIb: ZAMS Sources

The next step in our sequence brings us to Class IIIb. The four sources in this

class do not exhibit any near-IR excess, implying that they are somewhat older than the

Class IIIa stars. These stars do have a common trait though, they all have low

luminosities for their colors, which places them very near the ZAMS in the H-R diagram

(Jura et al. 1998). Interestingly, 3 out of the 4 sources (p Pictoris, HR 4796A, and HD

141569) in this class have been resolved in the mid-IR.

With respect to how these sources fit into the evolutionary sequence, we can ask

the question: how young are they? Luckily, for this sub-class we have an answer for that









question. One of the Class IIIb members is HR 4796A, which has a well-constrained age

of 8 3 Myr (Stauffer et al. 1995). Recent work by Barrado y Navascues et al. (1999)

uses Hipparcos data and evolutionary tracks to estimate the age of the archetype P

Pictoris at 20 10 Myr, similar to the age of HR 4796A. The third resolved source, HD

141569 has no published age values. However, we show in Chapter 5 that it is likely a

source that is transitioning from the Herbig Ae/Be class to the Vega-like class. Lagrange

et al. (2000) coin the term "old-pre-main-sequence" star when describing HD 141569,

indicating that it is more or less finished with its PMS evolution and is approaching the

ZAMS. The age estimates for HR 4796A and p Pictoris, along with their position on the

ZAMS seem to imply that these stars are relatively young, perhaps 10 to 30 Myr old.

Since it seems that they are finished with their PMS evolution, we suggest that they are

older then the Class liIa sources, and form the second step in our sequence.



Class IIIc: Post ZAMS Sources

The last sub-group in our sequence is Class IIIc. The remaining twenty-six stars in

our survey fall into this class. They represent sources that are the most evolved and have

most likely already moved onto and then off of the ZAMS and are now crossing the main

sequence in the middle stage of their lives. Class IIIc sources show no near-IR excess,

and little if any mid-IR excess. In fact, all of the sources that we could not model due to

uncertain excess determination fall into Class IIIc. None of the sources in this class

exhibit any signatures of youth, like emission lines in their spectra. We take the paucity

of near and mid-IR excess coupled with the lack of any signatures of youth to mean that

these are the most evolved sources in the sample. In reality, these sources could likely









Table 3-5: Evolutionary Class characteristics

Shortest
Class Excess Age H-R Diagram Class Charactristics
Name Wavelength (Myr) Position
(gtm)


Ha emission in spectra
Class IIIa 1.2 to 1.7 < 10 Pre-ZAMS Li seen in source spectra
Strong near-IR excess

no near-IR excess
Class IIIb 10- 20 10 to 20 ZAMS strong mid-IR excess
Good age estimates


little or no mid-IR excess
Class IIIc > 20 > 20 Post-ZAMS
no signatures of youth


form a new class, "Class IV" in the schemes of Andre (1994) and Hillenbrand et al.

(1992). A class that would represent sources already on the main sequence, completely

finished with the formation and PMS evolution.

In Table 3-5 we summarize the characteristics of the new sub-groups. To quantify

the idea of SED evolution we list the wavelengths at which the excess 'turns-on' for each

class and show that it increases with age. We also list approximate ages for each of the

groups and their corresponding position in the H-R diagram. Finally, we comment on

some of the common characteristics for each of the sub-classes that we use to tie each

group together. In the next and final section of this chapter we use the H-R diagram to

graphically illustrate our proposed evolutionary sequence.









Survey Sources in the HR Diagram

It is useful to investigate the position of our survey sources in the H-R diagram.

Such an investigation allows us to graphically see how the survey fits into the overall

scheme of stellar evolution, and it gives us another way to present our evolutionary

sequence. For this purpose we use a H-R diagram comprised of =41000 stars taken from

the Hipparcos database (Perryman et al. 1995). We have Hipparcos measured distances

for 90% of the stars in our survey, and we use them in conjunction with their Tycho

measured B-V values to place them in the diagram as shown in Figure 3-10. For most of

the sources this is the first time their newly measured distances have been used to place

them in the diagram. In fact, this is the first time ever that Hipparcos and Tycho data has

been used in conjunction with a significant number of Vega-like stars to illustrate their

position in such a diagram. Inspection of Figure 3-10 shows that several interloping

giants made their way into the survey, one in particular, SAO 26804, Is discussed in

detail in Chapter 6. However, generally the sources are on, or near the main sequence.

While it is instructive to see the whole survey in the diagram, the real value of this

kind of presentation comes into view when we discuss our proposed evolutionary

sequence. We present the sequence as a series of three panels in Figure 3-11. In Figure 3-

1 la we show our so-called Class Ilia sources. These represent the youngest of our survey

sources, and we propose that they are still moving onto the ZAMS. In Figure 3-1 Ib we

show our Class IIIb stars. These are the sources that have relatively well defined ages at

-10 Myr. Notice that we can now see that they all have low luminosities for their colors,

as reported by Jura et al. (1998). Since they are very close to the ZAMS we use them as a

useful fiducial point in the sequence. These sources are somewhat of a fulcrum point,




















S ,




.,
*~ 4 +


Si''
S2-

5-


SI I I I


0.5 1.0

B- V [mag]


0


1.5 2.0


Figure 3-10: The Vega-like survey sources in the H-R diagram. This figure shows the
sources of the survey plotted in a HR diagram comprised of -41000 stars from the
Hipparcos catalog. The four squares are the position of the disks that have been resolved
in the mid-IR, P Pictoris, HR 4796A, HD 141569, and 49 Ceti. The arrow is a reddening
vector. Hipparcos data from Perryman et al. (1995).


15
-0.


5


0.0


I I I






75





S *



5 5



10 01 10 -

(a) (b) (c)
0.5 00 05 0 1.5 00 05 1.0 1.5 00 05 1.0 1.5 2.0
B V mi agl- Hm B-V ],i,

Figure 3-11: Three steps in an evolutionary sequence on the H-R diagram. (a) Step 1:
Class IIIa sources, stars moving onto the ZAMS. (b) Step 2: Class IIIb sources, stars
which are on the ZAMS. (c) Step 3: Class IIIc sources, stars moving away from the
ZAMS.



about which the other stars in the survey pivot. On one side of the fulcrum are the Class

IIIa sources, which are younger and still moving onto the ZAMS. On the other side, we

have the Class IIIc sources that are most likely older and have already reached and

moved off of the ZAMS.

To investigate the timescales involved with the first stage of this sequence, we

present Figures 3-12, and 3-13. In Figure 3-12 we have plotted the Class IIIa and IIIb

stars in the H-R diagram with the PMS evolutionary tracks of Palla and Stahler (1993)

overlaid. Using the tracks we determine age estimates for the Class IIIa sources in the

range of 3 to 10 Myr, consistent with them being younger than the Class IIIb stars.

Indeed, the Class IIIb stars lie at the end of the PMS tracks while the Class IIIa sources

look to be still following them onto the ZAMS. The isochrones of Iben (1965) agree with

the age estimates given by the PMS tracks. In Figure 3-13 we see that most of the Class

IIIa sources lie between the 3 Myr and 10 Myr isochrones.
























r.

**,4 4''


s


0.5 1.0

B- V [mag]


Figure 3-12: H-R Diagram with the PMS evolutionary tracks for intermediate mass stars
of Palla and Stahler (1993) overlaid. The stellar birth line is the dotted line. The mass
associated with each evolutionary track is given on the left in units of M0. Tick marks on
each track correspond to the times listed in the legend. Age estimates for these sources
are in the 3 to 10 Myr range.


Time (yr)
1x10

1x105
3x100
1x10


Point
1
2
3
4
5
6
7


5


15
-0.


0.0


. m






















































, I *l I I n I .


0.0


0.5 1.0
B V [mag]


2.0


Figure 3-13: H-R Diagram with the isochrones of Iben (1965) overlaid. Also plotted are
the Class Ilia and Class IIIb stars. Class IIIa (circles) and Class IIIb (squares) stars are
plotted for comparison The times to reach each isochrone is given on the left side of each.


15 L
-0.


5


. .


5
~- .*


'" '.









As noted by Lagrange et al. (2000) a problem with using this method for age

estimates is that isochrones are normally bi-valued. That is, under normal circumstances

you cannot distinguish between a source moving onto the ZAMS and one evolving away

from it. Our sequence eliminates this issue since we use the shape and apparent evolution

of the SED of a source to determine whether or not is moving onto or away from the

ZAMS. Hence, we believe our method solves this problem for our survey.

That is in essence the extent of our proposed sequence. By sub dividing the

survey into three sub-classes we have come to one of the main conclusions of this work.

That is that we feel the evolution of the SEDs of the sources, coupled with the positions

of the sources in the H-R diagram is strong evidence that Vega-like sources in our sample

evolve in this manner. In the next chapters we move to talking about individual survey

sources. Chapter 4 discusses the face-on disk of HD 169142, Chapter 5 presents our work

on HD 141569, and in Chapter 6 we present results that 'de'-resolve the source SAO

26804. In Chapter 7 we discuss the OSCIR camera system and its important role in this

dissertation.














CHAPTER 4
THE FACE-ON DISK OF HD 169142

In this chapter we present Keck imaging of the source HD 169142. Our images

show the source to be resolved at both 10 and 18 Jm with strongly detected extended

emission seen in the form of a seemingly face-on disk with diameter approximately equal

to 1.2". At a distance of 145 pc (Sylvester et al. 1996) this corresponds to a radial extent

for the mid-IR emitting dust of -85 AU, which is very similar to the size of the mid-IR

emitting regions of the archetype P Pictoris and the source HD 141569 (Lagage & Pantin

1994; Fisher et al. 2000). Although we have a high degree of confidence in our detection

of extended emission associated with the source, we have no significant spatial

information on the distribution of the dust itself. This is primarily due to the fact that it is

extremely difficult to accurately remove the contribution of the star from the central

region of the emission. As we will discuss, the photospheric contribution to the total flux

of the source is minimal, however, the spatial deconvolution of that flux from the image

itself it not an easy task due to the relatively low signal-to-noise of the outer regions of

the extended emission. We can however use the global characteristics of the disk to infer

some of its properties. Using our images we place strong limits on the size of the

extended emission and show that the orientation of the disk is nearly face-on.

We also use our observations to model the mid-IR emitting dust as silicate Mie

spheres and determine a characteristic size and temperature for the grains. Since we have

no little spatial information on the grain distribution, we use our images to derive 'global'

dust parameters. We then use our derived grain parameters to discuss the possible









Table 4-1: Characteristics of HD 169142

Spectral Type: A5 Vet Teff: 8400 Kt

Distance: 145 pct log g: 4.2t
(B V): 0.29* M/Me: 2.0'
My: 2.3t L/Le: 14'
v sin(i): 55 2 km/sect R/Re: 1.7'

t Dunkin, Barlow, & Ryan (1997), T Sylvester et al. (1996), Allen (2000)



origin, and eventual fate, of the grains in the disk of this star. We also place HD 169142

into an emerging evolutionary sequence for this class of source and discuss how it may

be a bridge between the well-known class of Herbig Ae/Be stars and the Vega-like

sources.

Accurate stellar parameters are needed to confidently model the grains near HD

169142 and to interpret our new mid-IR images of the source. A literature search gives

the relevant characteristics of HD 169142 listed in Table 4-1 above. Note that HD

169142 was originally classified as a B9 V source in the list of Walker and Wolstencroft

(1988) but has since been re-classified as A5 V using high resolution optical

spectroscopy (Dunkin, Barlow, & Ryan 1997). Recent photometry has also refined the

rotation speed of the source and polarimetry of the source and has revealed that the

source exhibits variable polarization in the near-IR (Dunkin, Barlow and Ryan 1997).

These facts are important to our discussion since they give us clues to the nature of the

circumstellar disk. In the rest of the chapter we present our new observations, discuss the

results of our modeling of the grains in the disk, and comment on the evolutionary status

of HD 169142.









As we hinted at, the evolutionary status of HD 169142 is still very much in

question. It has been classified as a Vega-like star by many authors including both

Walker and Wolstencroft (1988) and Sylvester et al. (1996). However, HD 169142 is also

a member of various Herbig star lists like those of Malfait et al. (1998) and Corporon &

Lagrange (1999). The reason that HD 169142 is on both kinds of lists is because it is one

of several stars in our survey sample that exhibit characteristics of both a Herbig star and

a Vega-like source. HD 169142 meets two of criteria to be defined as a Herbig star by

having a spectral class earlier than FO and exhibiting single peaked Balmer emission line

profiles. HD 169142 also has Hel [X5876] in emission (Dunkin, Barlow, and Ryan 1997),

a fact that is relevant to its evolutionary status. The star does exhibit some Vega-like

characteristics though. In particular, both the existence of the large mid and far-IR excess,

and its characteristic shape are very similar to those of other Vega-like sources.

We believe that the possible transitional nature of HD 169142 is evident in its

spectral energy distribution (SED), which is shown in Figure 4-1. The optical-to-mm

SED shows that the source exhibits a large excess for all X > 1.7 plm. First discovered by

IRAS, the excess peaks between 30 to 40 gtm, which is very similar to the SEDs of all of

the Vega-like archetypes. Observations by Sylvester et al. (1996) revealed a strong near-

IR excess associated with the source in the H (1.7 gpm) and K bands (2.2 gtm) where they

measure an excess of 0.4 and 0.8 mag in the H and K bands respectively. The excess

becomes more pronounced at longer wavelengths and reaches 1.7 mag in the M-band

(Acen = 4.8 gim) (Sylvester et al. 1996). As we discuss in the observation section, the

excess is very pronounced in the mid-IR. In fact, the photosphere of the central star









1610
10

-12

10E




is 7
10 \ -
10



I I I I
1 10 100 1000
Wavelength (pm)

Figure 4-1: SED of HD 169142. The solid line is a model photosphere the points are
observed fluxes. The IR excess of HD 169142 is seen at all wavelengths > 1.7 pnm. The
near-IR excess can be interpreted as a sign of youth since it implies there is hot material
very close to the star and that the inner disk region has yet to be processed or cleared.
SED from Sylvester et al. (1996)



only accounts for a couple percent of the total flux at 10.8 gmm, and an order of magnitude

less than that at 18.2 pim.

Using the IRAS long wavelength data as a diagnostic Walker & Wolstencroft

(1988) assigned a temperature of T = 115 K to the circumstellar dust around HD 169142.

As we will see this value is low compared to the temperature we derive from our mid-IR

data (T = 175 K). This is not an unexpected result though since Walker & Wolstencroft

fit the 25 and 60 pm fluxes in the SED, while we use 10 and 18 tm data.








Mid-Infrared Observations at Keck

We observed HD 169142 as part of our Vega-like survey at the Keck II telescope

in 1999 May using OSCIR. On the night of 03 May 1999 UT we first detected the

extended emission associated with the source in the N-band (ko = 10.8 um, AX = 5.2 utm)

and IHW18 (Xo = 18.2 glm, AX = 1.7 gm) filters. Our observing sequence consisted of

first observing an 18 gim PSF star (a Boo). Then we observed HD 169142 for 20 minutes

chopped integration (10-min on-source) at 10.8 and 18.2 gtm. After the science

observations we observed a 10 lim PSF star (19 Sgr). Observations of an infrared

photometric standard to absolutely calibrate the HD 169142 data finished the observing

sequence (a Boo, and yAql). For the HD 169142 observations a Boo was used as the 18

mm PSF star since the chosen star was not bright enough to give a good signal-to-noise

detection in a reasonable integration time.

On Keck OSCIR the 128 x 128 pixel detector of OSCIR has a plate scale of

0.062"/pixel which gives a field of view of 7.9" x 7.9". The observations were made

using standard chop/nod techniques with an 8" chopper throw in declination. The Keck

autoguider system was used for all of the Keck observations. We estimate that there is 1

pixel (-0.06" on Keck) of "guiding jitter" inherent in any OSCIR observations made

while using it. On the Keck run in 1999 May the weather was non-photometric with thin,

but uniform, light cirrus clouds present during the night that HD 169142 was observed.

During post-processing of the data, chopped image pairs that were obviously

compromised by the cirrus were discarded. However, there is still some uncertainty in the

photometry of the source and the standard stars, which we take to be 10%. This









translates into the major component of the uncertainties associated with our flux

estimates.

Measurements of the full-widths at half maximum (FWHM) intensities of

comparison stars were approximately 0.45" and 0.49" at 10.8 and 18.2 glm, respectively.

Quadratic subtraction of the diffraction limits (A/D) of 0.22" at 10.8 gim and 0.37" at 18.2

p.m from these values from implies seeing of -0.3 to 0.4" in the 10 to 20 .m spectral

region. It is our experience that these values are typical for non-photometric nights on

Mauna Kea.

Our measured flux estimates of HD 169142 contain both the thermal emission

from the circumstellar grains, and emission directly from the photosphere of the central

star. To calculate the amount of photospheric emission the star emits in the mid-IR we

normalized the J-band (ken = 1.22 gm) flux estimate of Sylvester et al. (1996) to that of a

blackbody function with effective temperature, Teff = 8400 K. We then predicted that the

photospheric contribution to the 10.8 .m flux density is 41 mJy, or 1.7%. At 18.2 4im, the

photosphere only accounts for 0.2% (14 mJy) of the observed flux. Our photosphere-

subtracted flux estimates for HD 169142 are: 2283 228 mJy at 10.8 jm, and 7187

718 mJy at 18.2 mrn. These flux estimates are in agreement with those of Sylvester et al.

(1996). The 10.8 jm point is also consistent with the IRAS PSC 12 jm value of 2.95 Jy,

however our 18 jm point is low compared to the IRAS 25 jLm estimate of 18.4 Jy. Even

accounting for the spectral shape of the dust SED in this regime the IRAS point seems to

overestimate the flux from the source. The IRAS 25 jpm point also lies above the overall

level of the CGS3 spectrum of HD 169142 presented in Sylvester et al. (1996). We can

only speculate as to the reason for this and an obvious hypothesis is contamination of the









IRAS beam. Since it is the ratio of the fluxes (F10.8/F18.2) that lets us place an upper limit

to the grain sizes in our modeling, we believe the non-photometric quality of the sky will

not fundamentally change our modeling results.




HD 169142 Source Size

In this section we present our new mid-IR observations of HD 169142. These

observations represent the highest resolution mid-IR images currently possible. We

measured a FWHM for HD 169142 of 0.57"at 10.8 gm, and 0.62" at 18.2 gim. Measured

FWHM values of the PSF stars are 0.45" at 10.8 gim, and 0.48" at 18.2 g.m. Subtracting

these values quadratically from the HD 169142 data gives an inherent source size of

0.35" at 10.8 gAm and 0.39" at 18.2 g.m. Interestingly, these values match the peaks of the

intensity of the residual emission of the disk. Our mid-IR data is presented in Figure 4-2

in the form of normalized radial scans along the cardinal directions through HD 169142

and a nearby PSF star (19 Sgr). Also plotted in each of the panels is the residual emission

in the scan direction. Each of the scans through the source and PSF star was normalized

to have a maximum of one and the peaks of the scans were aligned. The residuals were

then calculated by differencing the two scans. An inherent assumption in this method is

that the star sits in the exact center of the emission, and therefore the exact center of the

disk. Recent work on the disk of HR 4796A by Wyatt et al. (1999) has shown that this

may not be true. In that work they introduce the concept of "pericenter glow" where the

long term perturbation of a disk by an object in orbit inside or outside the disk may shift

the disk with respect to its central star (Wyatt et al. 1999).






86


(a) N band (b) N-band
north-south east- west
0.8

0.6-

0.4

0.2-


-2 -1 0 1 -1 0 2

S (c) 1HW18 (d) IHW18
., north-south east est
0.8

0.6

0.4

0.2 /


-2 -1 0 1 -1 0 1 2
Offset (arcseconds)

Figure 4-2: Normalized scans through HD 169142 and a nearby PSF star. In all plots
HD 169142 is the solid line, the PSF star is the dashed line. The dotted line is the residual
emission, which is the difference of the source scan and the PSF scan. The four panels are
as follows: (a) 10.8 gim north-south direction. (b) 10.8 im east-west direction. (c)
18.2 gm north-south direction. (d) 18.2 pm east-west direction.



In the case of our HD 169142 data small (1 pixel) changes in the position of the

PSF star scan with respect to the source scan produced significant changes in the shape of

the residual emission, but under no circumstances could we make the residuals disappear.

We therefore are confident that the residual emission is present, even within a couple

tenths of an arcsecond from the peak of the emission, but we cannot say confidently say

anything about the structure of the residuals. The scans in Figure 4-2 are our best estimate

at the alignment of the source and PSF star, and therefore our best estimate at the

residuals. The residuals are present in scans through the source at any position angle at









approximately the same level of brightness, which is consistent with the disk being

almost face-on to our line of sight. Additionally, the overall shape of the residuals stays

relatively constant with scan position angle. The approximate face-on orientation of the

disk is also evident in our images. Both the images of the source and of the residuals are

close to circular although there is a slight asymmetry in the outermost region of the 18.2

gm residuals. This asymmetry is detected at a very low level and may well be an artifact

of the PSF removal. In a later section we discuss other evidence that predicts that the disk

should be face-on.

The difference in the widths of HD 169142 and the PSF star is very evident at

both 10.8 and 18.2 gim. Careful inspection of Figure 4-2, especially panels b and c shows

that HD 169142 is broader than the PSF star even in the very core of the scans. We

interpret this as meaning that there is excess emission from the dust coming from very

close to the central source. We see evidence for dust emission within 0.2" in the scans

and images, and it probably reaches in closer to the central source than that. This

interpretation is supported by the fact that HD 169142 exhibits a near-IR excess since

such an excess is caused by hot dust at temperatures of 500 to 1000 K. Calculations

show that blackbody grains need to be within a couple of AU of the star to reach these

temperatures. The fact that there may be dust this close to the star also has implications

for the evolutionary status of the disk that we address in a later section.




Modeling of Characteristic Grain Parameters

Here we present and discuss our modeling of the grains in the HD 169142 disk.

We can use our observations at two wavelengths to estimate basic parameters of the mid-








I I I I I


5 6 7 8 9
Wu cllcngh (.tm)


1.5xl613

I6 3

5xI 4


8 10 12 14 16 18
%'a ielcngth (|Im)


20 22 24


Figure 4-3: Ground-based and satellite spectra of HD 169142. This combination of
observations gives complete coverage from 5 to 24 plm, except for the region blocked by
atmospheric CO2 between 13.75 and 16 pm. In particular, note the "UIR" emission bands
between 7 and 9 pLm, and the sharp UIR peak at 11.3 p.m. Also present in the CGS3
spectrum is a broad silicate feature centered around 20 plm. Top panel: ISOPHOT spectra
from Walker & Heinrichsen (2000). Bottom panel: CGS3 spectrum from Sylvester et al.
(1996).



IR-emitting grains in the disk such as their temperature and approximate size. To derive

these properties we make an assumption about the composition of the grains.

To address the question of the composition of the mid-IR-emitting grains in the

disk of HD 169142 we present the spectra shown in Figure 4-3. Here we see two

moderate resolution spectra of the source that give complete wavelength coverage of the

thermal infrared region. The top panel of Figure 4-3 is an ISO-SWS spectrum reproduced


I I I I I I


10 11


I I I I II iI
I < l l i I I I I



I I X ^ l l l I I









from Walker & Heinrichsen (2000). The bottom panel is a CGS3 spectrum of HD 169142

from Sylvester et al. (1996). In these spectra we see compelling evidence that there are

both silicate grains and polycyclic aromatic hydrocarbons (PAHs) present in the disk.

The features seen between 7 and 9 p.m, and the sharp peak at 11.3 pm are normally

attributed to PAH grains. In fact, HD 169142 was the first Vega-like source to have these

features detected in its 10 p.m spectrum (Sylvester et al. 1994). Also present in the HD

169142 spectrum is a broad silicate feature that dominates the 20 p.m region, which is

caused by the stretching of Si:O bonds in the silicate molecules. Another clue to the

existence of silicate disk material is the fact that optical spectroscopy has shown that HD

169142 has a large under abundance in both Si and Mg. HD 169142 is deficient by 0.86

dex in Si, and 0.56 dex in Mg as compared to the Sun (Dunkin, Barlow, & Ryan 1997).

These values are by far the lowest abundance of these elements of any star in the 13

Vega-like sources studied by Dunkin, Barlow, & Ryan (1997). Dunkin, Barlow, & Ryan

(1997) suggests that the photospheric depletions of these elements is indicative of the

material residing in circumstellar grains, and indeed the presence of the 20 pm silicate

feature seems to support this hypothesis.

These results imply that there are at least two different grain populations in the

disk. This has consequences for our modeling of the grains since our models assume that

the grains are composed of the astronomical silicates of Draine and Lee (1984). However,

since we are working with the global flux estimates of the source it is impossible to de-

couple the emission of the silicate grains from that of the PAHs. To deal with this we

treat the PAH emission as a 'contamination' and run the models assuming that it









contributes varying amounts to the total 10.8 jim flux. Below we discuss our models and

this process in detail.



Model Results

Before we discuss the results of our modeling we introduce the model itself and

synopsize its operation. The University of Florida Dust Dynamics group developed our

model initially to work on the zodiacal dust of the Solar system. We have used these

thermal equilibrium models to analyze similar data on the disk of HR 4796A (Telesco et

al. 2000; Wyatt et al. 1999) and HD 141569 (Fisher et al. 2000; chapter 5). Our models

assume the grains are spherical Mie particles composed of the astronomical silicates of

Draine and Lee (1984) with a density p = 2.5 g cm3.

The results presented there we first need to discuss the operation of our models.

The primary inputs to the modeling code are the optical constants of the grains, and the

characteristics of the grain heating source. In this case the only heating source is HD

169142 itself and we use the data in Table 4-1 as our inputs. We also input a distance to

the source, a vector of grain sizes (diameters in gm) we want the code to model, and a

vector of wavelengths we want the code to calculate fluxes for. Our models then start

with the optical constants of astronomical silicates (Draine and Lee 1984) and use Mie

theory to calculate the absorption efficiencies (Qabs) for different sized particles and

different wavelengths. Once we know how efficiently a particle of a given size absorbs

and emits radiation, we can calculate what its temperature would be at a given distance

from the star. To do this we use the effective temperature of the star to work out the

stellar spectrum, and the luminosity of the star to work out the equilibrium temperature of




Full Text

PAGE 1

6($5&+,1* 7+( 62/$5 1(,*+%25+22' )25 352723/$1(7$5< '(%5,6 ',6.6 $ 6859(< 2) 9(*$/,.( 6285&(6 $1' $ ',6&866,21 2) 1(: ',6. (;$03/(6 %\ 52%(57 6&277 ),6+(5 $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

&RS\ULJKW E\ 5REHUW 6FRWW )LVKHU

PAGE 3

7KLV ZRUN LV GHGLFDWHG WR P\ IHOORZ LQKDELWDQWV RI DQG $

PAGE 4

$&.12:/('*0(176 ZRXOG ILUVW OLNH WR DFNQRZOHGJH P\ DGYLVRU 'U &KDUOHV 7HOHVFR IRU KLV UROH LQ WKLV ZRUN DQG IRU KLV YDOXDEOH IULHQGVKLS ,Q WKH WLPH VSDQQLQJ WKH ZRUN IRU WKLV GLVVHUWDWLRQ KDYH OHDUQHG IURP KLP LQ PDQ\ ZD\V ,Q WKH RIILFH WKH ODE RU WKH FRQWURO URRP KDYH DOZD\V HQMR\HG RXU GLVFXVVLRQV ,W VHHPV OLNH QRW VR ORQJ DJR WKDW ZH PHW IRU WKH ILUVW WLPH LQ D VPDOO RIILFH RQ WKH VHFRQG IORRU DQG WDONHG DERXW WKH LGHD RI WKLV SURMHFW 1RW ORQJ DIWHU WKDW FDPH WKH LQIDPRXV fUXQ RI PVf 7KHQ ZH ZHUH RII WR &KLOH ZKHUH ZH OHDUQHG WKDW WKH SRODU D[LV RI D WHOHVFRSH SRLQWV WR WKH 6RXWK SROH LQ WKH VRXWKHUQ KHPLVSKHUH DQG WKDW FDNH LV QRW DOZD\V ZKDW LW VHHPV :H KDG QLJKWV RI (O 1LR WKHUH DQG QLJKWV RI KLJK VWDNHV VFLHQFH 7KHQ ZH ZHQW WR .HFN DQG OHDUQHG ZKDW UHDOO\ PHDQV $W .HFN ZH ILUVW XVHG WKH XQLW fSL\f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fFKHFN WKLV RXWf KRSH WKDW VRPHKRZ FRQWULEXWHG WR WKH PDQ\ WDONV DERXW WKH 26&,5 LQWHUIDFH DQG WKH DFTXLVLWLRQ V\VWHP ZRXOG OLNH WR WKDQN .HYLQ +DQQD IRU KLV GHYHORSPHQW RI WKH 26&,5 HOHFWURQLFV V\VWHP DQG -HII -XOLDQ IRU KLV GHVLJQ DQG IDEULFDWLRQ RI FULWLFDO 26&,5 FRPSRQHQWV 2QH RI WKH ,9

PAGE 5

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

PAGE 6

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

PAGE 7

&ODVV ,OLD 7KH QHDU,5 1LQH &ODVV ,OOE =$06 6RXUFHV &ODVV ,,,F 3RVW =$06 6RXUFHV 6XUYH\ 6RXUFHV LQ WKH +5 'LDJUDP 7+( )$&(21 ',6. 2) +' 0LG,QIUDUHG 2EVHUYDWLRQV DW .HFN +' 6RXUFH 6L]H 0RGHOLQJ RI &KDUDFWHULVWLF *UDLQ 3DUDPHWHUV 0RGHO 5HVXOWV *UDLQ 6L]HV DQG 7HPSHUDWXUHV 'LVFXVVLRQ DQG &RQFOXVLRQV 'LVN 2ULHQWDWLRQ (YROXWLRQDU\ 6WDWXV &RQFOXVLRQV .(&. ,0$*,1* 2) +' 2EVHUYDWLRQV 6RXUFH 6L]H 'XVW 7HPSHUDWXUH DQG *UDLQ 6L]H &RPSDULVRQ WR 1,&026 ,PDJHV &RQFOXVLRQV $ERXW WKH 'LVN RI +' 6$2 $ 48(67,21 2) &/$66,),&$7,21 7KH 'HWHFWLRQ DQG 1RQGHWHFWLRQ RI WKH 6$2 'LVN 3UHYLRXV 2EVHUYDWLRQV 1HZ .HFN ,PDJLQJ ZLWK 26&,5 )LUVW$VFHQW *LDQW RU 0DLQ6HTXHQFH 'ZDUI" /XPLQRVLW\ &ODVV 9 $ 0DLQ6HTXHQFH 'ZDUI /LWKLXP $EXQGDQFH 3RVLWLRQ LQ WKH +5 'LDJUDP 6XPPDU\ DQG &RQFOXVLRQV ,167580(17$7,21 $&7,9,7,(6 7+( 26&,5 6<67(0 6\VWHP 2YHUYLHZ 7KH 'HZDU 2SWLFV (QWUDQFH :LQGRZ DQG )LOWHUV 'HWHFWRU 90( &UDWH &RQWURO &RPSXWHU 6XPPDU\ RI $FWLYLWLHV YLL

PAGE 8

$33(1',; 0,',5 $6752120< $ 6+257 &2856( ([WUDFWLQJ WKH 6RXUFH 6LJQDO 7KH 6WDQGDUG &KRS1RG 7HFKQLTXH /,67 2) 5()(5(1&(6 %,2*5$3+,&$/ 6.(7&+ YLLL

PAGE 9

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f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

PAGE 10

SRVLWLRQ RI JUDLQV WKDW DUH WR SP LQ GLDPHWHU LQ WKH GLVNV RI WKHVH VWDUV 7KH PLG,5 HPLWWLQJ JUDLQV RUELW WKH VWDUV DW GLVWDQFHV RI WHQV RI $8 VLPLODU WR WKH VL]H RI WKH 6RODU V\VWHP DQG WKHUHIRUH WUDFH WKH UHJLRQ RI DVVXPHG SODQHWDU\ IRUPDWLRQ LQ WKHVH GLVNV $GGLWLRQDOO\ ZH SODFH WKH VXUYH\ VWDUV LQWR WKH +5 GLDJUDP DQG XVH WKH FKDUDFWHULVWLFV RI WKHLU LQIUDUHG H[FHVV LQ FRQMXQFWLRQ ZLWK WKHLU SRVLWLRQV WR VXJJHVW D SURSRVHG HYROXWLRQDU\ VHTXHQFH IRU WKHP )LQDOO\ GLVFXVV WKH GHYHORSPHQW FKDUDFWHUL]DWLRQ DQG VXSSRUW RI WKH 26&,5 FDPHUD V\VWHP WKDW ZDV D IXQGDPHQWDO DVSHFW RI WKH ZRUN SUHVHQWHG LQ WKLV GLVVHUWDWLRQ [

PAGE 11

&+$37(5 ,1752'8&7,21 7KLV GLVVHUWDWLRQ IRFXVHV RQ WKH VWXG\ RI FLUFXPVWHOODU GLVNV DURXQG PDLQ VHTXHQFH VWDUV 7KH PRVW IXQGDPHQWDO TXHVWLRQ RQH FDQ DVN LV ZK\ LV WKH VWXG\ RI GLVNV LPSRUWDQW" 7KHUH DUH WZR IDFHWV WR WKH DQVZHU WR WKDW TXHVWLRQ 7KH ILUVW GHDOV ZLWK VWDU IRUPDWLRQ DQG WKH HYROXWLRQ RI VWHOODU REMHFWV GXULQJ WKH LQLWLDO VWDJHV RI WKHLU OLYHV &XUUHQW WKHRULHV RI VWDU IRUPDWLRQ OLNH WKDW RI $QGUH f VXJJHVW WKDW WKH IRUPDWLRQ RI D FLUFXPVWHOODU GLVN LV QHFHVVDU\ IRU WKH VXFFHVVIXO IRUPDWLRQ RI D ORZ RU LQWHUPHGLDWH PDVV 0 a 0f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f XQGHUVWDQGLQJ WKH IRUPDWLRQ DQG HYROXWLRQ RI FLUFXPVWHOODU GLVNV LV PRUH LPSRUWDQW WKDQ HYHU 7KH UHVHDUFK SUHVHQWHG LQ WKLV GLVVHUWDWLRQ UHODWHV PRUH WR WKH VHFRQG IDFHW SUHVHQWHG DERYH 2XU UHVHDUFK LV FHQWHUHG RQ WKH VWXG\ RI FLUFXPVWHOODU GLVNV DURXQG VWDUV WKDW DUH HLWKHU LQ WKH YHU\ ODVW VWDJHV RI WKHLU SUHPDLQVHTXHQFH 306f IRUPDWLRQ RU KDYH DOUHDG\ PRYHG RQWR RU SDVWf WKH ]HURDJHPDLQVHTXHQFH =$06f LQ WKH +5 GLDJUDP 7KHVH GLVNV DUH WKH VRFDOOHG f9HJDOLNHf RU GHEULV GLVNV

PAGE 12

)LJXUH 7KH VSHFWUDO HQHUJ\ GLVWULEXWLRQ 6('f RI 9HJD 6ROLG OLQH LV D PRGHO DWPRVSKHUH 'RWWHG OLQH LV D PRGLILHG EODFNERG\ ILW WR WKH GDWD ZLWK 7 DQG 4$f D $n )OX[ HVWLPDWHV IURP ,623+27 DQG ,5$6 6XEPLOOLPHWHU IOX[HV IURP =XFNHUPDQ DQG %HFNOLQ f )LJXUH IURP +HLQULFKVHQ HW DO f 7KH ,5$6 VDWHOOLWH GLVFRYHUHG WKH f9HJD SKHQRPHQRQf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f 6PLWK DQG 7HUULOH f SURYHG WKH GLVN K\SRWKHVLV ZLWK WKHLU

PAGE 13

FRURQDJUDSKLF LPDJH RI 3LFWRULV ZKLFK VKRZHG D QHDUO\ HGJHRQ GLVN rf DURXQG WKH VWDU ZLWK GLPHQVLRQV RI V RI $8 7KH SXEOLFDWLRQ RI WKLV LPDJH MXPSVWDUWHG WKH ILHOG DQG WKH VWXG\ RI 9HJDOLNH GLVNV KDV EHFRPH RQH RI WKH PRVW KHDYLO\ UHVHDUFKHG DVSHFWV LQ PRGHUQ DVWURQRP\ VLQFH WKHUH KDYH EHHQ DOPRVW SDSHUV SXEOLVKHG ZLWK WKH QDPH f%HWD 3LFWRULVf LQ WKH WLWOH 6LQFH SODQHWV DUH WKRXJKW WR IRUP LQ WKH GXVW\ HQYLURQPHQWV DURXQG VWDUV WKHUH VHHPV WR EH D JURZLQJ FRQVHQVXV WKDW WKH 9HJD SKHQRPHQRQ LV LQWLPDWHO\ FRQQHFWHG ZLWK WKH RFFXUUHQFH RI SODQHWDU\ V\VWHPV ,QGHHG ZH OLYH LQVLGH RXU RZQ 9HJDOLNH GLVN WKH VRFDOOHG =RGLDFDO fFORXGf GLVN DURXQG WKH 6XQ 0DQ\ RI WKH FKDUDFWHULVWLFV RI WKH 9HJDn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f DQG VXEVHTXHQW QHDU,5 SPf REVHUYDWLRQV FRQILUP WKDW ZDUS H[LVWV DQG VXJJHVW WKDW D SODQHW ZLWK D ar LQFOLQDWLRQ FRXOG FDXVH LW 0RXLOOHW HW DO f ,Q WKH PLG,5 WR SPf WKH GLVN RI +5 $ KDV EHHQ LPDJHG DW af UHVROXWLRQ E\ 7HOHVFR HW DO f -D\DZDUGKDQD HW DO f DQG .RHPHU HW DO f VKRZLQJ HYLGHQFH IRU DQ LQQHU KROH RI DSSUR[LPDWHO\ 6RODU V\VWHP GLPHQVLRQV 2XU PRWLYDWLRQ IRU WKLV GLVVHUWDWLRQ LV WR FKDUDFWHUL]H D QXPEHU RI WKHVH 9HJDOLNH GLVNV LQ WKH PLG,5 7R WKLV HQG ZH XVHG D PRGHUQ PLGLQIUDUHG FDPHUD V\VWHP ZLWK ODUJH

PAGE 14

DSHUWXUH WHOHVFRSHV WR FRQGXFW D VXUYH\ RI QHDUO\ 9HJDOLNH VWDUV LQ WKH PLG,5 DQG SPf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f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f ,Q IDFW &KXUFKZHOO f VKRZV WKDW WKHUH LV QR SODFH LQ WKH JDOD[\ ZKHUH DFWLYH VWDU IRUPDWLRQ LV RFFXUULQJ ZKHUH WKHUH LV QRW

PAGE 15

VLJQLILFDQW &2 HPLVVLRQ 6LQFH &2 LV D PDMRU FRQVWLWXHQW RI PROHFXODU FORXGV LW VHHPV YHU\ UHDVRQDEOH WR WKLQN WKDW VWDUV IRUP RXW RI WKH PDWHULDO LQ WKHVH *0&V 7KH HDUOLHVW VWDJH RI WKH IRUPDWLRQ RI D VWDU LV WKH IUDJPHQWDWLRQ DQG FROODSVH RI SDUW RI D *0& 7KH SDVVLQJ RI D JDODFWLF VSLUDO GHQVLW\ ZDYH RU D FORVH HQFRXQWHU ZLWK D QHDUE\ VWDU PD\ WULJJHU WKH FROODSVH :KDWHYHU WKH WULJJHU WKH SURFHVV RI VWDU IRUPDWLRQ LV XQGHUZD\ ZKHQ D IUDJPHQW RI DSSUR[LPDWHO\ $8 fEUHDNVRII IURP WKH PDLQ FORXG DQG VWDUWV LWV FROODSVH 7KH OXPLQRVLW\ DVVRFLDWHG ZLWK WKHVH fSURWRVWDUVf LV DW ILUVW GHULYHG IURP WKH JUDYLWDWLRQDO HQHUJ\ DVVRFLDWHG ZLWK WKLV FROODSVH $W VRPH SRLQW LQ WKLV SURFHVV WKHUH LV HQRXJK OXPLQRVLW\ DVVRFLDWHG ZLWK WKH SURWRVWDU WKDW LW FDQ EH REVHUYHG GLUHFWO\ :H EHJLQ RXU PRUH GHWDLOHG GLVFXVVLRQ RI VWDU IRUPDWLRQ DW WKLV SRLQW IROORZLQJ WKH ZRUN RI /DGD f DQG $QGUH HW DO f ,Q )LJXUH ZH VKRZ WKH GLIIHUHQW VWDJHV LQ WKH HYROXWLRQDU\ VHTXHQFH RI \RXQJ VWHOODU REMHFWV 2Q WKH ULJKW VLGH RI WKH ILJXUH WKHUH LV D PRGHO VSHFWUDOHQHUJ\GLVWULEXWLRQ 6('f RI WKH VRXUFH 7KH PLGGOH SDQHOV VKRZ D VNHWFK RI WKH V\VWHP DQG WKH OHIW VLGH OLVWV UHOHYDQW PDVVHV DQG WLPHVFDOHV IRU HDFK &ODVV $ &ODVV VRXUFH LV WKH HDUOLHVW REVHUYDEOH VWDJH RI VWDU IRUPDWLRQ &ODVV VRXUFHV DUH RQO\ YLVLEOH LQ WKH PLOOLPHWHU UHJLPH RU WKURXJK WKH GHWHFWLRQ RI &2 VSHFWUDOO\ 7KH GXVW VKHOOV VXUURXQGLQJ WKHVH VRXUFHV DUH VWLOO VR GHQVH WKH\ DUH RSWLFDOO\ WKLFN WR HYHQ PLG DQG IDU,5 UDGLDWLRQ %HFDXVH FROOLPDWHG &2 RXWIORZV DUH RIWHQ DVVRFLDWHG ZLWK &ODVV VRXUFHV LW LV EHOLHYHG WKDW D FHQWUDOL]HG FRUH KDV IRUPHG E\ WKLV VWDJH DQG WKDW PDWWHU IURP WKH VXUURXQGLQJ VKHOO LV DFWLYHO\ DFFUHWLQJ RQWR LW $W WKLV VWDJH WKH VKHOO LV OLNHO\ VWLOO PRUH PDVVLYH WKDQ WKH SURWRVWDU DW LWV FRUH

PAGE 16

&/$66 +RUQ RH HUU WDQ SKRWr" $JAM:9 +F}0 &/$66 /RWr DFHUU WDQ SKRVr" r }m9 0HO0 &/$66 4 RSW FRWU WKLFN GDN $JR :r\U &/$66 ,,, 2SWDR8\ WKK GLVN} $JWLO2f\U m0ArmU0M )LJXUH 6FKHPDWLF RI ORZ DQG LQWHUPHGLDWH PDVV VWDU IRUPDWLRQ E\ /DGD f DQG $QGUH HW DO f 7KH IORZ RI PDWWHU RQWR WKH SURWRVWDU FRQWLQXHV XQDEDWHG SDVW WKH WUDQVLWLRQ LQWR WKH &ODVV SKDVH ZKLFK RFFXUV RQ WLPHVFDOHV RI a \U $W WKLV SRLQW WKH IRUPDWLRQ RI WKH SURWRVWDU LV DOPRVW FRPSOHWH DQG LW LV QRZ GHWHFWDEOH WKURXJK WKH LQIUDUHG GRZQ WR SHUKDSV SP 7KHUH DUH VWLOO FROOLPDWHG RXWIORZV RI PROHFXODU JDV IRU H[DPSOH &2 DVVRFLDWHG ZLWK &ODVV REMHFWV LQGLFDWLQJ WKDW WKH LQQHU UHJLRQV RI WKH VKHOO DUH VWLOO EHLQJ

PAGE 17

DFFUHWHG RQWR WKH SURWRVWDU 7KH DPRXQW RI PDWHULDO DURXQG WKH VWDU LV VWLOO ODUJH XSZDUGV RI 0# &ODVV REMHFWV DUH DOVR QRUPDOO\ DVVRFLDWHG ZLWK H[WHQGHG PLOOLPHWHU FRQWLQXXP HPLVVLRQ 6RPH IRUP RI GLVN KDV OLNHO\ IRUPHG DURXQG WKH SURWRVWDU DW WKLV VWDJH %\ WKH WLPH WKH V\VWHP EHFRPHV D &ODVV ,, VRXUFH WKH PLOOLPHWHU FRQWLQXXP KDV EHFRPH PXFK PRUH FRPSDFW DQG WKHUH LV UDUHO\ DQ\ HYLGHQFH IRU RXWIORZV DVVRFLDWHG ZLWK WKH VRXUFH 7KH DJH RI WKH V\VWHP LV QRZ a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

PAGE 18

(YROXWLRQDU\ 6WDWXV RI 9HJDOLNH 'LVNV $V VHHQ LQ WKH ODVW VHFWLRQ WKH 9HJDOLNH VRXUFHV PRVW UHVHPEOH VWDUV LQ WKH ODVW VWDJHV RI VWDU IRUPDWLRQ 7R PRUH FOHDUO\ GHILQH ZKDW D f9HJDOLNHf V\VWHP LV ZH XVH WKH GHILQLWLRQ VXJJHVWHG E\ /DJUDQJH HW DO f ,Q WKHLU UHYLHZ WKH\ VXJJHVW WKH IROORZLQJ FULWHULD IRU GHILQLQJ D 9HJDOLNH V\VWHP f /MXVW/r f 0GXVWJDVf m 0T f 'XVW G\QDPLFV QRW FRQWUROOHG E\ JDV 0JDV m 0G86W f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f 7KHUH LV DOVR VRPH LVVXH ZLWK WKH QDPH fPDLQVHTXHQFHf EHLQJ DQ LQWHJUDO SDUW RI WKH GHILQLWLRQ RI D 9HJDOLNH V\VWHP 7KH GHILQLWLRQ RI /DJUDQJH HW DO f DERYH GHILQHV WKH FODVV LQ WHUPV RI WKH SK\VLFDO VWDWH RI WKH FLUFXPVWHOODU PDWWHU QRW WKH H[DFW HYROXWLRQDU\ VWDWH RI WKH FHQWUDO VWDU 7KH VWDU LWVHOI PD\ RU PD\ QRW KDYH UHDFKHG WKH

PAGE 19

7DEOH 5HVROYHG 9HJDOLNH 'LVNV 6RXUFH 1DPH 'SFf 6SHFWUDO 7\SH $JH \Uf 'LVN 5DGLXV DW *LYHQ :DYHOHQJWK $8f SP SP SP SP SP H(UL .9 f[O f§ f§ f§ f§ D 3V$ $9 O[O D /\U $9 [O S 3LFWRULV $9 [ +5 $ $9 sf[O r +' %9 O[O2 r +' $9 f[O r %&r LU f§ %9 26&,5 HVWLPDWH VHH 7HOHVFR HW DO f PDLQ VHTXHQFH E\ WKH WLPH LWV GLVN PHHWV WKH DERYH FULWHULD 7KLV LV UHOHYDQW WR WKLV GLVVHUWDWLRQ VLQFH ZH KDYH LQYHVWLJDWHG D QXPEHU RI VWDUV WKDW VHHP WR EH WUDQVLWLRQLQJ IURP &ODVV ,, WR &ODVV ,,, :KLOH WKH VWDUV PD\ QRW \HW KDYH UHDFKHG WKH =$06 WKH\ FOHDUO\ H[KLELW FKDUDFWHULVWLFV UHPLQLVFHQW RI PDLQVHTXHQFH VWDUV /DJUDQJH HW DO f FRLQHG WKH WHUP fROG SUHPDLQVHTXHQFHf VWDUV 2306f WR GHVFULEH WKHVH VRXUFHV 7KH\ DUH DQ LQWHUHVWLQJ FODVV RI REMHFW VLQFH WKH\ UHSUHVHQW WKH WUDQVLWLRQ EHWZHHQ WKH SUHPDLQ VHTXHQFH VWDUV RI WKH VWDU IRUPLQJ UHJLRQV DQG WKH PDLQVHTXHQFH VWDUV LQ WKH VRODU QHLJKERUKRRG %HFDXVH WKH 9HJDOLNH GLVNV DUH RSWLFDOO\ WKLQ WHQXRXV VWUXFWXUHV WKH\ DUH YHU\ GLIILFXOW WR GHWHFW ,Q WKH \HDUV VLQFH 6PLWK DQG 7HUULOH f SXEOLVKHG WKHLU ZDWHUVKHG LPDJH RI 3 3LFWRULV RQO\ VHYHQ RWKHU 9HJDOLNH GLVNV KDYH EHHQ GLUHFWO\ LPDJHG ,Q 7DEOH ZH OLVW WKH 9HJDOLNH GLVNV WKDW KDYH EHHQ UHVROYHG DW DQ\ ZDYHOHQJWK 7KLV LV KRZHYHU UDSLGO\ FKDQJLQJ 1HZ LQVWUXPHQWV FRXSOHG ZLWK ODUJH DSHUWXUH WHOHVFRSHV DUH JLYLQJ XV WKH RSSRUWXQLW\ WR GHWHFW PRUH RI WKHVH GLVNV WKDQ HYHU EHIRUH 7KLV LV PDGH HYLGHQW E\ WKH IDFW WKDW RI WKH VL]H HVWLPDWHV LQ 7DEOH KDYH

PAGE 20

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f YHU\ FORVH WR $8f WR WKH VWDUV HJ +' &KDSWHU f 2WKHUV OLNH +' :HLQEHUJHU HW DO f DQG 3 3LFWRULV .DODV t -HZLWW f DUH DVVRFLDWHG ZLWK QHDU,5 UDGLDWLRQ WKDW LV VFDWWHUHG IURP WKH GXVW LQ WKHLU GLVNV 7KLV VFDWWHUHG UDGLDWLRQ LV VHHQ RXW WR KXQGUHGV RI $8 LQ WKHVH WZR FDVHV DQG LV OLNHO\ EHLQJ VFDWWHUHG RII WKH GXVW JUDLQV WKDW DUH UHVSRQVLEOH IRU WKH IDU,5VXEPPPP HPLVVLRQ GHWHFWHG DURXQG WKHVH V\VWHPV 7KH PLG,5 IRUPV D EULGJH EHWZHHQ WKHVH WZR UHJLPHV ,W FDQ EH VDLG WKDW WKH ORQJ ZDYHOHQJWK HPLVVLRQ FRPHV IURP WKH f.XSLHU EHOWVf DQG SHUKDSV f2RUW FORXGVf RI WKH 9HJDOLNH VRXUFHV ZKLOH WKH QHDU,5 HPLVVLRQ FRPHV

PAGE 21

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f LPDJLQJ RI D ODUJH VDPSOH RI 9HJDOLNH VWDUV :H XQGHUWRRN WKLV SURMHFW ZLWK WKH KRSLQJ WR FKDUDFWHUL]H D QXPEHU RI GLVNV DW WKHVH ZDYHOHQJWKV DQG ZH VXFFHHGHG E\ PDNLQJ WKH ILUVW GHWHFWLRQ RI H[WHQGHG PLG,5 HPLVVLRQ DURXQG WZR VWDUV +' DQG +' :H GLG QRW GHWHFW DQ\ H[WHQVLRQ DURXQG WKH UHPDLQGHU RI WKH VXUYH\ VDPSOH ,Q &KDSWHU ZH GLVFXVV RXU VDPSOH RXU REVHUYDWLRQV RI WKH VXUYH\ VRXUFHV DQG WKH GDWD UHGXFWLRQ VWHSV ZH XVHG &KDSWHU SUHVHQWV RXU FRQFOXVLRQV DERXW WKH VXUYH\ DV D ZKROH DQG ZH SODFH RXU VDPSOH VRXUFHV LQWR ZKDW PD\ EH DQ HYROXWLRQDU\ VHTXHQFH ,Q &KDSWHU ZH GLVFXVV WKH QHZO\ GLVFRYHUHG GLVN DURXQG WKH VWDU +' DQG LQYHVWLJDWH WKH SURSHUWLHV RI WKH GXVW LQ WKDW GLVN WKURXJK UDGLDWLYH HTXLOLEULXP PRGHOV :H SUHVHQW VLPLODU UHVXOWV IRU +' LQ &KDSWHU )RU +' ZH GHULYH JUDLQ VL]H HVWLPDWHV IRU WKH PLG,5HPLWWLQJ JUDLQV DQG FRPSDUH RXU PLG,5 LPDJHV RI WKLV GLVN WR QHDU,5 LPDJHV IURP +67 ,Q &KDSWHU ZH SUHVHQW REVHUYDWLRQV WKDW fGHfUHVROYH WKH VRXUFH 6$2 D VWDU SUHYLRXVO\ WKRXJKW WR EH DVVRFLDWHG ZLWK D 9HJDOLNH GLVN :H VKRZ WKDW LW LV OLNHO\ WKDW 6$2 LV D OXPLQRVLW\ &ODVV ,,, VWDU DQG QRW RQ WKH

PAGE 22

PDLQ VHTXHQFH &KDSWHU GLVFXVVHV WKH 26&,5 LQVWUXPHQW DQG LWV UROH LQ WKLV GLVVHUWDWLRQ :H FORVH ZLWK DQ $SSHQGL[ RQ PLG,5 REVHUYLQJ DQG GLVFXVV WKH VSHFLDOL]HG WHFKQLTXHV XVHG LQ WKDW ZDYHOHQJWK UHJLPH

PAGE 23

&+$37(5 2%6(59$7,216 $1' '$7$ 5('8&7,21 :H KDYH XVHG IURQWOLQH LQIUDUHG LQVWUXPHQWDWLRQ DQG ODUJH DSHUWXUH WHOHVFRSHV WR VXUYH\ DSSUR[LPDWHO\ 9HJDOLNH VRXUFHV LQ WKH QRUWKHUQ DQG VRXWKHUQ VN\ 0RVW RI WKH VXUYH\ ZDV FRQGXFWHG DW WKH %ODQFR PHWHU WHOHVFRSH DW WKH &HUUR 7ROROR ,QWHU$PHULFDQ 2EVHUYDWRU\ &7,2f 3DUWV RI WKH VXUYH\ ZHUH DOVR FRQGXFWHG DW WKH 1$6$ ,QIUDUHG 7HOHVFRSH )DFLOLW\ ,57)f DQG WKH : 0 .HFN 2EVHUYDWRU\ .HFNf 7KH SURMHFW FHQWHUHG RQ LPDJLQJ HDFK RI WKH VXUYH\ VRXUFHV DW DQG SP XVLQJ WKH 2EVHUYDWRU\ 6SHFWURPHWHU DQG &DPHUD IRU WKH ,QIUDUHG 26&,5f 7KH 26&,5 V\VWHP LV GLVFXVVHG LQ GHWDLO LQ &KDSWHU )RU PRVW RI WKH VRXUFHV RXU LPDJHV DUH WKH ILUVW PLG,5 REVHUYDWLRQV RI WKHP VLQFH WKRVH RI WKH ,5$6 VDWHOOLWH $ OLWHUDWXUH VHDUFK IRU RWKHU PLG,5 REVHUYDWLRQV RI RXU VXUYH\ VRXUFHV UHWXUQHG RQO\ WZR IXUWKHU VWXGLHV )DMDUGR$FRVWD 7HOHVFR DQG .QDFNH f LPDJHG ILYH RI WKH VRXUFHV DW af UHVROXWLRQ DQG 6\OYHVWHU HW DO f SUHVHQWHG PLG,5 VSHFWUD RI D GR]HQ RI WKH VRXUFHV RQ RXU OLVW $ VPDOO QXPEHU RI RXU VRXUFHV KDYH TXHVWLRQDEOH FODVVLILFDWLRQ DQG KDYH EHHQ LQFOXGHG LQ VWXGLHV RI +HUELJ $H%H VWDUV DOVR ,Q SDUWLFXODU WKH VWXGLHV RI YDQ GHQ $QFNHU HW DO f DQG YDQ GHQ $QFNHU f FRQWDLQ PHPEHUV RI RXU VDPSOH $OWKRXJK WKH VWDUV LQ RXU VXUYH\ KDYH EHHQ VWXGLHG LQ RWKHU ZDYHOHQJWK UHJLPHV RXU PLG,5 LPDJLQJ KHUH UHSUHVHQWV WKH KLJKHVW UHVROXWLRQ PDSSLQJ RI WKHVH VRXUFHV WR GDWH 2XU REVHUYDWLRQV W\SLFDOO\ KDYH VXE DUFVHFRQG UHVROXWLRQ OLPLWV ZLWK VRPH DV ORZ DV f $W WKH DYHUDJH GLVWDQFH RI RXU VXUYH\ VWDUV SFf DW WKHVH UHVROXWLRQV ZH DUH WUDFLQJ HPLVVLRQ IURP GXVW WKDW LV WHQV RI $8V IURP WKH VWDU D UHJLRQ ZKHUH SODQHWDU\ V\VWHPV DUH ERP DQG HYROYH :H FDQQRW \HW

PAGE 24

GLUHFWO\ GHWHFW DQ\ SODQHWV DURXQG WKHVH VWDUV +RZHYHU ZH FDQ GHWHFW WKH HIIHFWV RI KLGGHQ SODQHWV RQ WKH GLVNV WKH\ LQKDELW $Q H[DPSOH RI WKLV LGHD LV WKH LQQHU KROHV SUHGLFWHG E\ WKH 6('V RI VRPH RI WKH VRXUFHV $Q LQQHU KROH ZLWK D GLDPHWHU RI DSSUR[LPDWHO\ $8 ZDV SUHGLFWHG LQ WKH GLVN RI +5 $ E\ -XUD HW DO f DQG ZDV WKHQ GLUHFWO\ LPDJHG E\ -D\DZDUGKDQD HW DO f .RHPHU HW DO f DQG 7HOHVFR HW DO f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f >KHUHDIWHU ::@ 2QH RI WKH ILUVW VHDUFKHV RI WKH ,5$6 GDWDEDVH DIWHU WKH GLVFRYHU\ RI WKH IRXU DUFKHW\SHV :: LV RQH RI WKH SULPDU\ OLVWV RI 9HJDOLNH VRXUFHV XVHG WRGD\ :: SUHVHQW D OLVW RI VRXUFHV WKDW KDYH FKDUDFWHULVWLFV VLPLODU WR 9HJD DQG WKH RWKHU DUFKHW\SHV 7KHLU VHOHFWLRQ FULWHULD DUH VKRZQ EHORZ 6RXUFHV PXVW EH DVVRFLDWHG ZLWK EULJKW YLVXDO VRXUFHV 6$2 VWDUVf EXW QRW ZLWK D ZHOONQRZQ HPLVVLRQOLQH VWDU 6RXUFHV PXVW KDYH D SP SP IOX[ GHQVLW\ UDWLR VLPLODU WR WKDW RI WKH SURWRW\SHV 7KH UDQJH RI WKH DFFHSWHG UDWLRV FRUUHVSRQGV WR EODFN ERG\ WHPSHUDWXUHV RI WKH GXVW IURP WR 6RXUFHV PXVW VKRZ HYLGHQFH IRU H[WHQVLRQ LQ RQH RI PRUH RI WKH ,5$6 EDQGV LQ WKH ,5$6 :RUNLQJ 6XUYH\ 'DWDEDVH

PAGE 25

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f :: FDOFXODWHG WHPSHUDWXUHV IRU WKH GXVW XVLQJ WKH ,5$6 DQG SP IOX[HV WR ILW WKH GXVW HPLVVLRQ ZLWK D EODFNERG\ FXUYH %\ XVLQJ SXEOLVKHG % DQG 9 PDJQLWXGHV WR PRGHO WKH SKRWRVSKHUH :: SORWWHG WKH 6('V RI WKH VRXUFHV 7KHLU SORWV JLYH XV D ILUVW ORRN DW WKH DPRXQW RI H[FHVV DVVRFLDWHG ZLWK HDFK VRXUFH DQG ZH XVHG WKHP WR KHOS SULRULWL]H WKH VHTXHQFH LQ ZKLFK ZH REVHUYHG WKH VWDUV 2XU VHFRQGDU\ OLVWV DUH WKRVH RI 6\OYHVWHU HW DO f DQG 0DQQLQJV DQG %DUORZ f 7KH 6\OYHVWHU HW DO f OLVW ZDV SDUWLFXODUO\ XVHIXO VLQFH WKHLU VHOHFWLRQ SURFHVV ZDV VLPLODU WR ZKDW ZH KDG LQ PLQG IRU WKLV SURMHFW 7KH\ LQFOXGHG REMHFWV RQ WKHLU OLVW WKDW PD[LPL]HG WKHLU FKDQFHV RI GHWHUPLQLQJ GLVN DQG JUDLQ SDUDPHWHUV 7KHLU VRXUFHV DUH WKHUHIRUH EULJKW LQ WKH LQIUDUHG UHODWLYHO\ FORVH WR WKH 6XQ DQG KDYH ODUJH ,5 H[FHVVHV DVVRFLDWHG ZLWK WKHP 7KHLU OLVW FRQWDLQV D WRWDO RI VRXUFHV RI ZKLFK ZH REVHUYHG GXULQJ RXU VXUYH\ 7KH 6\OYHVWHU HW DO f OLVW GRHV KDYH VRPH RYHUODS ZLWK WKH :: OLVW ZLWK D WRWDO RI VWDUV FRPPRQ WR ERWK $ XVHIXO IDFHW RI WKH 6\OYHVWHU HW DO f UHVHDUFK LV WKDW WKH\ SUHVHQWHG PLG,5 VSHFWUD IRU RI WKHLU VRXUFHV WDNHQ ZLWK &*6 RQ 8.,57 :H XVHG WKHVH VSHFWUD WR KHOS SULRULWL]H RXU REVHUYDWLRQV DQG WR FRPSDUH WR RXU UHVXOWV RQ WKH GLVNV RI +' &KDSWHU f DQG +' &KDSWHU

PAGE 26

f 7KH EHWWHU GHILQHG 6('V RI WKH VWDUGLVN V\VWHPV LQ 6\OYHVWHU HW DO f ZHUH DOVR YHU\ XVHIXO LQ RXU VRXUFH VHOHFWLRQ 7KH WKLUG OLVW ZH XVHG WR VHOHFW RXU VXUYH\ VWDUV IURP LV WKDW RI 0DQQLQJV t %DUORZ f 7KHLU PHWKRG RI VRXUFH LGHQWLILFDWLRQ ZDV EDVHG RQ WKH FURVVFRUUHODWLRQ RI WKH 0LFKLJDQ &DWDORJ RI 7ZR'LPHQVLRQDO 6SHFWUDO 7\SHV ZLWK WKH ,5$6 )DLQW 6RXUFH 6XUYH\ &DWDORJ 7KH 0DQQLQJV DQG %DUORZ OLVW FRQWDLQV VRPH QHZ 9HJDOLNH VRXUFHV QRW FRQWDLQHG RQ HLWKHU WKH 6\OYHVWHU HW DO f RU :: OLVW 2XU SULPDU\ XVH RI WKH 0DQQLQJV DQG %DUORZ VDPSOH ZDV WR VHDUFK IRU 9HJDOLNH VWDUV DW 6RXWKHUQ GHFOLQDWLRQV ,Q WKH GHFDGH EHWZHHQ WKH SXEOLFDWLRQ RI WKH :DONHU DQG :ROVWHQFURIW f SDSHU DQG WKH 0DQQLQJV DQG %DUORZ f OLVW VLJQLILFDQW ZRUN ZDV GRQH RQ WKH VSHFWUDO FODVVLILFDWLRQ RI WKH 9HJDOLNH VWDUV ,Q VRPH RI WKH VRXUFHV RQ WKH :: OLVW DUH OLVWHG DV OXPLQRVLW\ &ODVV ,,, RU ,9 DQG D IHZ KDG QR OXPLQRVLW\ FODVVLILFDWLRQ DW DOO 0DQQLQJV DQG %DUORZ f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

PAGE 27

7KH VRXUFHV ZH REVHUYHG IRU RXU VXUYH\ DUH OLVWHG LQ 7DEOH ,Q WRWDO ZH REVHUYHG VRXUFHV DW ERWK DQG _LP 7KUHH RWKHU VRXUFHV ZHUH RQO\ REVHUYHG LQ RQH ILOWHU EHFDXVH RI SRRU REVHUYLQJ FRQGLWLRQV ,Q 7DEOH ZH SUHVHQW ZKLFK OLVW WKH REMHFWV FDPH IURP DQG VHH WKDW LQ WRWDO ZH REVHUYHG VRXUFHV IURP :DONHU DQG :ROVWHQFURIW f XQLTXH VRXUFHV IURP 6\OYHVWHU HW DO f DQG VRXUFHV IURP 0DQQLQJV DQG %DUORZ 2QH VWDU XVHG DV SDUW RI WKH VXUYH\ +5 $ +' f ZDV QRW SUHVHQW RQ DQ\ RI RXU VRXUFH OLVWV :H DOVR OLVW WKH HTXDWRULDO FRRUGLQDWHV -f DQG GLVWDQFH WR HDFK VRXUFH DV OLVWHG LQ WKH +LSSDUFRV GDWDEDVH 2QO\ RI RXU VDPSOH VWDUV GR QRW KDYH D +LSSDUFRV PHDVXUHG SDUDOOD[ DQG WKHUHIRUH GLVWDQFH 9DOXHV RI %9f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f GHWHFWRU IURP 5RFNZHOO%RHLQJ &KDSWHU PRUH IXOO\ GLVFXVVHV WKH UROH RI 26&,5 LQ WKLV GLVVHUWDWLRQ $V QRWHG SUHYLRXVO\ ZH FROOHFWHG GDWD IRU WKLV UHVHDUFK RQ WKH ,57) &7,2 P DQG .HFN ,, WHOHVFRSHV %HFDXVH RI WKH GLIIHUHQW DSHUWXUHV RI WKH WHOHVFRSHV VRPH LPSRUWDQW FKDUDFWHULVWLFV RI 26&,5 FKDQJHG DV ZH PRYHG IURP VLWH WR VLWH 7DEOH OLVWV WKH SDUDPHWHUV DQG WKHLU YDOXHV RQ HDFK WHOHVFRSH 7KH VXUYH\ ZDV FRQGXFWHG XVLQJ WKH VWDQGDUG fFKRSQRGf WHFKQLTXH ZLWK FKRS IUHTXHQFLHV RI D IHZ +] DQG FKRS WKURZV LQ WKH UDQJH RI f WR f $SSHQGL[ $

PAGE 28

7DEOH 6XUYH\ VRXUFH GDWD 6RXUFH 1DPH 6SHFWUDO &ODVV 'LVWDQFH SFfD 5$D f '(& f 0Y %9fD 5HI +' ),9 :: +' $,9 :: +' $9 :: +' %9 6\O +' $9 0% +' ),9 :: +' .9 :: +' )9 :: +' $9 6\O +' *2 :: +' $9 :: +' $9 0% +' $9 :: +' %,9 6\O +' $9 :: +' .9 :: +' ), :: +' $9 :: +' $ :: +' $9 f§ +' *9 r 6\O +' $9 :: +' $9 r 6\O +' )9 :: +' %9 :: +' %9 0% +' $9 r 6\O +' :: +' $9 6\O +' )9 :: +' $9 6\O +' $O 9 0% +' $9 r :: +' $9 :: +' $ r :: +' *29 :: +' $9 :: +' $9 6\O +' r f§ f§ :: 7 6SHFWUDO FODVVLILFDWLRQV IURP 0DQQLQJV t %DUORZ f 'DWD WDNHQ GLUHFWO\ IURP WKH +LSSDUFRV DQGRU 7\FKR FDWDORJV r $PELJXRXV GLVWDQFH DQG DEVROXWH PDJQLWXGH VHH &KDSWHU r 'LVWDQFH IURP :DONHU t :ROVWHQFURIW f RU 6\OYHVWHU HW DO f

PAGE 29

7DEOH 26&,57HOHVFRSH &KDUDFWHULVWLFV 7HOHVFRSH $SHUWXUH Pf )RFDO 5DWLR 26&,5 3ODWHVFDOH DUFVHFf 26&,5 )LHOG RI 9LHZ DUFVHFf &KRS 7KURZ DUFVHFf &KRS )UHT +]f ,57) ) &7,2 ) .HFN ) JLYHV D WKRURXJK H[SODQDWLRQ RI WKHVH VWDQGDUG PLG,5 REVHUYLQJ WHFKQLTXHV DQG PRUH IXOO\ GHVFULEHV ZK\ WKHVH REVHUYDWLRQDO SDUDPHWHUV ZHUH FKRVHQ 'XULQJ WKH SODQQLQJ VWDJHV RI WKH VXUYH\ ZH GHFLGHG WR REVHUYH DOO RI WKH VRXUFHV LQ D FRQVLVWHQW PDQQHU ZLWK IROORZXS REVHUYDWLRQV PDGH ZKHQ ZDUUDQWHG )RU WKH VXUYH\ REVHUYDWLRQV ZH PDGH GHHS 1 ;R SP $; SPf DQG ,+: ;R SP $; SPf LQWHJUDWLRQV ZLWK H[SRVXUH WLPHV UDQJLQJ IURP WR PLQXWHV RI FKRSSHGLQWHJUDWLRQ WR PLQXWHV RQVRXUFHf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

PAGE 30

2EVHUYDWLRQDO 6WUDWHJ\ 2EVHUYDWLRQV IRU WKLV ZRUN ZHUH PDGH RYHU D SHULRG RI WKUHH \HDUV DW WKH DERYH PHQWLRQHG WHOHVFRSHV :H IROORZHG D VHW REVHUYLQJ VWUDWHJ\ IRU HDFK RI WKH REVHUYDWLRQV PDGH :KHQ REVHUYLQJ D VFLHQFH VRXUFH ZH DOVR PDGH D VHULHV RI REVHUYDWLRQV LQ VXSSRUW RI WKH DFWXDO GDWD RQ WKH 9HJDOLNH VRXUFH LWVHOI 7KH VHTXHQFH RI REVHUYDWLRQV PDGH LV DV IROORZV 2EVHUYDWLRQ RI SKRWRPHWULF IOX[ FDOLEUDWRU 2EVHUYDWLRQ RI D QHDUE\ SRLQWVSUHDGIXQFWLRQ 36)f VWDU 2EVHUYDWLRQ RI WKH VFLHQFH VRXUFH 2EVHUYDWLRQ RI WKH 36) VWDU 7KHUH ZDV QRUPDOO\ QR QHHG WR REVHUYH D fSRLQWLQJf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r RI WKH VFLHQFH REMHFW ,Q VRPH FDVHV WKH 36) VWDUV ZHUH XS WR r DZD\ 2XU

PAGE 31

FKRSSHG LQWHJUDWLRQ WLPHV IRU WKH 36) VWDUV ZHUH WR PLQXWHV WR PLQXWHV RQ VRXUFHf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

PAGE 32

1RUPDOL]HG )OX[ 2IIVHW DUFVHFRQGVf 2IIVHW DUFVHFRQGVf )LJXUH 1LJKWO\ YDULDWLRQ RI WKH SRLQWVSUHDGIXQFWLRQ 36)f DW SP OHIWf DQG SP ULJKWf 3ORWWHG DUH VFDQV WKURXJK WKH ILYH 36) PHDVXUHPHQWV DW SP DQG WKH WKUHH PHDVXUHPHQWV DW SP RQ WKH QLJKW RI 0D\ ZLWK 26&,5 RQ .HFN ,, 7KH HDUOLHVW PHDVXUHPHQWV RI WKH QLJKW DUH WKH QDUURZHVW ODWHU PHDVXUHPHQWV ZHUH SURJUHVVLYHO\ EURDGHU E\ f DW SP DQG f DW SP 6LPLODU DQDO\VLV GRQH IRU RWKHU QLJKWV VKRZ WKDW WKHVH YDOXHV DUH VOLJKWO\ KLJKHU WKDQ QRUPDO )RU PRVW QLJKWV WKH ):+0 RI WKH 36) ZDV VWDEOH WR ZLWKLQ f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

PAGE 33

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f %ULHIO\ WKH 26&,5 GHWHFWRU LV UHDGRXW DSSUR[LPDWHO\ HYHU\ PV GXULQJ QRUPDO REVHUYDWLRQV 7KH GDWD IURP WKH UHDGRXWV LV VDYHG LQ EXIIHUV LQ D 90( FRQWURO FUDWH RQ WKH EDFN RI WKH WHOHVFRSH 2QFH HYHU\ VHFRQGV WKH EXIIHUV DUH VHQW GRZQ D ILEHU RSWLF FDEOH FRQQHFWLQJ WKH 90( FUDWH DQG WKH FRQWURO FRPSXWHU 2QFH WKH GDWD LV VHQW WR WKH FRQWURO FRPSXWHU LW LV ZULWWHQ WR GLVN LQ RQH RI WKHVH G ),76 ILOHV 7KH DGYDQWDJH RI WKLV LV WKDW WKH REVHUYHU KDV DFFHVV WR WKH HQWLUH GDWD VWUHDP RI WKH REVHUYDWLRQ DIWHU WKH IDFW :KLOH WKLV SURGXFHV GDWD ILOHV LQ WKH WR 0% UDQJH KDYLQJ DFFHVV WR WKH GDWD LQ VHFRQG TXDQWD LV DQ LQYDOXDEOH DVVHW GXULQJ WKH GDWD UHGXFWLRQ $OO RI WKH GDWD UHGXFWLRQ IRU WKLV GLVVHUWDWLRQ ZDV GRQH LQ ,'/ XVLQJ WKH fIWRROVf WR DFFHVV WKH 26&,5 G ),76 ILOHV DQG WKH fZWRROVf WR UHGXFH WKH GDWD LQ D *8, HQYLURQPHQW 5HPRYDO RI &RQWDPLQDWHG 'DWD 2QH RI WKH DGYDQWDJHV RI KDYLQJ DFFHVV WR WKH HQWLUH GDWD VWUHDP LV HYLGHQFHG LQ WKH YHU\ ILUVW VWHS RI DQ\ 26&,5 GDWD UHGXFWLRQ WKH UHPRYDO RI FRQWDPLQDWHG GDWD VHWV 7KH DGYDQWDJH LV WKDW ZH FDQ UHPRYH GDWD LQ VHFRQG LQFUHPHQWV ZLWKRXW FKDQJLQJ WKH RYHUDOO TXDOLW\ RI WKH GDWD DV D ZKROH 7KH PDLQ UHDVRQ WKDW SRUWLRQV RI WKH GDWD VWUHDP PXVW EH UHPRYHG LV GXH WR IOXFWXDWLRQV LQ WKH EDFNJURXQG $V H[SODLQHG LQ $SSHQGL[ $

PAGE 34

G VDR BLWV 1%DQGf %DFNJURXQG )LJXUH %DFNJURXQG DW SP GXULQJ DQ REVHUYDWLRQ RI +' DW .HFN ,, +HUH ZH SORW bZHOO D PHDVXUH RI KRZ FORVH WR VDWXUDWLRQ WKH 26&,5 GHWHFWRU LVf YV IUDPH QXPEHU IRU DQ REVHUYDWLRQ RI +' DW .HFN ,, 'XULQJ WKH UHGXFWLRQ SURFHVV IUDPH QXPEHUV WR ZHUH UHPRYHG GXH WR WKH ODUJH EDFNJURXQG FKDQJH DFFXUDWH UHPRYDO RI WKH EDFNJURXQG LV SDUDPRXQW LQ PLG,5 REVHUYDWLRQV 8VLQJ WKH URXWLQH fIEVWDI ZH SURGXFHG SORWV IRU HDFK VXUYH\ VWDU REVHUYDWLRQ OLNH WKH RQH VKRZQ LQ )LJXUH DERYH ,Q WKLV ILJXUH ZH SORW fbZHOI DV D IXQFWLRQ RI IUDPH QXPEHU IRU DQ REVHUYDWLRQ RI WKH VFLHQFH VRXUFH +' DW .HFN ,, 7KH TXDQWLW\ fbZHOI LV D PHDVXUH RI WKH EDFNJURXQG VHHQ E\ WKH 26&,5 GHWHFWRU GXULQJ HDFK RI LWV a PV LQWHJUDWLRQV ([SHULHQFH KDV VKRZQ WKDW DQ DFFHSWDEOH EDFNJURXQG YDULDWLRQ LV b FKDQJH LQ fbZHOO? ,Q WKLV FDVH ZH WKHUHIRUH UHPRYH WKH IUDPHV EHWZHHQ QXPEHU WR EHFDXVH RI WKH ODUJH FKDQJH LQ ZHOO GXULQJ WKRVH UHDGRXWV 7KLV ODUJH FKDQJH LQ fbZHOI ZDV PRVW OLNHO\ GXH WR D IDLQW EDQG RI FLUUXV FORXGV PRYLQJ WKURXJK WKH ILHOG RI

PAGE 35

YLHZ RI 26&,5 2QFH DQ\ FRQWDPLQDWHG IUDPHV DUH UHPRYHG IURP WKH GDWD ZH PRYH RQWR WKH QH[W VWHS RI WKH UHGXFWLRQ ZKLFK LV WKH FUHDWLRQ RI D VLQJOH LPDJH IURP WKH LQGLYLGXDO IUDPHV LQ WKH G ),76 )GH &URVV&RUUHODWLRQ RI ,PDJHV 2QFH DQ\ FRQWDPLQDWHG IUDPHV DUH UHPRYHG IURP WKH GDWD ZH KDYH D VHULHV RI VR FDOOHG fVLJf IUDPHV WR ZRUN ZLWK 7KHVH DUH WKH ILQDO SURGXFWV RI D FRPSOHWH QRGF\FOH D VLQJOH [ LPDJH WKDW KDV WKH EDFNJURXQG IURP WKH VN\ DQG WHOHVFRSH IXOO\ UHPRYHG )RU RXU VXUYH\ PRGH REVHUYDWLRQV ZH W\SLFDOO\ KDG WR RI WKHVH fVLJf IUDPHV WR ZRUN ZLWK IRU HDFK ILOWHU )RU VRXUFHV WKDW DUH QRW EULJKW HQRXJK WR EH VHHQ LQ HDFK LQGLYLGXDO fVLJf IUDPH ZH SHUIRUPHG ZKDW LV FDOOHG D fVWUDLJKWVWDFNf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

PAGE 36

WKH ILQDO LPDJH IURP D G ),76 ILOH PD\ KDYH D QRQ]HUR PHDQ VN\ 7R FRUUHFW IRU WKLV ZH XVH WKH VN\ILW URXWLQH ZULWWHQ E\ 'UV -LP 'H %XL]HU DQG 5REHUW 3LD 7KLV URXWLQH DOORZV \RX WR PDVN DQ\ SRUWLRQ RI WKH DUUD\ IRU H[DPSOH DURXQG \RXU VRXUFH DQG WKHQ LW ILWV WKH UHPDLQLQJ XQPDVNHG EDFNJURXQG ZLWK D GLPHQVLRQDO SRO\QRPLDO VXUIDFH RI VSHFLILHG RUGHU W\SLFDOO\ WR fIODWWHQf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f 7KH IOX[ GHQVLWLHV IRU WKHVH VWDUV ZHUH FDOFXODWHG E\ LQWHJUDWLQJ WKH PRGHOV IRU WKH VWDU WKURXJK WKH SDVVEDQG RI WKH 26&,5 ILOWHUV :H XVHG WKH IROORZLQJ UHODWLRQ WR FDOFXODWH WKH EDQGSDVV DYHUDJHG IOX[ GHQVLW\ VWDQGDUG VWDU IOX[ GHQVLW\ )? U. )Y: a n7ILOWHUAfn7DWUDQAff G$ $ )MO -;? U; n7ILOWHU$ff7DWUDQ$ff G$ ; -[? ZKHUH 7I_WHU DQG 7DWUDQ DUH WKH WUDQVPLVVLRQ FXUYHV RI WKH 26&,5 ILOWHU DQG WKH DWPRVSKHUH UHVSHFWLYHO\ $O DQG $ DUH WKH ZDYHOHQJWKV ZKHUH WKH WUDQVPLVVLRQ RI WKH ILOWHU GURSV WR ]HUR DQG F LV WKH VSHHG RI OLJKW 2Q DYHUDJH ZH REVHUYHG VWDQGDUGV DW ERWK DQG SP

PAGE 37

RU WLPHV SHU QLJKW GXULQJ WKH VXUYH\ REVHUYDWLRQV (DFK RI WKHVH GDWD ZDV UHGXFHG DQG D FDOLEUDWLRQ fFDOff YDOXH WKDW FRQYHUWV WKH LQVWUXPHQWDO XQLWV RI $'8VHF LQWR WKH SK\VLFDO XQLWV RI P-\ ZDV FDOFXODWHG 7KH fFDOf YDOXH ZDV WKHQ DSSOLHG WR WKH UHGXFHG VFLHQFH GDWD WR FUHDWH PDSV LQ P-\SL[HO :H FRPPHQW KHUH RQ WKH XQFHUWDLQWLHV DVVRFLDWHG ZLWK WKH SKRWRPHWULF FDOLEUDWLRQ VLQFH WKH\ DUH WKH GRPLQDQW XQFHUWDLQWLHV ZH GHDOW ZLWK IRU WKH VXUYH\ REVHUYDWLRQV 7KH HIIHFWV RI DWPRVSKHULF WUDQVPLVVLRQ DOZD\V GRPLQDWH WKH SKRWRPHWULF XQFHUWDLQWLHV LQ PLG,5 $V )LJXUH $O VKRZV VHH DSSHQGL[ $f WKH PLG,5 DWPRVSKHULF ZLQGRZV DW DQG LP DUH ULGGOHG ZLWK DWPRVSKHULF DEVRUSWLRQ IHDWXUHV IURP ZDWHU YDSRU &&7 DQG 2 $ YDULDWLRQ LQ WKH FROXPQ GHQVLW\ RI WKHVH VSHFLHV KDV D GUDPDWLF HIIHFW RQ WKH WUDQVSDUHQF\ RI WKH DWPRVSKHUH LQ WKH PLG,5 ,QGHHG LW LV WKHVH YDULDWLRQV RI WKH VN\ EDFNJURXQG WKDW UHTXLUHV WKH XVH RI FKRSSLQJ LQ WKH PLG,5 9DQ GHU %OLHN HW DO f PHDVXUH VKRUW WHUP YDULDWLRQV LQ WKH DWPRVSKHULF WUDQVPLVVLRQ RI b IRU WKH SP ZLQGRZ DQG XSZDUGV RI b LQ WKH SP ZLQGRZ /RRNLQJ DW WKH FDOLEUDWLRQ GDWD GLUHFWO\ UHODWHG WR RXU VXUYH\ ZKLFK FRQVLVWV RI LQGLYLGXDO VWHOODU REVHUYDWLRQV ZH ILQG WKDW WKH RYHUDOO XQFHUWDLQW\ LQ WKH DEVROXWH FDOLEUDWLRQ LV b DW ERWK DQG SP 7KH GLVFUHSDQF\ ZLWK WKH YDQ GHU %OLHN HW DO f ORQJ ZDYHOHQJWK FRQFOXVLRQ LV PRVW OLNHO\ UHODWHG WR WKH IDFW WKDW RXU SP ILOWHU KDV D EDQGSDVV RQ RQO\ $ƒ SP UHODWLYHO\ QDUURZ ZKHQ FRPSDUHG WR WKH EURDGEDQG SP ILOWHUV GLVFXVVHG LQ WKHLU SDSHU :H DGRSW sb XQFHUWDLQWLHV IRU DOO RI RXU PHDVXUHG 26&,5 IOX[ GHQVLWLHV 7KH DLUPDVV FRUUHFWLRQV LQ WKH PLG,5 DUH JHQHUDOO\ VPDOO 8QGHU JRRG VN\ FRQGLWLRQV D UXOHRIWKXPE PHDVXUH IRU WKH DLUPDVV FRUUHFWLRQ LQ WKH 1EDQG SPf LV PDJDLUPDVV (YHQ VR ZH DWWHPSWHG WR SHUIRUP DLUPDVV FRUUHFWLRQV IRU DOO RI RXU

PAGE 38

7DEOH 6WDQGDUG 6WDU )OX[ 'HQVLWLHV )OX[ 'HQVLW\ -\f 6WDQGDUG 6WDU _LP 1%DQGf MDP ,+:f D /\U D &0Dn D &U% D %RRf D +\D D 7DX 3 $QGn 3 *HP 3 *UX 3 3HJ \ $TO \&UX \5HW ; 9HO 80DI W f§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f YV DLUPDVV WR FRUUHFW WKH VFLHQFH REVHUYDWLRQV IRU DLUPDVV 7KHVH FRUUHFWLRQV UDUHO\ PDGH D PRUH WKDQ b FKDQJH LQ WKH IOX[ HVWLPDWH IRU D VXUYH\ VRXUFH ZHOO ZLWKLQ WKH b SKRWRPHWULF HUURUV DVVLJQHG WR RXU 26&,5 SKRWRPHWU\

PAGE 39

)ODWILHOG &RUUHFWLRQ )LJXUH VKRZV DQ LPDJH RI WKH 26&,5 GHWHFWRU XQGHU XQLIRUP LOOXPLQDWLRQ LQ WKH 1EDQG _LPf 7KHUH DUH DSSUR[LPDWHO\ KRW SL[HOV GLVWULEXWHG DFURVV WKH DUUD\ WKDW KDYH VLJQLILFDQWO\ GLIIHUHQW UHVSRQVH WKDQ WKH RWKHUV 7KHUH DUH DOVR DERXW GHDG SL[HOV 2YHUDOO WKH XQLIRUPLW\ RI WKH GHWHFWRU LV YHU\ JRRG KRZHYHU WKHUH LV D VPDOO DPRXQW RI YLJQHWWLQJ LQ WKH ORZHU ULJKW FRPHU RI WKH DUUD\ 7KH UHVSRQVH RI WKH DUUD\ LV JHQHUDOO\ YHU\ IODW WKRXJK WKH IODWILOHG YDULHV b DFURVV WKH DUUD\ $OO RI WKH VWUXFWXUH VHHQ LQ )LJXUH LV fIL[HGSDWWHUQf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b RI WKH VXUYH\ GDWD :H DOVR XVHG WKLV URXWLQH ZKHQ ZH PDQXDOO\ UHGXFHG VWDQGDUG VWDU GDWD RU REWDLQHG IOX[ HVWLPDWHV IRU 36) VWDUV )RU IDLQW VRXUFHV ZH XVHG D PDQXDO DSHUWXUH IRU WKH SKRWRPHWU\ )RU FRQVLVWHQF\ DOO PDQXDO DSHUWXUHV XVHG KDG D UDGLXV U f 7KH PHDVXUHPHQW HUURUV DVVRFLDWHG ZLWK WKH SKRWRPHWU\ LH DSL[1SL[fOf ZHUH DOZD\V GRPLQDWHG E\ WKH b SKRWRPHWULF HUURU IRU DOO VXUYH\ VRXUFHV 2XU REVHUYHG

PAGE 40

FRORU FRUUHFWHG 26&,5 IOX[ GHQVLW\ HVWLPDWHV IRU WKH VXUYH\ VRXUFHV DUH SUHVHQWHG LQ 7DEOH ,Q &KDSWHU ZH DOVR GLVFXVV WKH UHPRYDO RI WKH VWHOODU SKRWRVSKHUH IURP WKRVH YDOXHV WR FDOFXODWH D YDOXHV IRU WKH H[FHVV HPLVVLRQ IURP WKH FLUFXPVWHOODU GXVW &RORU &RUUHFWLRQ )OX[ GHQVLW\ HVWLPDWHV IRU REMHFWV REVHUYHG WKURXJK ZLGH EDQGSDVV LQIUDUHG ILOWHUV QHHG WR KDYH D FRUUHFWLRQ DSSOLHG WR WKHP FDOOHG D fFRORU FRUUHFWLRQf 7KLV LV SDUWLFXODUO\ WUXH RI WKH 26&,5 1EDQG ILOWHU WKDW KDV D EDQGSDVV RI SP 7KH FRORU FRUUHFWLRQ PXVW EH DSSOLHG VLQFH WKH VSHFWUDO VKDSHV RI WKH IOX[ FDOLEUDWLRQ VWDU DQG VFLHQFH REMHFW DUH GLIIHUHQW WKURXJK WKH EDQGSDVV RI WKH ILOWHU %HFDXVH VWHOODU WHPSHUDWXUHV DUH KLJK .f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n7f %97ff WKURXJK WKH SDVVEDQG 7KH FRORU FRUUHFWLRQ WHUP LV DSSOLHG WR VFDOH WKDW IXQFWLRQ WR JLYH XV WKH FRUUHFW LQEDQG IOX[ IRU WKH VFLHQFH VRXUFH

PAGE 41

:H RXWOLQH WKH SURFHGXUH IRU WKLV FRUUHFWLRQ EHORZ VWDUWLQJ ZLWK WKH GHILQLWLRQ RI WKH HIIHFWLYH ZDYHOHQJWK RI WKH 1EDQG ILOWHU ;HIIf 6LQFH WKH 26&,5 GHWHFWRU LV D SKRWRQ FRXQWHU IRU WKHVH SXUSRVHV ;HII LV GHILQHG LQ WHUPV RI WKH SKRWRQ ZLWK WKH DYHUDJH HQHUJ\ LQ WKH EDQGSDVV 7KH FRORU FRUUHFWLRQ IDFWRU DVVXPHV WKDW WKH UDWLR RI LQVWUXPHQWDO FRXQWV IRU WKH FDOLEUDWLRQ VWDU $'86f WR WKDW RI WKH SURJUDP REMHFW $'83f LV HTXDO WR WKH UDWLR RI QXPEHU RI SKRWRQV GHWHFWHG IURP WKH FDOLEUDWLRQ VWDU 1\Vf WR WKH SURJUDP VRXUFH 1\Sf 7KLV HTXDOLW\ LV VKRZQ EHORZ LQ HTXDWLRQ $'WI B 1 \3 f $'W 1 \V WKH QXPEHU RI SKRWRQV D VRXUFH ZLOO JHQHUDWH WKURXJK D EDQGSDVV LV :KHUH )Y LV WKH IOX[ GHQVLW\ RI WKH VRXUFH ZLWK WHPSHUDWXUH 7 DQG RSWLFDO GHSWK [Y DQG LV GHILQHG DV f :H DOVR GHILQH WKH fTXDQWXP HIILFLHQF\f RI WKH V\VWHP DV 4 V\V 7IOWHAf7DWUDQDf4(;f

PAGE 42

ZKHUH WKLV UHODWLRQ WDNHV LQWR DFFRXQW WKH 4( RI WKH 26&,5 GHWHFWRU WKH DWPRVSKHULF WUDQVPLVVLRQ DQG WKH WUDQVPLVVLRQ RI WKH 26&,5 ILOWHU 6XEVWLWXWLQJ f LQWR f JLYHV 1 e OH <%97f 4 SH GY V\V KY f ,I ZH DUH JLYHQ D PRQRFKURPDWLF IOX[ GHQVLW\ RI WKH VRXUFH DW VRPH IUHTXHQF\ )YR XVLQJ HTXDWLRQ f DQG VROYLQJ IRU 4 ZH FDQ GHILQH WKH IROORZLQJ UHODWLRQ  YR f OH n‘%:7f VXEVWLWXWLQJ HTXDWLRQ f LQWR f JLYHV 1 YR W OH %97f %97f ‘V\Vn KY GY f ZKLFK LV DQ H[SUHVVLRQ IRU WKH QXPEHU RI SKRWRQV SURGXFHG E\ D VRXUFH ZLWK IOX[ GHQVLW\ )Y WKURXJK WKH SDVVEDQG RI WKH ILOWHU 5HFDOOLQJ HTXDWLRQ f $', B 1 \3 $'OI 1 \V ZH FDQ XVH HTXDWLRQ f WR UHODWH WKH QXPEHU RI SKRWRQV UHFHLYHG IURP WKH SURJUDP VRXUFH 1f WR WKH FRXQWV PHDVXUHG IURP WKH SURJUDP VRXUFH $'83f DQG WKH QXPEHU RI FRXQWV PHDVXUHG IURP WKH FDOLEUDWLRQ VWDU $'86f )LUVW VROYLQJ f IRU 1f DQG WKHQ VXEVWLWXWLQJ LQ H[SUHVVLRQV IRU WKH QXPEHU RI SKRWRQV UHFHLYHG IURP WKH VWDU DQG SURJUDP VRXUFH IURP f JLYHV

PAGE 43

WKH DEVHQFH RI WKH H 7f WHUPV RQ WKH ULJKW KDQG VLGH RI HTXDWLRQ f LV GXH WR WKH IDFW WKDW WKH FDOLEUDWLRQ VWDU LV DVVXPHG WR EH D VLPSOH EODFNERG\ :H FDQ QRZ VROYH f IRU WKH IOX[ GHQVLW\ RI WKH SURJUDP REMHFW DW YR )YRSf f ,Q HTXDWLRQ f ZH KDYH HTXDWHG WKH IOX[ GHQVLW\ RI WKH SURJUDP VRXUFH DW WKH PRQRFKURPDWLF IUHTXHQF\ YR WR WKUHH NQRZQ TXDQWLWLHV $'83 )YR? DQG $'86 7KH ILUVW WHUP RQ WKH ULJKW KDQG VLGH RI f LV WKH PHDVXUHG LQVWUXPHQWDO FRXQWV RI WKH SURJUDP VRXUFH 7KH VHFRQG WHUP LV VLPSO\ WKH UDWLR RI WKH JLYHQ IOX[ GHQVLW\ RI WKH FDOLEUDWLRQ VWDU DW YR WKH PHDVXUHG LQVWUXPHQWDO FRXQWV IRU WKH FDOLEUDWLRQ VWDU 7KLV LV WKH fFDOf YDOXH PHQWLRQHG LQ WKH FDOLEUDWLRQ VHFWLRQ 7KH WKLUG WHUP LV WKH FRORU FRUUHFWLRQ WHUP ,W LV WKLV IDFWRU WKDW LV DSSOLHG WR WKH GDWD WR DFFRXQW IRU WKH GLIIHUHQW VSHFWUDO VKDSHV RI WKH FDOLEUDWLRQ VWDU DQG SURJUDP REMHFW WKURXJK WKH EDQGSDVV RI WKH ILOWHUV 7R FRORU FRUUHFW RXU IOX[HV ZH XVHG D SURJUDP ZULWWHQ IRU 0$7+&$' 8VLQJ RXU UDZ DQG _LP IOX[ GHQVLW\ HVWLPDWHV DV D VWDUWLQJ SRLQW WKH FRGH LWHUDWHV WR VLPXOWDQHRXVO\ VROYH IRU 7 W DQG FRORU FRUUHFWLRQ $OO RI RXU IOX[ GHQVLW\ HVWLPDWHV

PAGE 44

SUHVHQWHG LQ WKLV GLVVHUWDWLRQ DUH FRORU FRUUHFWHG )RU WKH VDPSOH DV D ZKROH WKH PHDQ FRORU FRUUHFWLRQ IRU RXU EURDG EDQG -LP IOX[ GHQVLW\ HVWLPDWHV ZDV DSSUR[LPDWHO\ b 7KH -LP HVWLPDWHV KDG D PHDQ FRUUHFWLRQ RI ab 7KH -LP YDOXH LV ORZHU GXH WR WKH PXFK QDUURZHU SDVVEDQG RI WKH -LP ILOWHU &RORU FRUUHFWLRQV IRU -LP 1 EDQGf IOX[HV RQ WKH RUGHU RI WR b DUH FRQVLVWHQW ZLWK WKH ZRUN RI +DQQHU HW DO f 5HVROYHG RU 8QUHVROYHG 7KH 4XHVWLRQ 3HUKDSV WKH PRVW IXQGDPHQWDO TXHVWLRQ ZH DWWHPSWHG WR DQVZHU LQ WKLV GLVVHUWDWLRQ LV DUH RXU VDPSOH 9HJDOLNH VRXUFHV UHVROYHG" )RU WKH PRVW SDUW WKH DQVZHU WR WKDW TXHVWLRQ LV QR :H ILQG WKDW b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

PAGE 45

$UFVHFRQGV $UFVHFRQGV )LJXUH 6FDQV RI D UHVROYHG D t Ff DQG XQUHVROYHG VRXUFH E t Gf D DQG Ff 6FDQV RI +' DQG 36) VWDU DW SP DQG SP UHVSHFWLYHO\ +' LV WKH VROLG OLQH WKH 36) VWDU LV GDVKHG 7KH GRWWHG OLQH LV D *DXVVLDQ ILW WR WKH GDWD E DQG Gf 6FDQ RI +' DW SP Ef DQG SP Gf SP GDWD IRU +' DQG 36) VWDU KDYH D SL[HO f ):+0f *DXVVLDQ VPRRWK DSSOLHG WR ERRVW WKH VLJQDO WR QRLVH RI WKH +' GHWHFWLRQ $QRWKHU ZD\ ZH LQYHVWLJDWHG WKH GDWD WR WU\ WR DQVZHU WKH TXHVWLRQ RI UHVROXWLRQ ZDV WKURXJK VFDQV LH OLQHFXWVf WKURXJK WKH VFLHQFH REMHFWV DQG FRUUHVSRQGLQJ 36) VWDUV :H ILQG WKH EHVW ZD\ WR YLVXDOL]H WKH GDWD LQ WKLV IRUP LV WKURXJK SORWV OLNH )LJXUH ,Q )LJXUH ZH VKRZ VFDQV WKDW DUH UHSUHVHQWDWLYH RI D UHVROYHG DQG XQUHVROYHG VRXUFH 7KH UHVROYHG VRXUFH SDQHO D t Ff LV +' ZKLFK ZH REVHUYHG DW .HFN ,, LQ 0D\ 7KLV VRXUFH LV GLVFXVVHG LQ GHWDLO LQ &KDSWHU :H FRQWUDVW +' ZLWK D UHSUHVHQWDWLYH XQUHVROYHG VRXUFH +' $OVR REVHUYHG DW .HFN WKH +' GDWD KDV WKH VDPH UHVROXWLRQ DV WKH +' REVHUYDWLRQV

PAGE 46

2QH LPPHGLDWHO\ VHHV WKH GLIIHUHQFHV LQ WKH WZR VHWV RI SDQHOV +' LV FOHDUO\ EURDGHU WKDQ WKH 36) VWDU DW ERWK DQG SP ZKLOH WKH +' DQG 36) VWDU VFDQV OLH RQ WRS RI HDFK RWKHU ,W LV WKH H[WHQGHG HPLVVLRQ RI +' WKDW FDXVHV WKLV EURDGHQLQJ RI LWV VFDQ ZLWK UHVSHFW WR WKH 36) VWDU &ORVH LQVSHFWLRQ RI SDQHO Df VKRZV WKDW WKHUH LV VLJQLILFDQW H[WHQGHG HPLVVLRQ IURP +' GHWHFWHG RXW WR D UDGLXV RI af $W SP WKH QRLVH LQ WKH VRXUFH VFDQ SUHYHQWV D GHWHUPLQDWLRQ RI WKH H[DFW H[WHQW RI WKH H[WHQGHG HPLVVLRQ KRZHYHU HYHQ ZLWK WKH UHODWLYHO\ ORZ VLJQDOWR QRLVH RI WKH +' SP GDWD WKH GLIIHUHQFH LQ ZLGWK RI LW DQG WKH 36) VWDU LV HDVLO\ GLVWLQJXLVKDEOH LQ SDQHO Ff ,PDJHV RI +' DOVR H[KLELW D fIX]]LQHVVf WKDW LV QRW SUHVHQW ZKHQ REVHUYLQJ D WUXH SRLQW VRXUFH 7KLV HIIHFW LV GLIILFXOW WR GHVFULEH EXW LW LV YHU\ HYLGHQW ZKHQ ORRNLQJ DW WKH GDWD RQ D PRQLWRU 7KH VFDQV RI +' DUH UHSUHVHQWDWLYH RI WKH XQUHVROYHG VRXUFHV LQ WKH VXUYH\ 7KHUH LV YLUWXDOO\ QR GLIIHUHQFH LQ WKH ):+0 PHDVXUHPHQWV RI +' DQG WKH 36) VWDU DW HLWKHU RU SP 7KHUH LV DOVR QR HYLGHQFH IRU IDLQW H[WHQGHG HPLVVLRQ DW WKH ORZHVW OHYHOV RI SDQHOV Ef DQG Gf 8VLQJ WKHVH VFDQV LQ FRQMXQFWLRQ ZLWK DQ LQ GHSWK LQVSHFWLRQ E\ H\H ZH FDQ FRQILGHQWO\ FRQFOXGH WKDW +' LV XQUHVROYHG DW WKLV DQJXODU VFDOH DW ERWK DQG SP ,Q WKH QH[W FKDSWHU ZH PRYH RQWR WKH GLVFXVVLRQ RI RXU VXUYH\ GDWD

PAGE 47

&+$37(5 6859(< ',6&866,21 ,Q WKLV FKDSWHU ZH GLVFXVV RXU VXUYH\ GDWD :H GR QRW JLYH IXUWKHU GHWDLOV RQ WKH PHFKDQLFV RI PDNLQJ WKH VXUYH\ UDWKHU ZH GLVFXVV RXU RYHUDOO LQWHUSUHWDWLRQV RI WKH GDWD ,Q WKH ILUVW VHFWLRQV RI WKLV FKDSWHU ZH SUHVHQW VL]H OLPLWV RQ WKH GLVNV RI WKH XQUHVROYHG VRXUFHV DQG JLYH RXU GHULYHG JUDLQ SDUDPHWHUV IRU WKHLU GXVW :H WKHQ FRPSDUH WKH XQUHVROYHG VXUYH\ VRXUFHV WR 3LFWRULV DQG +5 $ DQG VKRZ WKDW LI WKH VXUYH\ VWDUV ZHUH DW WKH GLVWDQFH RI 3LFWRULV SFf DERXW b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

PAGE 48

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f +' &KDSWHU f DQG SRVVLEO\ &HWL ZHUH UHVROYHG GXULQJ WKH VXUYH\ 6LQFH RYHU b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

PAGE 49

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f f LQ WKH OLPLWLQJ VL]H FROXPQf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f REVHUYHG QLQH RI WKH VDPSOH ZLWK ,62 EXW RQO\ DW DQG SP DQG DW UHODWLYHO\ ORZ VSDWLDO UHVROXWLRQ 7KH RQO\ RWKHU REVHUYDWLRQV RI D VLJQLILFDQW QXPEHU RI WKH VXUYH\ VWDUV LV WKDW RI 6\OYHVWHU HW DO f LQ ZKLFK PLG,5 VSHFWUD RI RI WKH VRXUFHV ZHUH SUHVHQWHG EXW QR LPDJLQJ 7DEOH DOVR OLVWV RXU FRORU FRUUHFWHG REVHUYHG IOX[ GHQVLWLHV RI WKH VXUYH\ VRXUFHV DW DQG SP 7KH IOX[ GHQVLWLHV SUHVHQWHG LQ 7DEOH DUH WKH VXP RI WKH SKRWRVSKHULF HPLVVLRQ RI WKH VWDU DQG WKH WKHUPDO HPLVVLRQ IURP WKH FLUFXPVWHOODU GXVW :H SUHVHQW WKHVH YDOXHV KHUH LQ WKLV PDQQHU VR WKDW WKH\ FDQ EH GLUHFWO\ FRPSDUHG WR RWKHU REVHUYDWLRQV )RU RXU DQDO\VLV RI WKH GXVW SURSHUWLHV ZH UHPRYH WKH VWHOODU

PAGE 50

7DEOH 2EVHUYHG 3URSHUWLHV RI WKH 6XUYH\ 6RXUFHV 6RXUFH 1DPH )OQP -\f )O XUQ -\f ,5$6 SP -\f ,5$6 SP -\f ,5$6 SP -\f ,5$6 SP -\f /LPLWLQJ 6L]H $8f +' +' +' +' / +' / / +' +' +' +' f +' +' f +' +' / +' +' +' +' +' +' +' +' f +' f +' / +' +' / / +' f +' f +' f +' +' f +' +' f +' +' +' +' +' +' :H DGRSW b HUURUV RQ WKH 26&,5 SKRWRPHWU\ DW DQG SP f 'HQRWHV VRXUFH ZLWK QHDU,5 H[FHVV DV OLVWHG E\ 6\OYHVWHU HW DO f / LQ IOX[ FROXPQ GHQRWHV XSSHU OLPLW XVHG LQ WHPSHUDWXUH DQG RSWLFDO GHSWK FDOFXODWLRQ

PAGE 51

FRQWULEXWLRQ IURP WKH REVHUYHG IOX[ GHQVLW\ 7KLV SURFHGXUH DQG RXU UHVXOWV DUH GLVFXVVHG LQ WKH QH[W VHFWLRQ )RU WKH IHZ VRXUFHV WKDW ZH GLG QRW GHWHFW DW HLWKHU RU SP ZH OLVW D D XSSHU OLPLW LQ WKH DSSURSULDWH FROXPQ LQ 7DEOH 7KHVH OLPLWV ZHUH FDOFXODWHG XVLQJ DQ DSHUWXUH ZLWK UDGLXV $'f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n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

PAGE 52

REVHUYHG IOX[ GHQVLW\ HVWLPDWHV KDYH FRQVHTXHQFHV RQ WKH ILQDO UHVXOWV 7KH SURFHGXUH ZH XVHG WR FDOFXODWH WKH SKRWRVSKHULF FRQWULEXWLRQ RI HDFK VWDU WR RXU REVHUYHG IOX[ GHQVLW\ HVWLPDWH LV RXWOLQHG EHORZ 8VH D SXEOLVKHG YDOXH RU VSHFWUDO W\SH RI WKH VWDU WR ILQG WKH HIIHFWLYH WHPSHUDWXUH RI LWV SKRWRVSKHUH 7HIIf 0RGHO WKH 6(' RI WKH VWHOODU SKRWRVSKHUH DV D EODFNERG\ IXQFWLRQ ZLWK WHPSHUDWXUH 7HII DQG QRUPDOL]H WKH EODFNERG\ IXQFWLRQ WR REVHUYHG SP .EDQGf YDOXHV 8VH WKH EODFNERG\ IXQFWLRQ WR SUHGLFW WKH IOX[HV HPLWWHG DW DQG SP IRU HDFK 7HII 7KHQ IRUP WKH UDWLRV )LQP)QPf DQG )LQP)QPf DV D IXQFWLRQ RI 7HII 0XOWLSO\ WKH REVHUYHG SP IOX[ YDOXH E\ WKH FRUUHFW UDWLRV WR SUHGLFW WKH SKRWRVSKHULF IOX[ DW DQG SP 6XEWUDFW WKH SUHGLFWHG IOX[ HVWLPDWHV IURP RXU REVHUYHG HVWLPDWHV ZKLFK OHDYHV RQO\ WKH FRQWULEXWLRQ RI WKH GXVW GHILQHG DV WKH H[FHVV HPLVVLRQ 7ZR TXHVWLRQV LPPHGLDWHO\ FRPH WR PLQG FRQFHUQLQJ WKLV SURFHGXUH f LV LW OHJLWLPDWH WR XVH WKH UDWLRV )LRQP)QPf DQG )LQP)QPf LQ WKH FDOFXODWLRQ DQG f LV WKH DVVXPSWLRQ WKH SKRWRVSKHUH EHKDYHV DV D EODFNERG\ DFFXUDWH HQRXJK" ,Q VKRUW WKH DQVZHU WR ERWK LV \HV $V LOOXVWUDWHG LQ )LJXUH LQ WKH PLGO5 ZH DUH ZRUNLQJ RQ WKH 5DOHLJK-HDQV WDLO RI WKH EODFNERG\ GLVWULEXWLRQ IRU HYHQ WKH FRROHVW VWDUV LQ RXU VDPSOH .f DQG WKH VWHOODU SKRWRVSKHUHV IROORZ WKH ZHOONQRZQ Yn IDOORII LQ WKLV UHJLPH &ORVH LQVSHFWLRQ RI WKH FXUYH LQ )LJXUH VKRZV WKHUH LV V VOLJKW GHYLDWLRQ IURP 5DOHLJK-HDQV IDOORII DW SP EXW WKLV LV D UHODWLYHO\ VPDOO GLVFUHSDQF\ DQG RQO\ DSSOLHV WR RQH RI RXU VXUYH\ VRXUFHV :H DGGUHVV WKH VHFRQG TXHVWLRQ E\ SORWWLQJ WKUHH TXDQWLWLHV LQ )LJXUH WKH QHDU DQG PLGO5 SRUWLRQ D EODFNERG\ IXQFWLRQ ZLWK 7 D PRGHO DWPRVSKHUH IRU 9HJD IURP &RKHQ f DQG IOX[ GHQVLW\ HVWLPDWHV IRU 9HJD IURP 26&,5 REVHUYDWLRQV $OO WKUHH FXUYHV KDYH EHHQ QRUPDOL]HG WR XQLW\ DW

PAGE 53

)LJXUH %ODFNERG\ SORWV IRU WHPSHUDWXUHV WKDW EUDFNHW WKH HIIHFWLYH WHPSHUDWXUHV 7HIIf RI WKH VWDUV LQ RXU 9HJDOLNH VDPSOH 2XU VSHFWUDO W\SHV RI RXU VDPSOH VWDUV UDQJH IURP D %9 .f WR .9 .f 7KH PHDQ 7HII RI WKH VDPSOH LV 7KH YHUWLFDO GRWWHG OLQHV GHQRWH DQG SP IURP OHIW WR ULJKWf SP )RU WKH 26&,5 REVHUYDWLRQV ZH KDYH DOVR SORWWHG HUURU EDUV WKDW PDUN WKH sb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

PAGE 54

)LJXUH &RPSDULVRQ RI 26&,5 GDWD EODFNERG\ IXQFWLRQ DQG PRGHO DWPRVSKHUH GDWD IRU 9HJD (UURU EDUV RQ 26&,5 GDWD DUH sb DQG UHSUHVHQW WKH XQFHUWDLQO\ LQ RXU PHDVXUHG IOX[ YDOXHV VHYHQWHHQ RI WKH VXUYH\ VWDUV WKLV SURFHGXUH UHWXUQV QHJDWLYH H[FHVVHV DW HLWKHU RU SP FOHDUO\ QRW D OHJLWLPDWH UHVXOW :H EHOLHYH WKDW WKHVH QRQSK\VLFDO UHVXOWV DUH SULPDULO\ GXH WR WKH sb XQFHUWDLQWLHV LQ RXU 26&,5 IOX[ HVWLPDWHV 6LQFH WKH GHWHUPLQDWLRQ RI WKH PDJQLWXGH RI WKH H[FHVV LV GLUHFWO\ UHODWHG WR RXU REVHUYHG PLG,5 IOX[ HVWLPDWHV DQ\ XQFHUWDLQW\ LQ WKRVH HVWLPDWHV WUDQVODWHV GLUHFWO\ LQWR XQFHUWDLQWLHV LQ RXU HVWLPDWHV RI WKH H[FHVVHV )RU WKHVH VHYHQWHHQ VRXUFHV WKH DPRXQW RI WKHLU PLG,5 H[FHVV LV ZLWKLQ RXU REVHUYDWLRQDO XQFHUWDLQWLHV DQG ZH WKHUHIRUH FDQQRW FDOFXODWH WKH DPRXQW RI H[FHVV WKH\ H[KLELW %HFDXVH RI WKLV ZH DUH IRUFHG WR UHPRYH WKHVH VHYHQWHHQ VWDUV IURP RXU DQDO\VLV RI WKH GLVN JUDLQ SURSHUWLHV

PAGE 55

&OHDUO\ WKLV KDV D GUDPDWLF HIIHFW RQ WKH UHVXOWV RI RXU VXUYH\ %HFDXVH RI WKLV LVVXH ZH KDYH RQO\ PRGHOHG WKH JUDLQV DVVRFLDWHG ZLWK RI WKH REVHUYHG V\VWHPV RU b RI RXU VDPSOH +RZHYHU ZH XVH WKH IDFW WKDW VRPH VWDUV H[KLELW OLWWOH RU QR H[FHVV LQ WKH PLG,5 LQ WKH GLVFXVVLRQ RI RXU SURSRVHG HYROXWLRQDU\ VHTXHQFH SUHVHQWHG ODWHU LQ WKLV FKDSWHU ,QGHHG WKHVH VRXUFHV ZLWK OLWWOH RU QR PLG,5 H[FHVV IRUP RQH RI WKH WKUHH VXEn FODVVHV ZH GLYLGH RXU VXUYH\ LQWR DQG UHSUHVHQW WKH ODVW VWDJH RI RXU SURSRVHG VHTXHQFH :H GR KDYH UREXVW HVWLPDWHV IRU WKH DQG SP H[FHVVHV RI WKH UHPDLQLQJ VXUYH\ VRXUFHV DQG ZH SUHVHQW WKHP LQ 7DEOH /LVWHG E\ +' QXPEHU ZH SUHVHQW RXU H[FHVV HVWLPDWHV LQ XQLWV RI IOX[ GHQVLW\ DQG DV D SHUFHQWDJH RI RXU REVHUYHG IOX[ HVWLPDWH $ OLWHUDWXUH VHDUFK DQG XVH RI WKH 6,0%$' GDWDEDVH JDYH WKH VSHFWUDO W\SHV IRU HDFK RI WKH VRXUFHV LQ WKH WDEOH :H DOVR OLVW WKH HIIHFWLYH 7HIIf ZH XVHG IRU HDFK VWDU LQ RXU FDOFXODWLRQV RI WKH H[FHVV 7KH PDMRULW\ RI WKHVH YDOXHV ZHUH WDNHQ IURP $OOHQ f ZKLOH RWKHUV ZHUH WDNHQ IURP WKH OLWHUDWXUH LQ SDUWLFXODU 'XQNLQ %DUORZ DQG 5\DQ Ef 2QH LPSRUWDQW FRQFOXVLRQ WKDW ZH FDQ LQIHU IURP 7DEOH LV WKDW DOWKRXJK RXU VDPSOH LV ELDVHG WRZDUG VWDUV RI $W\SH ZLWKLQ WKH VDPSOH WKHUH LV QR DSSDUHQW FRUUHODWLRQ EHWZHHQ VSHFWUDO W\SH DQG DPRXQW RI PLG,5 H[FHVV 7KLV LV VXSSRUWHG E\ WKH OLWHUDWXUH ZKHUH LW KDV EHHQ IRXQG WKDW DW OHDVW b RI QHDUE\ ILHOG VWDUV RI DOO VSHFWUDO W\SHV EHWZHHQ $ WR KDYH FLUFXPVWHOODU GXVW V\VWHPV OLNH WKRVH DVVRFLDWHG ZLWK RXU VDPSOH /DJUDQJH %DFNPDQ t $UW\PRZLF] f :H DOVR VHH WKDW SHUFHQWDJH ZLVH WKHUH LV YDU\LQJ DPRXQWV RI SP H[FHVV DVVRFLDWHG ZLWK RXU VDPSOH VWDUV 7KH H[FHVVHV RI WZHOYH VWDUV LQ 7DEOH DFFRXQWV IRU PRUH WKDQ b RI WKH REVHUYHG SP IOX[ VHYHQ RI WKH VWDUV KDYH LQWHUPHGLDWH YDOXHV RI SP H[FHVV EHWZHHQ WR

PAGE 56

7DEOH ([FHVV &KDUDFWHULVWLFV RI WKH 6XUYH\ 6RXUFHV 6RXUFH 1DPH 6S 7\SH 7HII SP ([FHVV -\f b ([FHVV SPf SP ([FHVV -\f b ([FHVV SPf +' $9 +' $9 +' *2 +' $9 r +' $9 +' $9 +' .9 r +' ), r +' $ +' $9 r +' $9 +' $9 +' %9H r +' $9 +' +' $9 +' )9 +' $9 +' $9 +' $9H +' $ r +' .,,, +' .9 r ,Q VS 7\SH FROXPQ GHQRWHV PXOWLSOH VWDU V\VWHP $PELJXRXV FODVVLILFDWLRQ VHH &KDSWHU bf DQG WKUHH VWDUV KDYH OLWWOH _LP H[FHVV bf &RXSOHG ZLWK WKH VHYHQWHHQ VRXUFHV WKDW KDYH QR PHDVXUDEOH H[FHVV DQG DUH QRW OLVWHG LQ 7DEOH WKHUH DUH WZHQW\ VWDUV WKDW H[KLELW b H[FHVV DW SP 7KLV LV RXU ILUVW ORRN DW WKH WKUHH VXEFODVVHV ZH EUHDN WKH VXUYH\ LQWR ZLWK UHJDUGV WR RXU SURSRVHG HYROXWLRQDU\ VHTXHQFH $V ZH ZLOO

PAGE 57

VHH WKH DPRXQW RI WKH f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f DQG /DRU DQG 'UDLQH f 7KHUH LV HYLGHQFH IRU SDUWLFOHV ZLWK WKLV FRPSRVLWLRQ LQ ERWK LQWHUSODQHWDU\ GXVW SDUWLFOHV JDWKHUHG KLJK LQ WKH (DUWKfV DWPRVSKHUH /HLQHUW DQG *ULLQ f DQG LQ GLVNV VLPLODU WR WKRVH VWXGLHG KHUH 6\OYHVWHU HW DO f

PAGE 58

SUHVHQWHG PLG,5 VSHFWUD RI VRXUFHV LQ RXU VXUYH\ DQG GHILQLWLYHO\ GHWHFWHG VLOLFDWHV LQ VHYHQ RI WKHP 2WKHU VLJQLILFDQW GHWHFWLRQV RI VLOLFDWH PDWHULDOV LQ 9HJDOLNH GLVNV DUH WKRVH LQ WKH DUFKHW\SDO 9HJDOLNH VRXUFH 3LFWRULV 7HOHVFR DQG .QDFNH f DQG LQ WKH VRXUFH 2SK )DMDUGR$FRVWD 7HOHVFR t .QDFNH f :H DOVR PDNH WKH DVVXPSWLRQV WKDW WKH PRGHO SDUWLFOHV KDYH D GHQVLW\ S J FPn DQG WKDW WKH\ DUH VSKHULFDO :H PDNH WKH DVVXPSWLRQ DERXW WKH GHQVLW\ VLQFH fDVWURQRPLFDO VLOLFDWHVf LV QRW D SK\VLFDO PDWHULDO DQG LWV PHDVXUHG GHQVLW\ LV XQGHILQHG 7KH YDOXH RI J FP LV XVHG VLQFH LW LV UHSUHVHQWDWLYH RI LQWHUSODQHWDU\ GXVW SDUWLFOHV *XVWDIVRQ f :LWK UHJDUGV WR WKH DVVXPSWLRQ DERXW WKH VKDSH RI WKH JUDLQV RQH PXVW ILUVW UHDOL]H WKDW WKH PHWKRGV IRU FDOFXODWLQJ WKH RSWLFDO FRQVWDQWV IRU JUDLQV DUH OLPLWHG 5LJRURXV VROXWLRQV IRU OLJKW VFDWWHULQJ IURP SDUWLFOHV DUH RQO\ DYDLODEOH IRU VSKHULFDO JUDLQV XVLQJ 0LH WKHRU\ DQG LQILQLWH F\OLQGHUV DV GHVFULEHG LQ %RKUHQ t +XIIPDQ f 1HZ VROXWLRQV IRU PRUH FRPSOLFDWHG DJJUHJDWH SDUWLFOHV KDYH UHFHQWO\ EHFRPH DYDLODEOH ;X t *XVWDIVRQ f EXW WKHVH PHWKRGV DUH FRPSXWDWLRQDOO\ LQWHQVLYH DQG EH\RQG WKH VFRSH RI WKH PRGHOLQJ SUHVHQWHG KHUH 5HFHQW DGYDQFHV LQ WKH ZRUN RQ WKH FRPSRVLWLRQ DQG VWUXFWXUH RI SDUWLFOHV LQ FLUFXPVWHOODU GLVNV KDV VKRZQ WKDW WKHVH DVVXPSWLRQV OLNHO\ RYHUVLPSOLI\ WKH JUDLQV HJ *XVWDIVRQ f KRZHYHU WKLV VRUW RI DQDO\VLV SURYLGHV D JRRG VWDUWLQJ SRLQW IRU PRUH GHWDLOHG PRGHOV ZKLFK LQFRUSRUDWH PRUH FRPSOH[ JUDLQ VWUXFWXUHV ,Q D IROORZLQJ VHFWLRQ ZH GLVFXVV WKH OLPLWDWLRQV RI RXU PRGHOV DQG WRXFK RQ KRZ GLIIHUHQW FRPSRVLWLRQV DQGRU JUDLQ PRUSKRORJ\ FKDQJHV RXU UHVXOWV 8VLQJ WKH RSWLFDO FRQVWDQWV IRU DVWURQRPLFDO VLOLFDWHV IURP /DRU DQG 'UDLQH f RXU UDGLDWLYH HTXLOLEULXP PRGHOV XVH 0LH WKHRU\ WR FDOFXODWH WKH DEVRUSWLRQ FRHIILFLHQWV 4DEVf RI GLIIHUHQW VL]HG SDUWLFOHV DW GLIIHUHQW GLVWDQFHV IURP WKH FHQWUDO VWDU

PAGE 59

2QFH ZH NQRZ KRZ HIILFLHQWO\ D SDUWLFOH RI D JLYHQ VL]H GLDPHWHU 'f HPLWV DQG DEVRUEV UDGLDWLRQ ZH FDQ ZRUN RXW ZKDW LWV WHPSHUDWXUH ZLOO EH DW DQ\ GLVWDQFH IURP WKH VWDU Uf E\ LWHUDWLYHO\ VROYLQJ WKH HTXDWLRQ IURP *XVWDIVRQ f 7'Uf >4DEV![r 4DEV!7'Uf@ [ 7EE f :KHUH 4DEV!Mr LV WKH DEVRUSWLRQ HIILFLHQF\ RI WKH JUDLQ DYHUDJHG RYHU WKH VWHOODU VSHFWUXP ZKLFK KDV EHHQ DSSUR[LPDWHG E\ D EODFNERG\ ZLWK WHPSHUDWXUH 7rf DQG 4DEV!M'Uf LV WKH VDPH TXDQWLW\ DYHUDJHG RYHU D EODFNERG\ VSHFWUXP RI WHPSHUDWXUH 7 7EE LV WKH HTXLOLEULXP WHPSHUDWXUH RI WKH JUDLQ LQ GHJUHHV .HOYLQ LI LW ZHUH D EODFNERG\ DQG LV JLYHQ E\ 7EE [ Un [ /r/f f ZKHUH U LV WKH GLVWDQFH RI WKH JUDLQ IURP WKH VWDU LQ $8 DQG /m LV WKH VWDUV OXPLQRVLW\ LQ XQLWV RI /# [ HUJ VHF :H FDQ DOVR FDOFXODWH WKH WKHUPDO HPLVVLRQ IURP WKH GXVW UHFHLYHG DW WKH (DUWK DW D JLYHQ ZDYHOHQJWK ,Q WKH RSWLFDOO\ WKLQ FDVH ZKLFK ZH DVVXPH IRU RXU VXUYH\ VRXUFHV WKLV FDQ EH ZULWWHQ DV )9; Uf 4DEV; 'f [ 4'f [ %9>; 7' Uf@ f ZKHUH 4DEVA 'f LV WKH JUDLQV HIILFLHQF\ DV D IXQFWLRQ RI ZDYHOHQJWK DQG GLDPHWHU e'f LV WKH VROLG DQJOH VXEWHQGHG E\ WKH JUDLQ DW WKH (DUWK DQG %Y>A 7' Uf@ LV WKH 3ODQFN IXQFWLRQ IRU WKH WHPSHUDWXUH RI WKH JUDLQ 8VLQJ WKH OXPLQRVLW\ DQG HIIHFWLYH WHPSHUDWXUH RI WKH VWDUV DORQJ ZLWK WKH DVVXPHG RSWLFDO SURSHUWLHV RI WKH JUDLQV RXU PRGHOV XVH HTXDWLRQV f DQG f WR FDOFXODWH WHPSHUDWXUHV IRU JUDLQV RI GLIIHUHQW VL]HV DW YDU\LQJ GLVWDQFHV IURP WKH VWDUV

PAGE 60

3DUWLFOH GLDPHWHU cMOP )LJXUH 0RGHO WHPSHUDWXUH FDOFXODWLRQV IRU VSKHULFDO 0LH SDUWLFOHV WR $8 IURP +' 7KH VKDSH WR WKH WHPSHUDWXUH FXUYHV LV GXH WR WKH FKDQJHV LQ WKH YDOXHV RI WKH JUDLQ HPLVVLRQ DQG DEVRUSWLRQ HIILFLHQFLHV 7KH VKDGLQJ PDUNV WKH WKUHH UHJLRQV GHVFULEHG LQ WKH WH[W 7R VKRZ DQ H[DPSOH RI RXU PRGHO WHPSHUDWXUH FDOFXODWLRQV LQ )LJXUH ZH SORW WKH FDOFXODWHG WHPSHUDWXUH DJDLQVW JUDLQ GLDPHWHU IRU SDUWLFOHV EHWZHHQ WR $8 IURP WKH VWDU +' D VRXUFH WKDW ZH UHVROYHG DW .HFN ,, VHH &KDSWHU f :H VHH WKDW JUDLQV DW WKHVH GLVWDQFHV UHDFK WHPSHUDWXUHV RI WR 7KLV LV WKH WHPSHUDWXUH UDQJH ZH GHULYH IRU WKH PDMRULW\ RI WKH VXUYH\ VRXUFHV WKDW KDYH ZHOO GHILQHG H[FHVV YDOXHV DQG LV RQH RI WKH FRQFOXVLRQV RI RXU ZRUN 7KDW LV WKH PLG,5 H[FHVV HPLVVLRQ IURP 9HJDOLNH VRXUFHV WUDFHV PDWHULDO WKDW LV DW WHPSHUDWXUHV EHWZHHQ WR 2QFH ZH KDYH FDOFXODWHG WKH WHPSHUDWXUH RI WKH JUDLQV DV D IXQFWLRQ RI GLVWDQFH IURP WKH VWDU DQG GLDPHWHU 7'Uf ZH FDQ XVH HTXDWLRQ f LQ FRQMXQFWLRQ ZLWK WKH JUDLQ

PAGE 61

-\6U DW [P )LJXUH 3ORWV RI HPLWWHG IOX[ GHQVLW\ SHU XQLW VROLG DQJOH DW SP OHIWf DQG SP ULJKWf IRU JUDLQV WR $8 +' 5HJLRQV VKDGHG DV GHVFULEHG LQ WH[W HIILFLHQFLHV WR FDOFXODWH WKH DPRXQW RI HPLVVLRQ IURP D JUDLQ DV D IXQFWLRQ RI ZDYHOHQJWK )9; Uf ,Q )LJXUH ZH SORW WKH HPLWWHG IOX[ GHQVLW\ SHU XQLW VROLG DQJOH LH VSHFLILFLQWHQVLW\f DW DQG SP IRU JUDLQV QHDU +' 7KLV LV WKH TXDQWLW\ 4DEV; 'f [ %YIW 7' Uf@ IURP WKH ULJKW KDQG VLGH RI HTXDWLRQ f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

PAGE 62

3DUWLFOH GLDPHWHU cMP )LJXUH )OX[ GHQVLW\ UDWLR SORW IRU +' 7KH FXUYHG OLQHV UHSUHVHQW WKH IOX[ GHQVLW\ UDWLR HPLWWHG E\ PRGHO JUDLQV EHWZHHQ WR $8 IURP +' 7KH KRUL]RQWDO OLQH PDUNV RXU REVHUYHG _LP SPf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

PAGE 63

,W LV WKH LQWHUDFWLRQ RI WKH DEVRUSWLRQ DQG HPLVVLRQ HIILFLHQFLHV RI WKH JUDLQ WKDW FDXVHV WKH VKDSH RI WKH FXUYHV LQ )LJXUHV DQG 7KLV f6f VKDSH LV FKDUDFWHULVWLF RI RXU PRGHOV DQG LV VHHQ WR VRPH H[WHQW LQ DOO RI WKH UHVXOWV IRU WKH VXUYH\ VRXUFHV 7KLV LV EHFDXVH LW LV XOWLPDWHO\ WKH DEVRUSWLRQ DQG HPLVVLRQ HIILFLHQFLHV WKDW GHWHUPLQH WKH HTXLOLEULXP WHPSHUDWXUH RI WKH JUDLQ ZLWK UHVSHFW WR WKH UDGLDWLRQ ILHOG 7KH WHPSHUDWXUH RI WKH JUDLQV WKHQ GHWHUPLQHV WKH DPRXQW RI HPLVVLRQ DW D JLYHQ ZDYHOHQJWK )LJXUH f DQG WKH UDWLR RI WKH HPLVVLRQ DW WZR ZDYHOHQJWKV LV KRZ ZH FRQQHFW WKH PRGHOV WR WKH REVHUYDWLRQV )LJXUH f 7KHUHIRUH WKH HIIHFWV RI WKH YDU\LQJ HIILFLHQFLHV DUH VHHQ GLUHFWO\ LQ DOO RI WKH YDULRXV PRGHO RXWSXWV 7KLV LV QRW VXUSULVLQJ VLQFH WKHVH DUH UDGLDWLYH HTXLOLEULXP PRGHOV ZKLFK PHDQV WKDW WKH LQWHUDFWLRQ RI WKH JUDLQV ZLWK UDGLDWLRQ LV WKH PRVW IXQGDPHQWDO SK\VLFDO SURFHVV ZLWK ZKLFK ZH DUH GHDOLQJ 7R GLVFXVV WKH UHDVRQV EHKLQG WKLV FKDUDFWHULVWLF f6f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t ,, WKH DEVRUSWLRQ HIILFLHQF\ UHDFKHV D PD[LPXP UHVXOWLQJ LQ WKH PD[LPXP JUDLQ WHPSHUDWXUH IRU D JLYHQ GLVWDQFH IURP WKH VWDU $V ZH PRYH WKURXJK UHJLRQ ,, WRZDUG

PAGE 64

UHJLRQ ,,, WKH DEVRUSWLRQ HIILFLHQF\ RI WKH JUDLQV VWD\V UHODWLYHO\ FRQVWDQW EXW WKH HPLVVLRQ HIILFLHQF\ LQFUHDVHV ZKLFK UHVXOWV LQ FRROHU WHPSHUDWXUHV IRU WKH JUDLQV 1HDU WKH ERXQGDU\ RI UHJLRQV ,, t ,,, WKH JUDLQ WHPSHUDWXUHV DFWXDOO\ GLS EHORZ WKH EODFNERG\ WHPSHUDWXUH IRU JUDLQV DW D JLYHQ GLVWDQFH IURP WKH VWDU 7KLV VHHPLQJO\ LQFRQJUXRXV UHVXOW VWHPV IURP WKH IDFW WKDW IRU JUDLQV ZLWK SP WKHLU HPLVVLRQ HIILFLHQF\ FDQ JR XS DV KLJK DV GXH WR HPLVVLRQ LQ VLOLFDWH UHVRQDQFHV DQG WKH\ EHFRPH VXSHU HIILFLHQW HPLWWHUV :\DWW HW DO f ,Q UHJLRQ ,,, ZH PRYH RXW RI WKH UHJLPH ZKHUH WKH\ JUDLQV DUH VXSHU HPLWWHUV DQG WKHLU WHPSHUDWXUH FOLPEV EDFN XS WRZDUG WKH EODFNERG\ WHPSHUDWXUH IRU JUDLQV DW WKDW GLVWDQFH IURP WKH VWDU 7KH VDPH RYHUDOO VKDSH FDQ EH VHHQ LQ WKH FXUYHV LQ )LJXUHV DQG :H KDYH VKDGHG WKHVH ILJXUHV VLPLODUO\ WR LOOXVWUDWH WKH WKUHH UHJLRQV 7KH HIIHFWV RI WKH FKDQJLQJ HIILFLHQFLHV DUH HVSHFLDOO\ HYLGHQW LQ )LJXUH VLQFH WKHUH ZH DUH ORRNLQJ DW WKH TXDQWLW\ 4DEV$ 'f [ %9>$ 7' Uf@ DQG WKH YDULDWLRQV LQ 4DEV GLUHFWO\ FKDQJH WKH VKDSH RI WKH SORWV &RORU 7HPSHUDWXUHV DQG 2SWLFDO 'HSWKV :H FDQ DOVR XVH HTXDWLRQ f WR FDOFXODWH D YDOXH IRU WKH PLG,5 RSWLFDO GHSWK RI WKH PDWHULDO DURXQG WKH VXUYH\ VRXUFHV ,I ZH XVH RXU VL]H OLPLWV LQ 7DEOH WR FDOFXODWH D YDOXH IRU WKH VROLG DQJOH e'ff VXEWHQGHG E\ WKH HQWLUH PLG,5HPLWWLQJ UHJLRQ DQG QRWH WKDW 4DEV 7Y WKURXJK WKH UHODWLRQ 7 WF'f [ 4DEV [ QG [/ f ZKHUH W'f LV WKH FURVV VHFWLRQDO DUHD RI D JUDLQ ZLWK GLDPHWHU QG LV WKH QXPEHU GHQVLW\ RI WKH JUDLQV DORQJ WKH OLQH RI VLJKW DQG / LV WKH OLQHRIVLJKW SDWK OHQJWK ZH FDQ WKHQ VROYH IRU D FRQVLVWHQW 7 7 SDLU 8VLQJ RXU REVHUYDWLRQV DW WKH WZR GLIIHUHQW

PAGE 65

ZDYHOHQJWKV DQG SPf DQG HTXDWLRQ f ZH WKHQ KDYH WZR HTXDWLRQV DQG WZR XQNQRZQV IRU WKH WHPSHUDWXUH DQG [ IRU WKH PLG,5HPLWWLQJ GXVW )LR QP e [ [R [ %Y> SP 7@ f DQG )LQP e [ WL [ %Y> SP 7@ f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f FDQ EH FDOFXODWHG IURP LWV RSWLFDO FRQVWDQWV XVLQJ 0LH WKHRU\ 4SU LV UHODWHG WR LWV DEVRUSWLRQ DQG VFDWWHULQJ HIILFLHQFLHV WKURXJK WKH UHODWLRQ 4SU 4DEV 4VFD FRV !f ZKHUH WKH FRV WHUP DFFRXQWV IRU WKH IDFW WKDW UDGLDWLRQ LV VFDWWHUHG DV\PPHWULFDOO\ IURP WKH SDUWLFOHV :\DWW HW DO f 2QFH ZH KDYH 4SU FDOFXODWHG ZH FDQ FRQVLGHU WKH UDWLR RI WKH UDGLDWLRQ IRUFHV DFWLQJ RQ WKH SDUWLFOH WR WKH JUDYLWDWLRQDO IRUFHV DV D IXQFWLRQ RI SDUWLFOH GLDPHWHU 7KLV UDWLR FDOOHG > LV JLYHQ E\ WKH UHODWLRQ EHORZ

PAGE 66

)LJXUH 7KH TXDQWLW\ 3 DV D IXQFWLRQ RI JUDLQ GLDPHWHU IRU SDUWLFOHV QHDU +' +RUL]RQWDO OLQH PDUNV D YDOXH RI 3DUWLFOHV ZLWK 3 ZLOO EH UHPRYHG IURP WKH V\VWHP RQ K\SHUEROLF RUELWV LQ \U 3'f &S'f 4SU!7r /r/#f 00f f ZKHUH & n NJ Pnf S LV WKH SDUWLFOH GHQVLW\ LV WKH SDUWLFOH GLDPHWHU DQG 4SU![} 4SU'$f )[ G$ c )? G$ LV WKH SDUWLFOHfV UDGLDWLRQ SUHVVXUH HIILFLHQF\ DYHUDJHG RYHU WKH VWHOODU VSHFWUXP ZLWK DVVXPHG WHPSHUDWXUH 7r :\DWW HW DO f %\ FDOFXODWLQJ 3 DV D IXQFWLRQ RI SDUWLFOH GLDPHWHU ZH FDQ GHWHUPLQH ZKDW VL]HG SDUWLFOHV ZLOO EH UHPRYHG IURP WKH V\VWHP WKURXJK UDGLDWLRQ H[SXOVLRQ 3DUWLFOHV ZLWK 3 ZLOO EH UHPRYHG IURP WKH V\VWHP E\ UDGLDWLRQ H[SXOVLRQ RQ YHU\ VKRUW WLPHVFDOHV 2Q DYHUDJH WKH WLPH IRU UHPRYDO IRU WKH VXUYH\ VWDUV LV \U )LJXUH VKRZV 3'f IRU +' 7KH KRUL]RQWDO OLQH PDUNV 3 8VLQJ )LJXUH ZH VHH WKDW IRU +' DOO SDUWLFOHV VPDOOHU WKDQ SP KDYH S DQG ZLOO EH UHPRYHG IURP WKH V\VWHP TXLFNO\ :H FDQ WKHUHIRUH PDNH WKH FODLP WKDW JUDLQV

PAGE 67

ZLWK _LP DUH OLNHO\ QRW SULPRUGLDO DQG KDYH EHHQ UHSOHQLVKHG E\ VRPH PHFKDQLVP 7KH GHWHUPLQDWLRQ RI ZKHWKHU RU QRW WKH PLG,5HPLWWLQJ JUDLQV LQ WKH VXUYH\ GLVNV LV DQ LPSRUWDQW FRQFOXVLRQ RI WKH PRGHOLQJ VLQFH WKH SUHVHQFH RI fVHFRQGJHQHUDWLRQf GXVW LQ WKHVH GLVNV SODFHV WKHP ILUPO\ LQ WKH 9HJDOLNH FODVV /DJUDQJH HW DO f 3ORWV VLPLODU WR )LJXUH IRU DOO WKH PRGHOHG VXUYH\ VRXUFHV DOORZ XV WR VHW D OLPLW RQ WKH PLQLPXP VL]H RI JUDLQV WKDW ZRXOG QRW EH UHPRYHG IURP WKH V\VWHP WKURXJK UDGLDWLRQ H[SXOVLRQ 7KHVH f3/LPLWLQJf VL]HV DUH JLYHQ LQ WKH ODVW FROXPQ RI 7DEOH 7R UHLWHUDWH DOO JUDLQV VPDOOHU WKDQ WKH f3 /LPLWLQJf VL]H LH WKH EORZRXW VL]Hf ZLOO EH UHPRYHG IURP WKH V\VWHP E\ UDGLDWLRQ H[SXOVLRQ $QRWKHU G\QDPLFDO SURSHUW\ ZH LQYHVWLJDWH LV WKH OLIHWLPH RI WKH GLVN SDUWLFOHV ZLWK UHVSHFW WR 3R\QWLQJ5REHUWVRQ GUDJ 35 GUDJf 2QFH ZH KDYH FDOFXODWHG S'f ZH XVH WKH IROORZLQJ UHODWLRQ WR FDOFXODWH WKH 35 GUDJ OLIHWLPHV RI WKH JUDLQV DV D IXQFWLRQ RI GLDPHWHU WS5'f 2200fU3'ff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

PAGE 68

7DEOH 'HULYHG *UDLQ 3DUDPHWHUV 6RXUFH 1DPH 0LG,5 &RORU 7HPS .f IPLG,5 *UDLQ VL]H XSSHU OLPLW SPf *UDLQ 'LVWDQFH 8SSHU /LPLW $8f 0D[ 35 'UDJ /LIHWLPH \Uf /LPLWLQJ VL]H SPf +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' n ( ( f§ +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( +' ( ( 0HDQ YDOXHV SP $8 ( \U SP r 3 IRU DOO JUDLQ VL]HV DUH QRW SULPRUGLDO PDWHULDO DQG KDYH EHHQ UHSOHQLVKHG LQ VRPH ZD\ 2QH PHWKRG RI UHSOHQLVKPHQW LV WKURXJK WKH FROOLVLRQV RI ODUJHU ERGLHV LQ WKH GLVNV 5HSOHQLVKPHQW RI PDWHULDO LQ WKLV PDQQHU LV DSSDUHQWO\ RFFXUULQJ LQ WKH DUFKHW\SDO 9HJDOLNH GLVNV RI ERWK 3 3LFWRULV $UW\PRZLF] f DQG +5 $ :\DWW HW DO 7HOHVFR HW DO f

PAGE 69

7KH ODVW URZ RI 7DEOH FRQWDLQV WKH PHDQ YDOXHV RI HDFK RI WKH TXDQWLWLHV OLVWHG LQ WKH WDEOH :H FDOFXODWH WKHVH QXPEHUV VLPSO\ WR JLYH DQ LGHD RI WKH SURSHUWLHV RI WKHVH GLVNV LQ WKH EURDGHVW VHQVH &HUWDLQO\ WKHVH YDOXHV DUH RQO\ XVHIXO DV EHQFKPDUNV IRU WKH VXUYH\ VRXUFHV KRZHYHU LW LV LQWHUHVWLQJ WR FRPSDUH WKHP ZLWK YDOXHV IURP RWKHU 9HJDn OLNH GLVNV ,Q SDUWLFXODU WKH PHDQ XSSHU OLPLW WR WKH PLG,5HPLWWLQJ JUDLQV VL]H LV YHU\ FRQVLVWHQW ZLWK WKH JUDLQ VL]HV LQ RWKHU 9HJDOLNH GLVNV 6LPLODU PRGHOLQJ RI WKH +5 $ GLVN E\ :\DWW HW DO f DQG 7HOHVFR HW DO f VKRZV WKDW WKH JUDLQV LQ WKDW GLVN DUH DSSUR[LPDWHO\ SP LQ GLDPHWHU 0LG,5 DSHUWXUH SKRWRPHWU\ RI 3LFWRULV LPSOLHV WKHUH DUH WR SP JUDLQV LQ WKDW DUFKHW\SDO GLVN 7HOHVFR HW DO 7HOHVFR t .QDFNH $LWNHQ HW DO f 9HJD LWVHOI LV DOVR UHSRUWHG WR KDYH WR SP JUDLQV DV WKH GRPLQDQW SRSXODWLRQ LQ LWV GLVN 9DQ GHU %OLHN 3UXVWL t :DOWHUV f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

PAGE 70

7DEOH &RPSDULVRQ RI 8QUHVROYHG VRXUFHV WR $UFKHW\SDO 'LVNV 6RXUFH 1DPH 3UHGLFWHG DQJXODU VL]H DUFVHFf 6L]H DW 'KU $ DUFVHFf 6L]H DW 'S 5H DUFVHFf 6L]H RI 3 3LF DW 'VRXUFH 6L]H RI +5 $ DW '6RXUFH +' +' +' +' +' +' +' +' n +' +' +' +' +' +' +' +' +' +' +' +' +' +' r L /LNHO\ QRW D PDLQVHTXHQFH VWDU VXUYH\ VRXUFHV LV SF ZKLOH 3 3LFWRULV LV DW SF DQG +5 $ LV DW SF 7R DQVZHU WKLV TXHVWLRQ ZH fPRYHGf WKH XQUHVROYHG VRXUFHV WR WKH GLVWDQFHV WR WKRVH DUFKHW\SHV DQG FDOFXODWHG ZKDW WKHLU PRGHO SUHGLFWHG VL]H ZRXOG EH ,Q WKLV DQDO\VLV ZH DVVXPH WKDW WKH PD[LPXP H[WHQW RI WKH PLG,5HPLWWLQJ JUDLQV IURP WKH VWDUV LV JLYHQ E\ WKH XSSHU OLPLWV UHWXUQHG E\ RXU PRGHOV ZKLFK DUH OLVWHG LQ 7DEOH 8VLQJ WKHVH YDOXHV LQ FRQMXQFWLRQ ZLWK WKH GLVWDQFH HVWLPDWHV IRU WKH VWDUV JLYHQ LQ 7DEOH ZH FDQ

PAGE 71

FDOFXODWH D SUHGLFWHG DQJXODU VL]H IRU HDFK RI WKH GLVNV :H WKHQ VFDOHG WKRVH SUHGLFWHG VL]HV WR ZKDW WKH\ ZRXOG EH DW WKH GLVWDQFHV RI 3 3LFWRULV DQG +5 $ 7KHVH SUHGLFWHG DQG VFDOHG VL]HV DUH OLVWHG LQ 7DEOH $VVXPLQJ WKDW ZH DUH XVLQJ DQ WR P FODVV WHOHVFRSH WR PDNH WKH REVHUYDWLRQV E\ DQDORJ\ ZLWK +' &KDSWHU f ZH VHW WKH WKUHVKROG RI GHWHFWLRQ DW DQ DQJXODU VL]H f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b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

PAGE 72

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a $8 RI WKHLU VWDUV DQG KDYH GLDPHWHUV RI a _LP &RPSDUHG WR WKH a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fELUGfV QHVWf VWUXFWXUH 7KH fELUGfV QHVWf OLNH DSSHDUDQFH RI WKHVH JUDLQV RFFXUV EHFDXVH WKH JUDLQ LWVHOI LV DFWXDOO\ DQ DJJUHJDWH RI WHQV RU KXQGUHGV RI VPDOOHU SDUWLFOHV WKDW KDYH VWXFN WRJHWKHU WKURXJK FROOLVLRQV *XVWDIVRQ f $V QRWHG ZH KDYH DVVXPHG WKDW WKH REVHUYHG JUDLQV DUH VROLG DQG VSKHULFDO +RZHYHU LI WKH JUDLQV DUH DFWXDOO\ DJJUHJDWHV DQG FRPSOH[ LQ

PAGE 73

DSSHDUDQFH fIOXII\ff RXU RYHUDOO FRQFOXVLRQV DERXW SDUWLFOH OLIHWLPHV DUH QRW VLJQLILFDQWO\ FKDQJHG *XVWDIVRQ f SRLQWV RXW WKDW 0LH FDOFXODWLRQV IRU KRPRJHQHRXV VSKHUHV FRQVLVWHQWO\ XQGHUHVWLPDWH WKH YDOXH RI IRU DJJUHJDWHG GXVW PRGHOV E\ D IDFWRU RI WZR )RU RXU VXUYH\ VRXUFHV WKLV PHDQV WKDW HYHQ ODUJHU SDUWLFOHV ZRXOG KDYH DQG ZRXOG EH H[SHOOHG IURP WKH VWDUGLVN V\VWHPV LQ D VKRUW WLPH 6LQFH WKH 35 GUDJ OLIHWLPH RI D SDUWLFOH LV SURSRUWLRQDO WR BO :\DWW HW DO f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

PAGE 74

SUREDEO\ UHSOHQLVKHG SODFHV WKHP ILUPO\ LQWR WKH GHEULV GLVN FODVV DQG WKH VLPLODULW\ LQ WKHLU JUDLQ VL]HV WHPSHUDWXUHV DQG GLVWDQFHV IURP WKH FHQWUDO VWDUV WR WKRVH RI WKH DUFKHW\SHV LPSOLHV WKDW WKH\ DUH DW D VLPLODU HYROXWLRQDU\ VWDWH ,Q WKH IROORZLQJ VHFWLRQV ZH H[SDQG RQ WKLV LGHD RI VRXUFH HYROXWLRQ DQG SUHVHQW DQ HYROXWLRQDU\ VHTXHQFH IRU WKH VXUYH\ VWDUV $ 3URSRVHG (YROXWLRQDU\ 6HTXHQFH ,Q WKLV VHFWLRQ ZH SUHVHQW DQ HYROXWLRQDU\ VHTXHQFH ZH KDYH FRQVWUXFWHG IRU RXU VXUYH\ VRXUFHV XVLQJ WKH SURSHUWLHV RI WKHLU PLG,5 H[FHVVHV LQ FRQMXQFWLRQ ZLWK WKH FKDUDFWHULVWLFV RI WKH VWDUV 7KH LGHD WKDW WKH +HUELJ $H%H VWDUV DUH WKH SURJHQLWRUV RI WKH 9HJDOLNH VWDUV LV ZHOO UHSUHVHQWHG LQ WKH OLWHUDWXUH FI /DJUDQJH HW DO YDQ GHQ $QFNHU HW DO f 7UHQGV VHHQ LQ WKH FKDUDFWHULVWLFV RI SURSHUWLHV RI GLVNV DOVR VXSSRUW VXFK DQ HYROXWLRQ )RU H[DPSOH +ROODQG HW DO f VHHV D VWURQJ WUHQG RI GHFUHDVLQJ GLVN PDVV ZLWK DJH 7KHLU )LJXUH FOHDUO\ VKRZV WKDW WKH PDVV RI WKH GXVW DVVRFLDWHG ZLWK +HUELJ $H%H VWDUV LV RUGHUV RI PDJQLWXGHV JUHDWHU WKDQ WKDW LQ WKH WHQXRXV GLVNV LQ RXU VDPSOH +ROODQG HW DO f 0RUH UHOHYDQW WR WKH GLVFXVVLRQ RI RXU HYROXWLRQDU\ VHTXHQFH LV WKH WUHQG VHHQ LQ WKH HYROXWLRQ RI WKH VSHFWUDO HQHUJ\ GLVWULEXWLRQV 6('f RI VRXUFHV ZLWK DVVRFLDWHG FLUFXPVWHOODU GXVW %HORZ ZH GLVFXVV KRZ WKLV LGHD LV GLUHFWO\ UHODWHG WR RXU VXUYH\ VRXUFHV 6(' (YROXWLRQ )RU D JUDSKLFDO UHSUHVHQWDWLRQ RI ZKDW 6(' HYROXWLRQ ORRNV OLNH ZH UHLQWURGXFH WKH VFKHPH RI $QGUH f LQ )LJXUH 7KLV ILJXUH VKRZV KRZ WKH 6(' RI D VWDUGLVN

PAGE 75

)LJXUH 6(' HYROXWLRQ RI D VWDUGLVN V\VWHP PRYLQJ RQWR WKH =$06 0RVW RI RXU VXUYH\ VRXUFHV IDOO LQWR &ODVV ,,, EXW D VPDOO QXPEHU RI WKHP H[KLELW VRPH FKDUDFWHULVWLFV RI D &ODVV ,, VRXUFH 8VLQJ RXU VXUYH\ VRXUFHV ZH UHILQH WKH &ODVV ,,, JURXS KHUH E\ VXEn GLYLGLQJ LW LQWR WKUHH VPDOOHU SDUWV V\VWHP HYROYHV GXULQJ WKH ILUVW IHZ 0\U RI LWV H[LVWHQFH 7KH PRVW LPSRUWDQW WUHQG WR QRWLFH LQ UHJDUGV WR RXU SURSRVHG DGGLWLRQV WR WKLV VHTXHQFH LV KRZ WKH RYHUDOO DPRXQW RI H[FHVV HPLVVLRQ GHFUHDVHV DV WKH V\VWHP HYROYHV 7KDW LV DV WKH V\VWHP HYROYHV OHVV RI WKH RYHUDOO LQIUDUHG OXPLQRVLW\ FRPHV IURP WKH FLUFXPVWHOODU GXVW DQG WKH 6(' RI WKH V\VWHP DSSURDFKHV WKDW RI WKH VWDU LWVHOI D VLPSOH EODFNERG\ FXUYH %\ WKH WLPH WKH

PAGE 76

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f&ODVV ,OLDf VLQFH WKH 6(' RI WKHVH VRXUFHV LV VLPLODU WR WKDW RI D VRXUFH WKDW KDV MXVW HYROYHG LQWR &ODVV ,,, LQ WKH $QGUH f VFKHPH 7KH PLGGOH SDQHO RI )LJXUH VKRZV WKH 6(' RI +' D VRXUFH WKDW IDOOV LQWR RXU VHFRQG VXEFODVV QDPHG &ODVV ,OOEf $ORQJ ZLWK +' WKH RWKHU WKUHH PHPEHUV RI WKLV JURXS UHSUHVHQW DQ LQWHUPHGLDWH VWDJH RI HYROXWLRQ ZLWKLQ RXU VXUYH\ 7KH IRXU VRXUFHV LQ &ODVV ,OOE H[KLELW QR QHDU,5 H[FHVV KRZHYHU WKH\ DOO KDYH ZHOO GHILQHG H[FHVVHV LQ WKH PLG,5 3URFHVVLQJ RI WKH LQQHU GLVN UHJLRQV LV PRVW OLNHO\ VWLOO RQJRLQJ LQ WKHVH VRXUFHV ,QWHUHVWLQJO\ WKUHH RXW RI

PAGE 77

OH OH OH OH :DYHOHQJWK MDPf OH OH OH OH :DYHOHQJWK cDPf OH OH OH OH )LJXUH 6(' HYROXWLRQ ZLWKLQ RXU VXUYH\ WRSf 6(' RI +' 1RWH WKH VWURQJ QHDU,5 H[FHVV DVVRFLDWHG ZLWK WKLV VRXUFH PLGGOHf 6(' RI +' 7KLV VRXUFH UHSUHVHQWV DQ LQWHUPHGLDWH HYROXWLRQDU\ VWHS 7KHUH LV QR QHDU,5 H[FHVV DVVRFLDWH ZLWK WKLV VWDU ERWWRPf 6(' RI +' D VRXUFH WKDW UHSUHVHQWV WKH ODVW VWDJH RI HYROXWLRQ ZLWKLQ RXU VXUYH\ 1R QHDU,5 RU PLG,5 H[FHVV LV DVVRFLDWHG ZLWK WKLV VWDU

PAGE 78

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f ZKLFK H[KLELWV D VWURQJ QHDU,5 H[FHVV DV VHHQ LQ )LJXUH /LVWHG LQ 6\OYHVWHU HW DO f ZH VHH WKDW WKH QLQH VRXUFHV KDYH DQ DYHUDJH RI PDJ RI H[FHVV DW SP DQG PDJ RI H[FHVV DW SP 6\OYHVWHU HW DO f DOVR FDOFXODWHG EODFNERG\ ILWV WR WKH QHDU,5 H[FHVVHV RI WKH VRXUFHV DQG IRXQG WKDW JUDLQ WHPSHUDWXUHV LQ WKH UDQJH RI WR ILW WKH H[FHVV ZHOO ,Q RXU RZQ DQDO\VLV RI WKHVH VRXUFHV ZH ILQG WKDW WKH &ODVV ,OLD VWDUV H[KLELW RXW RI WKH WRS KLJKHVW PLG,5 RSWLFDO GHSWKV VHH 7DEOH f 7KH IDFW WKDW WKHVH VWDUV KDYH QHDU,5 H[FHVV DQG UHODWLYHO\ KLJK RSWLFDO GHSWKV PDNHV WKHP VLPLODU WR +HUELJ $H%H VWDUV DQG WKH\ DUH WKHUHIRUH PRVW OLNHO\ \RXQJ ,QGHHG DW OHDVW RI WKH &ODVV ,OLD VWDUV VKRZ K\GURJHQ HPLVVLRQ OLQHV LQ WKHLU VSHFWUD 6\OYHVWHU HW DO f DQRWKHU VLJQ RI

PAGE 79

:DYHOHQJWK -LPf )LJXUH 6(' RI +' ZLWK $fn SORWWHG IRU FRPSDULVRQ 7KH GLDPRQGV DUH IOX[ HVWLPDWHV IRU +' IURP 6\OYHVWHU HW DO f 6TXDUHV DUH RXU 26&,5 IOX[HV 7KH VROLG OLQH LV D EODFNERG\ IXQFWLRQ ZLWK 7HII 7KH GDVKHG OLQH IROORZV WKH UHODWLRQ )$f D $f \RXWK DV FRPSDUHG WR WKH RWKHU VXUYH\ VRXUFHV 6LQFH LW VHHPV WKHVH VRXUFHV DUH WKH \RXQJHVW LQ RXU VXUYH\ ZH XVH WKHVH VRXUFHV DV WKH VWDUWLQJ SRLQW LQ RXU HYROXWLRQDU\ VHTXHQFH 2QH RI WKH PDLQ GLVWLQFWLRQV EHWZHHQ &ODVV ,, DQG &ODVV ,,, VRXUFHV LV ZKHWKHU WKHLU GLVN LV RSWLFDOO\ WKLFN RU WKLQ &ODVV ,, VRXUFHV KDYH RSWLFDOO\ WKLFN GLVNV ZKLOH WKRVH DVVRFLDWHG ZLWK &ODVV ,,, VWDUV DUH RSWLFDOO\ WKLQ $V QRWHG E\ +LOOHQEUDQG HW DO f RQH RI WKH PRVW SRZHUIXO GLDJQRVWLFV RI D FLUFXPVWHOODU GLVN LV LWV 6(' LQ WKH QHDU,5 _LP $ SPf 2EMHFWV ZLWK IODW RSWLFDOO\ WKLFN GLVNV KDYH 6('V WKDW IROORZ D ; IDOORII ZDYHOHQJWK 7KLV IDFW JLYHV XV D FULWHULRQ ZH FDQ HPSOR\ WR SODFH RXU VXUYH\ VRXUFHV LQWR WKH FRUUHFW FODVV :H NQRZ WKDW DQ\ RSWLFDOO\ WKLFN GLVNV ZLOO IROORZ WKDW

PAGE 80

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t 5\DQ f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f ,QWHUHVWLQJO\ RXW RI WKH VRXUFHV 3LFWRULV +5 $ DQG +' f LQ WKLV FODVV KDYH EHHQ UHVROYHG LQ WKH PLG,5 :LWK UHVSHFW WR KRZ WKHVH VRXUFHV ILW LQWR WKH HYROXWLRQDU\ VHTXHQFH ZH FDQ DVN WKH TXHVWLRQ KRZ \RXQJ DUH WKH\" /XFNLO\ IRU WKLV VXEFODVV ZH KDYH DQ DQVZHU IRU WKDW

PAGE 81

TXHVWLRQ 2QH RI WKH &ODVV ,OOE PHPEHUV LV +5 $ ZKLFK KDV D ZHOOFRQVWUDLQHG DJH RI s 0\U 6WDXIIHU HW DO f 5HFHQW ZRUN E\ %DUUDGR \ 1DYDVFXHV HW DO f XVHV +LSSDUFRV GDWD DQG HYROXWLRQDU\ WUDFNV WR HVWLPDWH WKH DJH RI WKH DUFKHW\SH 3LFWRULV DW s 0\U VLPLODU WR WKH DJH RI +5 $ 7KH WKLUG UHVROYHG VRXUFH +' KDV QR SXEOLVKHG DJH YDOXHV +RZHYHU ZH VKRZ LQ &KDSWHU WKDW LW LV OLNHO\ D VRXUFH WKDW LV WUDQVLWLRQLQJ IURP WKH +HUELJ $H%H FODVV WR WKH 9HJDOLNH FODVV /DJUDQJH HW DO f FRLQ WKH WHUP fROGSUHPDLQVHTXHQFHf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

PAGE 82

7DEOH (YROXWLRQDU\ &ODVV FKDUDFWHULVWLFV &ODVV 1DPH 6KRUWHVW ([FHVV :DYHOHQJWK SPf $JH 0\Uf +5 'LDJUDP 3RVLWLRQ &ODVV &KDUDFWHULVWLFV +D HPLVVLRQ LQ VSHFWUD &ODVV ,OLD WR 3UH=$06 /L VHHQ LQ VRXUFH VSHFWUD 6WURQJ QHDU,5 H[FHVV QR QHDU,5 H[FHVV &ODVV ,OOE WR =$06 VWURQJ PLG,5 H[FHVV *RRG DJH HVWLPDWHV &ODVV ,,,F ! 3RVW=$06 OLWWOH RU QR PLG,5 H[FHVV QR VLJQDWXUHV RI \RXWK IRUP D QHZ FODVV f&ODVV ,9f LQ WKH VFKHPHV RI $QGUH f DQG +LOOHQEUDQG HW DO f $ FODVV WKDW ZRXOG UHSUHVHQW VRXUFHV DOUHDG\ RQ WKH PDLQ VHTXHQFH FRPSOHWHO\ ILQLVKHG ZLWK WKH IRUPDWLRQ DQG 306 HYROXWLRQ ,Q 7DEOH ZH VXPPDUL]H WKH FKDUDFWHULVWLFV RI WKH QHZ VXEJURXSV 7R TXDQWLI\ WKH LGHD RI 6(' HYROXWLRQ ZH OLVW WKH ZDYHOHQJWKV DW ZKLFK WKH H[FHVV fWXPVRQf IRU HDFK FODVV DQG VKRZ WKDW LW LQFUHDVHV ZLWK DJH :H DOVR OLVW DSSUR[LPDWH DJHV IRU HDFK RI WKH JURXSV DQG WKHLU FRUUHVSRQGLQJ SRVLWLRQ LQ WKH +5 GLDJUDP )LQDOO\ ZH FRPPHQW RQ VRPH RI WKH FRPPRQ FKDUDFWHULVWLFV IRU HDFK RI WKH VXEFODVVHV WKDW ZH XVH WR WLH HDFK JURXS WRJHWKHU ,Q WKH QH[W DQG ILQDO VHFWLRQ RI WKLV FKDSWHU ZH XVH WKH +5 GLDJUDP WR JUDSKLFDOO\ LOOXVWUDWH RXU SURSRVHG HYROXWLRQDU\ VHTXHQFH

PAGE 83

6XUYH\ 6RXUFHV LQ WKH +5 'LDJUDP ,W LV XVHIXO WR LQYHVWLJDWH WKH SRVLWLRQ RI RXU VXUYH\ VRXUFHV LQ WKH +5 GLDJUDP 6XFK DQ LQYHVWLJDWLRQ DOORZV XV WR JUDSKLFDOO\ VHH KRZ WKH VXUYH\ ILWV LQWR WKH RYHUDOO VFKHPH RI VWHOODU HYROXWLRQ DQG LW JLYHV XV DQRWKHU ZD\ WR SUHVHQW RXU HYROXWLRQDU\ VHTXHQFH )RU WKLV SXUSRVH ZH XVH D +5 GLDJUDP FRPSULVHG RI VWDUV WDNHQ IURP WKH +LSSDUFRV GDWDEDVH 3HUU\PDQ HW DO f :H KDYH +LSSDUFRV PHDVXUHG GLVWDQFHV IRU b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a 0\U 1RWLFH WKDW ZH FDQ QRZ VHH WKDW WKH\ DOO KDYH ORZ OXPLQRVLWLHV IRU WKHLU FRORUV DV UHSRUWHG E\ -XUD HW DO f 6LQFH WKH\ DUH YHU\ FORVH WR WKH =$06 ZH XVH WKHP DV D XVHIXO ILGXFLDO SRLQW LQ WKH VHTXHQFH 7KHVH VRXUFHV DUH VRPHZKDW RI D IXOFUXP SRLQW

PAGE 84

% 9 >PDJ@ )LJXUH 7KH 9HJDOLNH VXUYH\ VRXUFHV LQ WKH +5 GLDJUDP 7KLV ILJXUH VKRZV WKH VRXUFHV RI WKH VXUYH\ SORWWHG LQ D +5 GLDJUDP FRPSULVHG RI VWDUV IURP WKH +LSSDUFRV FDWDORJ 7KH IRXU VTXDUHV DUH WKH SRVLWLRQ RI WKH GLVNV WKDW KDYH EHHQ UHVROYHG LQ WKH PLG,5 3 3LFWRULV +5 $ +' DQG &HWL 7KH DUURZ LV D UHGGHQLQJ YHFWRU +LSSDUFRV GDWD IURP 3HUU\PDQ HW DO f

PAGE 85

)LJXUH 7KUHH VWHSV LQ DQ HYROXWLRQDU\ VHTXHQFH RQ WKH +5 GLDJUDP Df 6WHS &ODVV ,OLD VRXUFHV VWDUV PRYLQJ RQWR WKH =$06 Ef 6WHS &ODVV ,OOE VRXUFHV VWDUV ZKLFK DUH RQ WKH =$06 Ff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f RYHUODLG 8VLQJ WKH WUDFNV ZH GHWHUPLQH DJH HVWLPDWHV IRU WKH &ODVV ,OLD VRXUFHV LQ WKH UDQJH RI WR 0\U FRQVLVWHQW ZLWK WKHP EHLQJ \RXQJHU WKDQ WKH &ODVV ,OOE VWDUV ,QGHHG WKH &ODVV ,OOE VWDUV OLH DW WKH HQG RI WKH 306 WUDFNV ZKLOH WKH &ODVV ,OLD VRXUFHV ORRN WR EH VWLOO IROORZLQJ WKHP RQWR WKH =$06 7KH LVRFKURQHV RI ,EHQ f DJUHH ZLWK WKH DJH HVWLPDWHV JLYHQ E\ WKH 306 WUDFNV ,Q )LJXUH ZH VHH WKDW PRVW RI WKH &ODVV ,OLD VRXUFHV OLH EHWZHHQ WKH 0\U DQG 0\U LVRFKURQHV

PAGE 86

_ A L L L ‘ ‘ O O L O O L L OLOW % 9 >PDJ@ )LJXUH +5 'LDJUDP ZLWK WKH 306 HYROXWLRQDU\ WUDFNV IRU LQWHUPHGLDWH PDVV VWDUV RI 3DOOD DQG 6WDKOHU f RYHUODLG 7KH VWHOODU ELUWK OLQH LV WKH GRWWHG OLQH 7KH PDVV DVVRFLDWHG ZLWK HDFK HYROXWLRQDU\ WUDFN LV JLYHQ RQ WKH OHIW LQ XQLWV RI 0 7LFN PDUNV RQ HDFK WUDFN FRUUHVSRQG WR WKH WLPHV OLVWHG LQ WKH OHJHQG $JH HVWLPDWHV IRU WKHVH VRXUFHV DUH LQ WKH WR 0\U UDQJH

PAGE 87

% 9 >PDJ@ )LJXUH +5 'LDJUDP ZLWK WKH LVRFKURQHV RI ,EHQ f RYHUODLG $OVR SORWWHG DUH WKH &ODVV ,OLD DQG &ODVV ,OOE VWDUV &ODVV ,OLD FLUFOHVf DQG &ODVV ,OOE VTXDUHVf VWDUV DUH SORWWHG IRU FRPSDULVRQ 7KH WLPHV WR UHDFK HDFK LVRFKURQH LV JLYHQ RQ WKH OHIW VLGH RI HDFK

PAGE 88

$V QRWHG E\ /DJUDQJH HW DO f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fGHfUHVROYH WKH VRXUFH 6$2 ,Q &KDSWHU ZH GLVFXVV WKH 26&,5 FDPHUD V\VWHP DQG LWV LPSRUWDQW UROH LQ WKLV GLVVHUWDWLRQ

PAGE 89

&+$37(5 7+( )$&(21 ',6. 2) +' ,Q WKLV FKDSWHU ZH SUHVHQW .HFN LPDJLQJ RI WKH VRXUFH +' 2XU LPDJHV VKRZ WKH VRXUFH WR EH UHVROYHG DW ERWK DQG SP ZLWK VWURQJO\ GHWHFWHG H[WHQGHG HPLVVLRQ VHHQ LQ WKH IRUP RI D VHHPLQJO\ IDFHRQ GLVN ZLWK GLDPHWHU DSSUR[LPDWHO\ HTXDO WR f $W D GLVWDQFH RI SF 6\OYHVWHU HW DO f WKLV FRUUHVSRQGV WR D UDGLDO H[WHQW IRU WKH PLG,5 HPLWWLQJ GXVW RI $8 ZKLFK LV YHU\ VLPLODU WR WKH VL]H RI WKH PLG,5 HPLWWLQJ UHJLRQV RI WKH DUFKHW\SH S 3LFWRULV DQG WKH VRXUFH +' /DJDJH t 3DQWLQ )LVKHU HW DO f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fJOREDOf GXVW SDUDPHWHUV :H WKHQ XVH RXU GHULYHG JUDLQ SDUDPHWHUV WR GLVFXVV WKH SRVVLEOH

PAGE 90

7DEOH &KDUDFWHULVWLFV RI +' 6SHFWUDO 7\SH $ 9Hr 7HII .r 'LVWDQFH SFr ORJ J r %9f r 00t i 0Y r // i Y VLQLnf s NPVHFr r W 'XQNLQ %DUORZ t 5\DQ f 6\OYHVWHU HW DO f i $OOHQ f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f EXW KDV VLQFH EHHQ UHFODVVLILHG DV $ 9 XVLQJ KLJK UHVROXWLRQ RSWLFDO VSHFWURVFRS\ 'XQNLQ %DUORZ t 5\DQ f 5HFHQW SKRWRPHWU\ KDV DOVR UHILQHG WKH URWDWLRQ VSHHG RI WKH VRXUFH DQG SRODULPHWU\ RI WKH VRXUFH DQG KDV UHYHDOHG WKDW WKH VRXUFH H[KLELWV YDULDEOH SRODUL]DWLRQ LQ WKH QHDU,5 'XQNLQ %DUORZ DQG 5\DQ f 7KHVH IDFWV DUH LPSRUWDQW WR RXU GLVFXVVLRQ VLQFH WKH\ JLYH XV FOXHV WR WKH QDWXUH RI WKH FLUFXPVWHOODU GLVN ,Q WKH UHVW RI WKH FKDSWHU ZH SUHVHQW RXU QHZ REVHUYDWLRQV GLVFXVV WKH UHVXOWV RI RXU PRGHOLQJ RI WKH JUDLQV LQ WKH GLVN DQG FRPPHQW RQ WKH HYROXWLRQDU\ VWDWXV RI +'

PAGE 91

$V ZH KLQWHG DW WKH HYROXWLRQDU\ VWDWXV RI +' LV VWLOO YHU\ PXFK LQ TXHVWLRQ ,W KDV EHHQ FODVVLILHG DV D 9HJDOLNH VWDU E\ PDQ\ DXWKRUV LQFOXGLQJ ERWK :DONHU DQG :ROVWHQFURIW f DQG 6\OYHVWHU HW DO f +RZHYHU +' LV DOVR D PHPEHU RI YDULRXV +HUELJ VWDU OLVWV OLNH WKRVH RI 0DOIDLW HW DO f DQG &RUSRURQ t /DJUDQJH f 7KH UHDVRQ WKDW +' LV RQ ERWK NLQGV RI OLVWV LV EHFDXVH LW LV RQH RI VHYHUDO VWDUV LQ RXU VXUYH\ VDPSOH WKDW H[KLELW FKDUDFWHULVWLFV RI ERWK D +HUELJ VWDU DQG D 9HJDOLNH VRXUFH +' PHHWV WZR RI FULWHULD WR EH GHILQHG DV D +HUELJ VWDU E\ KDYLQJ D VSHFWUDO FODVV HDUOLHU WKDQ )2 DQG H[KLELWLQJ VLQJOH SHDNHG %DOPHU HPLVVLRQ OLQH SURILOHV +' DOVR KDV +HO >$@ LQ HPLVVLRQ 'XQNLQ %DUORZ DQG 5\DQ f D IDFW WKDW LV UHOHYDQW WR LWV HYROXWLRQDU\ VWDWXV 7KH VWDU GRHV H[KLELW VRPH 9HJDOLNH FKDUDFWHULVWLFV WKRXJK ,Q SDUWLFXODU ERWK WKH H[LVWHQFH RI WKH ODUJH PLG DQG IDU,5 H[FHVV DQG LWV FKDUDFWHULVWLF VKDSH DUH YHU\ VLPLODU WR WKRVH RI RWKHU 9HJDOLNH VRXUFHV :H EHOLHYH WKDW WKH SRVVLEOH WUDQVLWLRQDO QDWXUH RI +' LV HYLGHQW LQ LWV VSHFWUDO HQHUJ\ GLVWULEXWLRQ 6('f ZKLFK LV VKRZQ LQ )LJXUH 7KH RSWLFDOWRPP 6(' VKRZV WKDW WKH VRXUFH H[KLELWV D ODUJH H[FHVV IRU DOO ; SP )LUVW GLVFRYHUHG E\ ,5$6 WKH H[FHVV SHDNV EHWZHHQ WR SP ZKLFK LV YHU\ VLPLODU WR WKH 6('V RI DOO RI WKH 9HJDOLNH DUFKHW\SHV 2EVHUYDWLRQV E\ 6\OYHVWHU HW DO f UHYHDOHG D VWURQJ QHDU ,5 H[FHVV DVVRFLDWHG ZLWK WKH VRXUFH LQ WKH + SPf DQG EDQGV SPf ZKHUH WKH\ PHDVXUH DQ H[FHVV RI DQG PDJ LQ WKH + DQG EDQGV UHVSHFWLYHO\ 7KH H[FHVV EHFRPHV PRUH SURQRXQFHG DW ORQJHU ZDYHOHQJWKV DQG UHDFKHV PDJ LQ WKH 0EDQG NHHQ SPf 6\OYHVWHU HW DO f $V ZH GLVFXVV LQ WKH REVHUYDWLRQ VHFWLRQ WKH H[FHVV LV YHU\ SURQRXQFHG LQ WKH PLG,5 ,Q IDFW WKH SKRWRVSKHUH RI WKH FHQWUDO VWDU

PAGE 92

:DYHOHQJWK SPf )LJXUH 6(' RI +' 7KH VROLG OLQH LV D PRGHO SKRWRVSKHUH WKH SRLQWV DUH REVHUYHG IOX[HV 7KH ,5 H[FHVV RI +' LV VHHQ DW DOO ZDYHOHQJWKV SP 7KH QHDU,5 H[FHVV FDQ EH LQWHUSUHWHG DV D VLJQ RI \RXWK VLQFH LW LPSOLHV WKHUH LV KRW PDWHULDO YHU\ FORVH WR WKH VWDU DQG WKDW WKH LQQHU GLVN UHJLRQ KDV \HW WR EH SURFHVVHG RU FOHDUHG 6(' IURP 6\OYHVWHU HW DO f RQO\ DFFRXQWV IRU D FRXSOH SHUFHQW RI WKH WRWDO IOX[ DW SP DQG DQ RUGHU RI PDJQLWXGH OHVV WKDQ WKDW DW SP 8VLQJ WKH ,5$6 ORQJ ZDYHOHQJWK GDWD DV D GLDJQRVWLF :DONHU t :ROVWHQFURIW f DVVLJQHG D WHPSHUDWXUH RI 7 WR WKH FLUFXPVWHOODU GXVW DURXQG +' $V ZH ZLOO VHH WKLV YDOXH LV ORZ FRPSDUHG WR WKH WHPSHUDWXUH ZH GHULYH IURP RXU PLG,5 GDWD 7 .f 7KLV LV QRW DQ XQH[SHFWHG UHVXOW WKRXJK VLQFH :DONHU t :ROVWHQFURIW ILW WKH DQG SP IOX[HV LQ WKH 6(' ZKLOH ZH XVH DQG SP GDWD

PAGE 93

0LG,QIUDUHG 2EVHUYDWLRQV DW .HFN :H REVHUYHG +' DV SDUW RI RXU 9HJDOLNH VXUYH\ DW WKH .HFN ,, WHOHVFRSH LQ 0D\ XVLQJ 26&,5 2Q WKH QLJKW RI 0D\ 87 ZH ILUVW GHWHFWHG WKH H[WHQGHG HPLVVLRQ DVVRFLDWHG ZLWK WKH VRXUFH LQ WKH 1EDQG SP $; SPf DQG ,+: $R SP $; SPf ILOWHUV 2XU REVHUYLQJ VHTXHQFH FRQVLVWHG RI ILUVW REVHUYLQJ DQ SP 36) VWDU D %RRf 7KHQ ZH REVHUYHG +' IRU PLQXWHV FKRSSHG LQWHJUDWLRQ PLQ RQVRXUFHf DW DQG SP $IWHU WKH VFLHQFH REVHUYDWLRQV ZH REVHUYHG D SP 36) VWDU 6JUf 2EVHUYDWLRQV RI DQ LQIUDUHG SKRWRPHWULF VWDQGDUG WR DEVROXWHO\ FDOLEUDWH WKH +' GDWD ILQLVKHG WKH REVHUYLQJ VHTXHQFH D %RR DQG \ $TOf )RU WKH +' REVHUYDWLRQV D %RR ZDV XVHG DV WKH PP 36) VWDU VLQFH WKH FKRVHQ VWDU ZDV QRW EULJKW HQRXJK WR JLYH D JRRG VLJQDOWRQRLVH GHWHFWLRQ LQ D UHDVRQDEOH LQWHJUDWLRQ WLPH 2Q .HFN 26&,5 WKH [ SL[HO GHWHFWRU RI 26&,5 KDV D SODWH VFDOH RI fSL[HO ZKLFK JLYHV D ILHOG RI YLHZ RI f [ f 7KH REVHUYDWLRQV ZHUH PDGH XVLQJ VWDQGDUG FKRSQRG WHFKQLTXHV ZLWK DQ f FKRSSHU WKURZ LQ GHFOLQDWLRQ 7KH .HFN DXWRJXLGHU V\VWHP ZDV XVHG IRU DOO RI WKH .HFN REVHUYDWLRQV :H HVWLPDWH WKDW WKHUH LV a SL[HO f RQ .HFNf RI fJXLGLQJ MLWWHUf LQKHUHQW LQ DQ\ 26&,5 REVHUYDWLRQV PDGH ZKLOH XVLQJ LW 2Q WKH .HFN UXQ LQ 0D\ WKH ZHDWKHU ZDV QRQSKRWRPHWULF ZLWK WKLQ EXW XQLIRUP OLJKW FLUUXV FORXGV SUHVHQW GXULQJ WKH QLJKW WKDW +' ZDV REVHUYHG 'XULQJ SRVWSURFHVVLQJ RI WKH GDWD FKRSSHG LPDJH SDLUV WKDW ZHUH REYLRXVO\ FRPSURPLVHG E\ WKH FLUUXV ZHUH GLVFDUGHG +RZHYHU WKHUH LV VWLOO VRPH XQFHUWDLQW\ LQ WKH SKRWRPHWU\ RI WKH VRXUFH DQG WKH VWDQGDUG VWDUV ZKLFK ZH WDNH WR EH s b 7KLV

PAGE 94

WUDQVODWHV LQWR WKH PDMRU FRPSRQHQW RI WKH XQFHUWDLQWLHV DVVRFLDWHG ZLWK RXU IOX[ HVWLPDWHV 0HDVXUHPHQWV RI WKH IXOOZLGWKV DW KDOI PD[LPXP ):+0f LQWHQVLWLHV RI FRPSDULVRQ VWDUV ZHUH DSSUR[LPDWHO\ f DQG f DW DQG SP UHVSHFWLYHO\ 4XDGUDWLF VXEWUDFWLRQ RI WKH GLIIUDFWLRQ OLPLWV $'f RI f DW SP DQG f DW SP IURP WKHVH YDOXHV IURP LPSOLHV VHHLQJ RI a WR f LQ WKH WR SP VSHFWUDO UHJLRQ ,W LV RXU H[SHULHQFH WKDW WKHVH YDOXHV DUH W\SLFDO IRU QRQSKRWRPHWULF QLJKWV RQ 0DXQD .HD 2XU PHDVXUHG IOX[ HVWLPDWHV RI +' FRQWDLQ ERWK WKH WKHUPDO HPLVVLRQ IURP WKH FLUFXPVWHOODU JUDLQV DQG HPLVVLRQ GLUHFWO\ IURP WKH SKRWRVSKHUH RI WKH FHQWUDO VWDU 7R FDOFXODWH WKH DPRXQW RI SKRWRVSKHULF HPLVVLRQ WKH VWDU HPLWV LQ WKH PLG,5 ZH QRUPDOL]HG WKH -EDQG $AHQ SPf IOX[ HVWLPDWH RI 6\OYHVWHU HW DO f WR WKDW RI D EODFNERG\ IXQFWLRQ ZLWK HIIHFWLYH WHPSHUDWXUH 7HII :H WKHQ SUHGLFWHG WKDW WKH SKRWRVSKHULF FRQWULEXWLRQ WR WKH SP IOX[ GHQVLW\ LV P-\ RU b $W SP WKH SKRWRVSKHUH RQO\ DFFRXQWV IRU b P-\f RI WKH REVHUYHG IOX[ 2XU SKRWRVSKHUH VXEWUDFWHG IOX[ HVWLPDWHV IRU +' DUH s P-\ DW SP DQG s P-\ DW SP 7KHVH IOX[ HVWLPDWHV DUH LQ DJUHHPHQW ZLWK WKRVH RI 6\OYHVWHU HW DO f 7KH SP SRLQW LV DOVR FRQVLVWHQW ZLWK WKH ,5$6 36& SP YDOXH RI -\ KRZHYHU RXU SP SRLQW LV ORZ FRPSDUHG WR WKH ,5$6 SP HVWLPDWH RI -\ (YHQ DFFRXQWLQJ IRU WKH VSHFWUDO VKDSH RI WKH GXVW 6(' LQ WKLV UHJLPH WKH ,5$6 SRLQW VHHPV WR RYHUHVWLPDWH WKH IOX[ IURP WKH VRXUFH 7KH ,5$6 SP SRLQW DOVR OLHV DERYH WKH RYHUDOO OHYHO RI WKH &*6 VSHFWUXP RI +' SUHVHQWHG LQ 6\OYHVWHU HW DO f :H FDQ RQO\ VSHFXODWH DV WR WKH UHDVRQ IRU WKLV DQG DQ REYLRXV K\SRWKHVLV LV FRQWDPLQDWLRQ RI WKH

PAGE 95

,5$6 EHDP 6LQFH LW LV WKH UDWLR RI WKH IOX[HV ))f WKDW OHWV XV SODFH DQ XSSHU OLPLW WR WKH JUDLQ VL]HV LQ RXU PRGHOLQJ ZH EHOLHYH WKH QRQSKRWRPHWULF TXDOLW\ RI WKH VN\ ZLOO QRW IXQGDPHQWDOO\ FKDQJH RXU PRGHOLQJ UHVXOWV +' 6RXUFH 6L]H ,Q WKLV VHFWLRQ ZH SUHVHQW RXU QHZ PLG,5 REVHUYDWLRQV RI +' 7KHVH REVHUYDWLRQV UHSUHVHQW WKH KLJKHVW UHVROXWLRQ PLG,5 LPDJHV FXUUHQWO\ SRVVLEOH :H PHDVXUHG D ):+0 IRU +' RI fDW SP DQG f DW SP 0HDVXUHG ):+0 YDOXHV RI WKH 36) VWDUV DUH f DW SP DQG f DW SP 6XEWUDFWLQJ WKHVH YDOXHV TXDGUDWLFDOO\ IURP WKH +' GDWD JLYHV DQ LQKHUHQW VRXUFH VL]H RI f DW SP DQG f DW SP ,QWHUHVWLQJO\ WKHVH YDOXHV PDWFK WKH SHDNV RI WKH LQWHQVLW\ RI WKH UHVLGXDO HPLVVLRQ RI WKH GLVN 2XU PLG,5 GDWD LV SUHVHQWHG LQ )LJXUH LQ WKH IRUP RI QRUPDOL]HG UDGLDO VFDQV DORQJ WKH FDUGLQDO GLUHFWLRQV WKURXJK +' DQG D QHDUE\ 36) VWDU 6JUf $OVR SORWWHG LQ HDFK RI WKH SDQHOV LV WKH UHVLGXDO HPLVVLRQ LQ WKH VFDQ GLUHFWLRQ (DFK RI WKH VFDQV WKURXJK WKH VRXUFH DQG 36) VWDU ZDV QRUPDOL]HG WR KDYH D PD[LPXP RI RQH DQG WKH SHDNV RI WKH VFDQV ZHUH DOLJQHG 7KH UHVLGXDOV ZHUH WKHQ FDOFXODWHG E\ GLIIHUHQFLQJ WKH WZR VFDQV $Q LQKHUHQW DVVXPSWLRQ LQ WKLV PHWKRG LV WKDW WKH VWDU VLWV LQ WKH H[DFW FHQWHU RI WKH HPLVVLRQ DQG WKHUHIRUH WKH H[DFW FHQWHU RI WKH GLVN 5HFHQW ZRUN RQ WKH GLVN RI +5 $ E\ :\DWW HW DO f KDV VKRZQ WKDW WKLV PD\ QRW EH WUXH ,Q WKDW ZRUN WKH\ LQWURGXFH WKH FRQFHSW RI fSHULFHQWHU JORZf ZKHUH WKH ORQJ WHUP SHUWXUEDWLRQ RI D GLVN E\ DQ REMHFW LQ RUELW LQVLGH RU RXWVLGH WKH GLVN PD\ VKLIW WKH GLVN ZLWK UHVSHFW WR LWV FHQWUDO VWDU :\DWW HW DO f

PAGE 96

1RUPDOL]HG )OX[ )LJXUH 1RUPDOL]HG VFDQV WKURXJK +' DQG D QHDUE\ 36) VWDU ,Q DOO SORWV +' LV WKH VROLG OLQH WKH 36) VWDU LV WKH GDVKHG OLQH 7KH GRWWHG OLQH LV WKH UHVLGXDO HPLVVLRQ ZKLFK LV WKH GLIIHUHQFH RI WKH VRXUFH VFDQ DQG WKH 36) VFDQ 7KH IRXU SDQHOV DUH DV IROORZV Df SP QRUWKVRXWK GLUHFWLRQ Ef SP HDVWZHVW GLUHFWLRQ Ff SP QRUWKVRXWK GLUHFWLRQ Gf SP HDVWZHVW GLUHFWLRQ ,Q WKH FDVH RI RXU +' GDWD VPDOO SL[HOf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

PAGE 97

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f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

PAGE 98

)LJXUH *URXQGEDVHG DQG VDWHOOLWH VSHFWUD RI +' 7KLV FRPELQDWLRQ RI REVHUYDWLRQV JLYHV FRPSOHWH FRYHUDJH IURP WR SP H[FHSW IRU WKH UHJLRQ EORFNHG E\ DWPRVSKHULF &2L EHWZHHQ DQG SP ,Q SDUWLFXODU QRWH WKH f8,5f HPLVVLRQ EDQGV EHWZHHQ DQG SP DQG WKH VKDUS 8,5 SHDN DW SP $OVR SUHVHQW LQ WKH &*6 VSHFWUXP LV D EURDG VLOLFDWH IHDWXUH FHQWHUHG DURXQG SP 7RS SDQHO ,623+27 VSHFWUD IURP :DONHU t +HLQULFKVHQ f %RWWRP SDQHO &*6 VSHFWUXP IURP 6\OYHVWHU HW DO f ,5HPLWWLQJ JUDLQV LQ WKH GLVN VXFK DV WKHLU WHPSHUDWXUH DQG DSSUR[LPDWH VL]H 7R GHULYH WKHVH SURSHUWLHV ZH PDNH DQ DVVXPSWLRQ DERXW WKH FRPSRVLWLRQ RI WKH JUDLQV 7R DGGUHVV WKH TXHVWLRQ RI WKH FRPSRVLWLRQ RI WKH PLG,5HPLWWLQJ JUDLQV LQ WKH GLVN RI +' ZH SUHVHQW WKH VSHFWUD VKRZQ LQ )LJXUH +HUH ZH VHH WZR PRGHUDWH UHVROXWLRQ VSHFWUD RI WKH VRXUFH WKDW JLYH FRPSOHWH ZDYHOHQJWK FRYHUDJH RI WKH WKHUPDO LQIUDUHG UHJLRQ 7KH WRS SDQHO RI )LJXUH LV DQ ,626:6 VSHFWUXP UHSURGXFHG

PAGE 99

IURP :DONHU t +HLQULFKVHQ f 7KH ERWWRP SDQHO LV D &*6 VSHFWUXP RI +' IURP 6\OYHVWHU HW DO f ,Q WKHVH VSHFWUD ZH VHH FRPSHOOLQJ HYLGHQFH WKDW WKHUH DUH ERWK VLOLFDWH JUDLQV DQG SRO\F\FOLF DURPDWLF K\GURFDUERQV 3$+Vf SUHVHQW LQ WKH GLVN 7KH IHDWXUHV VHHQ EHWZHHQ DQG SP DQG WKH VKDUS SHDN DW SP DUH QRUPDOO\ DWWULEXWHG WR 3$+ JUDLQV ,Q IDFW +' ZDV WKH ILUVW 9HJDOLNH VRXUFH WR KDYH WKHVH IHDWXUHV GHWHFWHG LQ LWV SP VSHFWUXP 6\OYHVWHU HW DO f $OVR SUHVHQW LQ WKH +' VSHFWUXP LV D EURDG VLOLFDWH IHDWXUH WKDW GRPLQDWHV WKH SP UHJLRQ ZKLFK LV FDXVHG E\ WKH VWUHWFKLQJ RI 6L ERQGV LQ WKH VLOLFDWH PROHFXOHV $QRWKHU FOXH WR WKH H[LVWHQFH RI VLOLFDWH GLVN PDWHULDO LV WKH IDFW WKDW RSWLFDO VSHFWURVFRS\ KDV VKRZQ WKDW +' KDV D ODUJH XQGHU DEXQGDQFH LQ ERWK 6L DQG 0J +' LV GHILFLHQW E\ GH[ LQ 6L DQG GH[ LQ 0J DV FRPSDUHG WR WKH 6XQ 'XQNLQ %DUORZ t 5\DQ f 7KHVH YDOXHV DUH E\ IDU WKH ORZHVW DEXQGDQFH RI WKHVH HOHPHQWV RI DQ\ VWDU LQ WKH 9HJDOLNH VRXUFHV VWXGLHG E\ 'XQNLQ %DUORZ t 5\DQ f 'XQNLQ %DUORZ t 5\DQ f VXJJHVWV WKDW WKH SKRWRVSKHULF GHSOHWLRQV RI WKHVH HOHPHQWV LV LQGLFDWLYH RI WKH PDWHULDO UHVLGLQJ LQ FLUFXPVWHOODU JUDLQV DQG LQGHHG WKH SUHVHQFH RI WKH SP VLOLFDWH IHDWXUH VHHPV WR VXSSRUW WKLV K\SRWKHVLV 7KHVH UHVXOWV LPSO\ WKDW WKHUH DUH DW OHDVW WZR GLIIHUHQW JUDLQ SRSXODWLRQV LQ WKH GLVN 7KLV KDV FRQVHTXHQFHV IRU RXU PRGHOLQJ RI WKH JUDLQV VLQFH RXU PRGHOV DVVXPH WKDW WKH JUDLQV DUH FRPSRVHG RI WKH DVWURQRPLFDO VLOLFDWHV RI 'UDLQH DQG /HH f +RZHYHU VLQFH ZH DUH ZRUNLQJ ZLWK WKH JOREDO IOX[ HVWLPDWHV RI WKH VRXUFH LW LV LPSRVVLEOH WR GHn FRXSOH WKH HPLVVLRQ RI WKH VLOLFDWH JUDLQV IURP WKDW RI WKH 3$+V 7R GHDO ZLWK WKLV ZH WUHDW WKH 3$+ HPLVVLRQ DV D fFRQWDPLQDWLRQf DQG UXQ WKH PRGHOV DVVXPLQJ WKDW LW

PAGE 100

FRQWULEXWHV YDU\LQJ DPRXQWV WR WKH WRWDO _LP IOX[ %HORZ ZH GLVFXVV RXU PRGHOV DQG WKLV SURFHVV LQ GHWDLO 0RGHO 5HVXOWV %HIRUH ZH GLVFXVV WKH UHVXOWV RI RXU PRGHOLQJ ZH LQWURGXFH WKH PRGHO LWVHOI DQG V\QRSVL]H LWV RSHUDWLRQ 7KH 8QLYHUVLW\ RI )ORULGD 'XVW '\QDPLFV JURXS GHYHORSHG RXU PRGHO LQLWLDOO\ WR ZRUN RQ WKH ]RGLDFDO GXVW RI WKH 6RODU V\VWHP :H KDYH XVHG WKHVH WKHUPDO HTXLOLEULXP PRGHOV WR DQDO\]H VLPLODU GDWD RQ WKH GLVN RI +5 $ 7HOHVFR HW DO :\DWW HW DO f DQG +' )LVKHU HW DO FKDSWHU f 2XU PRGHOV DVVXPH WKH JUDLQV DUH VSKHULFDO 0LH SDUWLFOHV FRPSRVHG RI WKH DVWURQRPLFDO VLOLFDWHV RI 'UDLQH DQG /HH f ZLWK D GHQVLW\ S J FPn 7KH UHVXOWV SUHVHQWHG WKHUH ZH ILUVW QHHG WR GLVFXVV WKH RSHUDWLRQ RI RXU PRGHOV 7KH SULPDU\ LQSXWV WR WKH PRGHOLQJ FRGH DUH WKH RSWLFDO FRQVWDQWV RI WKH JUDLQV DQG WKH FKDUDFWHULVWLFV RI WKH JUDLQ KHDWLQJ VRXUFH ,Q WKLV FDVH WKH RQO\ KHDWLQJ VRXUFH LV +' LWVHOI DQG ZH XVH WKH GDWD LQ 7DEOH DV RXU LQSXWV :H DOVR LQSXW D GLVWDQFH WR WKH VRXUFH D YHFWRU RI JUDLQ VL]HV GLDPHWHUV LQ _LPf ZH ZDQW WKH FRGH WR PRGHO DQG D YHFWRU RI ZDYHOHQJWKV ZH ZDQW WKH FRGH WR FDOFXODWH IOX[HV IRU 2XU PRGHOV WKHQ VWDUW ZLWK WKH RSWLFDO FRQVWDQWV RI DVWURQRPLFDO VLOLFDWHV 'UDLQH DQG /HH f DQG XVH 0LH WKHRU\ WR FDOFXODWH WKH DEVRUSWLRQ HIILFLHQFLHV 4DEVf IRU GLIIHUHQW VL]HG SDUWLFOHV DQG GLIIHUHQW ZDYHOHQJWKV 2QFH ZH NQRZ KRZ HIILFLHQWO\ D SDUWLFOH RI D JLYHQ VL]H DEVRUEV DQG HPLWV UDGLDWLRQ ZH FDQ FDOFXODWH ZKDW LWV WHPSHUDWXUH ZRXOG EH DW D JLYHQ GLVWDQFH IURP WKH VWDU 7R GR WKLV ZH XVH WKH HIIHFWLYH WHPSHUDWXUH RI WKH VWDU WR ZRUN RXW WKH VWHOODU VSHFWUXP DQG WKH OXPLQRVLW\ RI WKH VWDU WR ZRUN RXW WKH HTXLOLEULXP WHPSHUDWXUH RI

PAGE 101

WKH SDUWLFOH %RWK WKH OXPLQRVLW\ DQG HIIHFWLYH WHPSHUDWXUH RI WKH VWDU DUH LQSXWV LQWR WKH PRGHO 2QFH ZH NQRZ WKH WHPSHUDWXUH RI WKH SDUWLFOH DQG LWV DEVRUSWLRQ HIILFLHQF\ 4DEVf ZH NQRZ KRZ PXFK UDGLDWLRQ LW ZLOO HPLW DW DQ\ JLYHQ ZDYHOHQJWK ZH FDQ ZULWH WKLV DV 4DEV%Y7f ZKHUH %97f LV WKH 3ODQFN IXQFWLRQ IRU WKH WHPSHUDWXUH RI WKH SDUWLFOH :H FDQ WKHQ SORW 4DEV%Y7f IRU GLIIHUHQW VL]HG SDUWLFOHV DW GLIIHUHQW GLVWDQFHV IURP WKH VWDU IRU D JLYHQ ZDYHOHQJWK 7KHVH SORWV DUH VKRZQ LQ WKH WRS WZR SDQHOV RI )LJXUH 6LQFH RXU REVHUYDWLRQV JLYH XV WKH UDWLR RI WKH IOX[HV WKH JUDLQV HPLW DW DQG SP ZH FDQ GLUHFWO\ FRPSDUH WKH PRGHO RXWSXW ZLWK RXU REVHUYDWLRQV E\ IRUPLQJ WKH UDWLR RI WKH RXWSXW DW WKH WZR ZDYHOHQJWKV 7KDW LV WKH UDWLR RI WKH 4DE6%Y7f SORWV DW WKH WZR ZDYHOHQJWKV WKH WRS WZR SDQHOV RI )LJXUH f LV MXVW WKH UDWLR RI WKH IOX[ GHQVLWLHV HPLWWHG E\ WKH SDUWLFOH LQ WKH WZR ZDYHEDQGV 7KH ODUJH SDQHO LQ )LJXUH LV WKH UHVXOW RI WDNLQJ WKH UDWLR RI WKH WRS WZR SDQHOV $ SRLQW RQ WKHVH UHVXOWLQJ FXUYHV LV WKH IOX[ UDWLR H[SHFWHG IRU D SDUWLFOH RI D JLYHQ VL]H DW D JLYHQ GLVWDQFH IURP WKH VWDU $OVR SORWWHG RQ WKLV SDQHO LV D KRUL]RQWDO OLQH PDUNHG b WKDW UHSUHVHQWV RXU REVHUYHG H[FHVV IOX[ UDWLR 7KH b DQG b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

PAGE 102

-\6U 3DUWLFOH GLDPHWHU PLFURQV )LJXUH 0RGHO RXWSXW IRU JUDLQV WR $8 IURP +' DVVXPLQJ WKH\ DUH VSKHULFDO 0LH SDUWLFOHV FRPSRVHG RI DVWURQRPLFDO VLOLFDWHV WRS OHIWf *UDLQ HPLVVLRQ DW SP WRS ULJKWf *UDLQ HPLVVLRQ DW SP ERWWRPf )OX[ GHQVLW\ UDWLR SORWV IRU JUDLQV QHDU +' 7KH KRUL]RQWDO OLQH PDUNHG b GHQRWHV RXU REVHUYHG IOX[ UDWLR 2WKHU OLQHV SORWWHG DVVXPH b DQG b FRQWDPLQDWLRQ RI WKH 1EDQG IOX[ E\ QRQn VLOLFDWH JUDLQV 7KH SRLQWV ZKHUH WKHVH OLQHV LQWHUVHFW WKH IOX[ UDWLR FXUYHV UHSUHVHQW JUDLQ VL]HV DQG GLVWDQFHV IURP WKH VRXUFH WKDW DUH FRQVLVWHQW ZLWK RXU REVHUYDWLRQV

PAGE 103

WR WKH REVHUYHG PLG,5 IOX[ UDWLR )LRQP)LQPf +RZHYHU VLQFH WKHUH LV HYLGHQFH WKDW WKHUH LV VWURQJ 3$+ HPLVVLRQ EHWZHHQ DQG _LP DQG DW SP LQ WKH VSHFWUD RI +' ZH FDQQRW VLPSO\ DVVXPH WKDW DOO RI WKH 1EDQG SPf HPLVVLRQ ZH GHWHFW FRPHV IURP VLOLFDWH JUDLQV 7R WU\ WR DFFRXQW IRU WKLV FRQWDPLQDWLRQ RI RXU SP IOX[ HVWLPDWH ZH UDQ WKUHH VHWV RI PRGHOV (DFK UXQ DVVXPHG WKDW QRQVLOLFDWH JUDLQV LH 3$+Vf FRQWULEXWHG D GLIIHUHQW DPRXQW RI WKH REVHUYHG SP IOX[ 7R JHW D IHHO IRU KRZ VWURQJO\ WKLV FRQWDPLQDWLRQ ZRXOG FKDQJH RXU UHVXOWV ZH UDQ PRGHOV DVVXPLQJ b b DQG b RI WKH SP IOX[ FDPH IURP WKH 3$+ JUDLQV 6\OYHVWHU HW DO f URXJKO\ HVWLPDWH WKDW XS WR b RI WKH IOX[ LQ WKH SP UHJLRQ LV HPLWWHG E\ WKH FDUERQDFHRXV 3$+ JUDLQV 6\OYHVWHU HW DO f 7KH JUDLQ VL]HV FRQVLVWHQW ZLWK RXU REVHUYDWLRQV DVVXPLQJ b QRQVLOLFDWH SP HPLVVLRQ UDQJH IURP JUDLQV ZLWK GLDPHWHU G SP $8 IURP WKH FHQWUDO VWDU WR G SP JUDLQV $8 IURP WKH VRXUFH 1RWH WKDW WKH FRQWDPLQDWLRQ RI RXU SP IOX[ HVWLPDWH E\ 3$+ HPLVVLRQ GRHV QRW GUDPDWLFDOO\ FKDQJH RXU UHVXOWV (YHQ ZLWK b FRQWDPLQDWLRQ ZKLFK LV DOPRVW DVVXUHGO\ KLJKHU WKDQ WKH WUXH DPRXQW RXU JUDLQ VL]H HVWLPDWHV FKDQJH E\ OHVV WKDQ D IDFWRU RI WZR 2XU UHVXOWV DUH YHU\ FRQVLVWHQW ZLWK WKH JUDLQ VL]HV LQ RWKHU 9HJDOLNH GLVNV 6LPLODU PRGHOLQJ RI WKH +5 $ GLVN E\ :\DWW HW DO f DQG 7HOHVFR HW DO f VKRZV WKDW WKH JUDLQV LQ WKDW GLVN DUH DSSUR[LPDWHO\ SP LQ GLDPHWHU 0LG,5 DSHUWXUH SKRWRPHWU\ RI 3LFWRULV LPSOLHV WKHUH DUH WR SP JUDLQV LQ WKDW DUFKHW\SDO GLVN 7HOHVFR HW DO 7HOHVFR t .QDFNH $LWNHQ HW DO f 9HJD LWVHOI LV UHSRUWHG WR KDYH WR SP JUDLQV DV WKH GRPLQDQW SRSXODWLRQ LQ LWV GLVN 9DQ GHU %OLHN 3UXVWL t :DOWHUV f ,Q &KDSWHU ZH SUHVHQW UHVXOWV RQ WKH GLVN RI +' ZKHUH ZH ILQG

PAGE 104

WKH PLG,5HPLWWLQJ JUDLQV DUH RI SP LQ VL]H DQG RUELW +' DW VLPLODU GLVWDQFHV 7KLV LV D YHU\ LQWHUHVWLQJ UHVXOW ZKHQ \RX FRQVLGHU WKH IDFW WKDW ZH QRZ KDYH HVWLPDWHV IRU WKH VL]H RI WKH PLG,5HPLWWLQJ JUDLQV LQ DW OHDVW ILYH UHVROYHG 9HJDOLNH GLVNV DQG WKH\ DUH DOO LQ WKH WR SP UDQJH 7KHVH VL]H HVWLPDWHV DUH YHU\ VLPLODU WR WKRVH ZH GHULYH IRU VRXUFHV REVHUYHG LQ RXU 9HJDOLNH VXUYH\ &KDSWHU f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f DORQJ ZLWK WKH RSWLFDO SURSHUWLHV RI WKH JUDLQV ZH FDQ FDOFXODWH WHPSHUDWXUHV IRU JUDLQV RI GLIIHUHQW VL]HV DW YDU\LQJ GLVWDQFHV IURP +' )LJXUH VKRZV RXU PRGHO WHPSHUDWXUH RXWSXW )RU SP JUDLQV $8 IURP WKH VWDU WKH PRGHO UHWXUQV D WHPSHUDWXUH RI 7 )RU WKH SP JUDLQV DW $8 ZH JHW D WHPSHUDWXUH 7 7KHVH WHPSHUDWXUHV DJUHH ZHOO ZLWK WKRVH IRU PLG,5HPLWWLQJ JUDLQV LQ RWKHU UHVROYHG 9HJDOLNH GLVNV :H GHULYH D WHPSHUDWXUH RI 7 IRU WKH JUDLQV DERXW $8 IURP WKH VRXUFH LQ WKH GLVN RI +' )LVKHU HW DO f DQG ZRUN E\ :\DWW HW DO f DQG 7HOHVFR HW DO f SODFHV D WHPSHUDWXUH RI 7 r RQ WKH PLG,5HPLWWLQJ JUDLQV LQ WKH GLVN RI +5 $ :H FDQ DOVR XVH RXU REVHUYDWLRQV WR FDOFXODWH D YDOXH IRU WKH RSWLFDO GHSWK RI WKH PLG,5HPLWWLQJ PDWHULDO 8VLQJ WKH REVHUYHG UDGLXV RI WKH H[WHQGHG HPLVVLRQ ff WR

PAGE 105

*UDLU 7HPSHUDWXUH QHDU +' *UDLQ 7HPSHUDWXUHV QHDU +' )LJXUH 0RGHO JUDLQ WHPSHUDWXUHV QHDU +' WRSf *UDLQ WHPSHUDWXUH DV D IXQFWLRQ RI VL]H DQG GLVWDQFH IURP WKH VWDU 'LVWDQFHV FDOFXODWHG DW $8 LQWHUYDOV IURP WR $8 ERWWRPf *UDLQ WHPSHUDWXUH YV GLVWDQFH IURP VRXUFH ,Q WKH ERWWRP SDQHO ZH VHH WKH IDPLOLDU 7 m 5 VKDSH WR WKH FXUYHV DOWKRXJK WKH FXUYHV GR QRW H[DFWO\ IROORZ WKLV UHODWLRQ DV ZH DUH QRW WUHDWLQJ WKHP DV EODFNERGLHV FDOFXODWH WKH VROLG DQJOH VXEWHQGHG E\ WKH VRXUFH ZH GHULYH D PLG,5 FRORU WHPSHUDWXUH IRU WKH JUDLQV RI 7PcGL5 ZLWK D FRUUHVSRQGLQJ RSWLFDO GHSWK 7PcGL5 7KHVH UHVXOWV DUH HQFRXUDJLQJ IRU WZR UHDVRQV )LUVWO\ WKLV UHODWLYHO\ VLPSOH FDOFXODWLRQ UHWXUQV D WHPSHUDWXUH IRU WKH JUDLQV WKDW LV FRQVLVWHQW ZLWK WKH PRUH GHWDLOHG PRGHOV 6HFRQGO\ RXU GHULYHG RSWLFDO GHSWK PHDVXUHPHQW RI LV YHU\ FORVH WR WKH YDOXH RI SUHVHQWHG E\ 6\OYHVWHU HW DO f IRU +' 7KLV YDOXH RI WKH RSWLFDO GHSWK LV

PAGE 106

LQWHUHVWLQJ VLQFH LW LV KLJKHU WKDQ WKDW RI WKH 9HJDOLNH DUFKHW\SHV EXW ORZ FRPSDUHG WR D +HUELJ $H%H VWDU 7KH FODVVLFDO 9HJDOLNH DUFKHW\SHV KDYH [ YDOXHV RQ WKH RUGHU RI WR n $UW\PRZLF] f ZKLOH WKH +HUELJ VRXUFHV JHQHUDOO\ KDYH YDOXHV LQ WKH WR RU KLJKHUf UDQJH YDQ GHQ $QFNHU f :H LQWHUSUHW WKH LQWHUPHGLDWH 7 YDOXH RI +' DV HYLGHQFH WKDW LW LV LQ IDFW DQ REMHFW LQ WUDQVLWLRQ IURP RQH FODVV WR WKH RWKHU 7KH LGHD WKDW WKH IUDFWLRQDO OXPLQRVLW\ RI D GLVN FKDQJHV DV LW HYROYHV LQ QRW QHZ %RWK +ROODQG HW DO f DQG %DUUDGR \ 1DYDVFXWHV HW DO f VHH D WUHQG RI GHFUHDVLQJ /LU/rf ZLWK UHVSHFW WR DJH RI WKH GLVN DQG +' ILWV ZHOO LQWR WKH WUHQGV VHHQ LQ ILJXUHV LQ ERWK RI WKRVH ZRUNV 7KH HIIHFWV RI UDGLDWLRQ RQ WKH SDUWLFOHV LQ WKH GLVN FDQ EH LQYHVWLJDWHG E\ FRQVLGHULQJ WKH UDWLR RI WKH UDGLDWLRQ IRUFH WR WKH JUDYLWDWLRQDO IRUFH IHOW E\ D JUDLQ 7KLV UDWLR FDOOHG S DOORZV XV WR GHWHUPLQH KRZ WKHVH IRUFHV DFW RQ D SDUWLFOH RI D JLYHQ VL]H DQG JLYH FOXHV WR WKH HYHQWXDO IDWH RI VXFK JUDLQV 3 FDQ EH FDOFXODWHG DV D IXQFWLRQ RI JUDLQ UDGLXV Df IURP WKH IROORZLQJ UHODWLRQ $XJHUHDX HW DO $UW\PRZLF] f 3 /r 435Df! 0r F S D ZKHUH D LV WKH JUDLQ UDGLXV 4S5Df! LV WKH UDGLDWLRQ SUHVVXUH HIILFLHQF\ IRU WKH JUDLQ DYHUDJHG RYHU WKH VWHOODU VSHFWUXP IRU D JLYHQ JUDLQ VL]H /r DQG 0r DUH WKH OXPLQRVLW\ DQG PDVV RI WKH FHQWUDO VWDU DQG S LV WKH DVVXPHG PDVV GHQVLW\ RI WKH JUDLQ 8VLQJ WKH VWHOODU SDUDPHWHUV LQ 7DEOH DQG DVVXPLQJ WKH JUDLQV DUH VLOLFDWH 0LH VSKHUHV ZLWK S J FPn ZH FDOFXODWH WKH YDOXHV RI 3 VKRZQ LQ WKH WRS SDQHO RI )LJXUH *UDLQV ZLWK 3 ZLOO EH UHPRYHG IURP WKH V\VWHP RQ XQERXQG K\SHUEROLF RUELWV :\DWW HW DO f ,Q WKH FDVH RI +' WKHVH JUDLQV DUH UHPRYHG RQ HVVHQWLDOO\ IUHHIDOO WLPHVFDOH ZKLFK LV \U IRU WKH PLG,5HPLWWLQJ JUDLQV LQ WKH GLVN ,W FDQ DOVR EH QRWHG WKDW

PAGE 107

%HWD IRU *UDLQV QHDU +' 35 'UDJ /LIHWLPH IRU *UDLQV 1HDU +' )LJXUH '\QDPLFDO SDUDPHWHUV IRU JUDLQV QHDU +' WRSf 7KH SDUDPHWHU )UDG)JUDYf IRU JUDLQV LQ WKH GLVN RI +' 3DUWLFOHV ZLWK ZLOO EH UHPRYHG IURP WKH V\VWHP LQ YHU\ VKRUW WLPHV \Uf ERWWRPf 35 GUDJ OLIHWLPH IRU JUDLQV QHDU +' *UDLQV KDYH GLDPHWHUV _LPf :H VHH WKDW HYHQ IRU WKH ODUJHVW JUDLQV SPf DW WKH ODUJHVW GLVWDQFH $8f UHWXUQHG E\ RXU PRGHOV WKH GUDJ OLIHWLPH LV VPDOO FRPSDUHG WR WKH SUHVXPHG DJH RI WKH V\VWHP JUDLQV ZLWK ZLOO KDYH WKHLU VSDFH PRWLRQ VLJQLILFDQWO\ HIIHFWHG E\ WKH UDGLDWLRQ ILHOG DQG ZLOO PRVW OLNHO\ EH RQ YHU\ HFFHQWULF RUELWV $XJHUHDX HW DO f $QRWKHU IRUFH WKDW HIIHFWV WKH JUDLQV 3R\QWLQJ5REHUWVRQ GUDJ 35 GUDJf 2QFH ZH NQRZ ZH FDQ FDOFXODWH WKH HIIHFWV RI WKLV IRUFH RQ SDUWLFOHV RI YDU\LQJ VL]HV 8VLQJ WKH UHODWLRQ IRU WS5 IURP :\DWW HW DO f

PAGE 108

WS5 0#0rf 5 ZH XVH RXU GHULYHG S YDOXHV WR SORW WKH 35 GUDJ OLIHWLPHV RI JUDLQV LQ WKH GLVN RI +' LQ WKH ERWWRP SDQHO RI )LJXUH )RU SP JUDLQV $8 IURP WKH FHQWUDO VWDU ZH FDOFXODWH D 35 GUDJ OLIHWLPH RI W35 \U IRU SP JUDLQV $8 IURP WKH VRXUFH WKLV WLPH LV W35 a [ \U 2QH LPPHGLDWHO\ VHHV WKDW WKH 35 GUDJ OLIHWLPH RI RXU GHULYHG JUDLQ VL]HV LV VPDOO ZKHQ FRPSDUHG WR WKH SUHVXPHG OLIHWLPH RI WKH FHQWUDO VWDU [ \Uf %HFDXVH WKH UHPRYDO SURFHVV KDSSHQV RQ D WLPHVFDOH WKDW LV PXFK OHVV WKDQ WKH DSSDUHQW DJH RI WKH VRXUFH WR 0\Uf ZH EHOLHYH WKDW WKH PLG,5HPLWWLQJ JUDLQV DUH QRW SULPRUGLDO DQG KDYH EHHQ UHSOHQLVKHG E\ VRPH PHFKDQLVP 2QH UHSOHQLVKPHQW PHFKDQLVP LV WKURXJK FROOLVLRQV RI ODUJHU ERGLHV DV LV DSSDUHQWO\ WKH FDVH IRU 3 3LFWRULV $UW\PRZLF] f DQG +5 $ 7HOHVFR HW DO :\DWW HW DO f 7KH LGHD WKDW WKHUH LV SURFHVVHG RU fVHFRQGJHQHUDWLRQf GXVW LQ WKH GLVN RI +' LV LPSRUWDQW VLQFH WKDW LV RQH RI WKH EDVLF FKDUDFWHULVWLFV RI D 9HJDOLNH GLVN :KHWKHU RU QRW WKHVH JUDLQV DUH WUXO\ fGHEULVf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f ,Q WKH QH[W VHFWLRQ ZH GLVFXVV RWKHU GDWD WKDW

PAGE 109

7DEOH 6XPPDU\ RI +' JUDLQ SURSHUWLHV )LR QP r s P-\ 7PGHL.f WR )LQPr s P-\ 'PRGH.OLUQf WR WPLG,5 5PRGHOL$8fA WR 3PLG,5 + WS5\Uf [OWRO 7PLG,5 7ZZi 2EVHUYHG IOX[ GHQVLW\i :DONHU t :ROVWHQFURIW f $VVXPHV b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

PAGE 110

fHTXDWRU RQf DQG WKHLU GLVNV ZRXOG WKHUHIRUH SUREDEO\ EH FORVH WR HGJHRQ $Q H[DPSOH RI WKLV LV WKH DUFKHW\SH 3LFWRULV ZKLFK KDV D PHDVXUHG YVLQLf NPVHF DQG D GLVN LQFOLQDWLRQ RI r %DFNPDQ t 3DUHVFH f 7KH VRXUFH +' DOVR KDV D KLJK URWDWLRQDO YHORFLW\ NPVHFf DQG D FORVH WR HGJHRQ GLVN UHVROYHG LQ ERWK WKH QHDU DQG PLG,5 :HLQEHUJHU HW DO )LVKHU HW DO f &RQYHUVHO\ 9HJDOLNH VRXUFHV WKDW KDYH ORZ URWDWLRQDO YHORFLWLHV VKRXOG KDYH GLVNV WKDW DUH IDFHRQ $Q H[DPSOH RI WKLV VLWXDWLRQ LV 9HJD LWVHOI ZKLFK KDV YVLQf NPVHF %DFNPDQ t 3DUHVFH f DQG DQ DOPRVW IDFHRQ GLVN WKDW KDV EHHQ UHVROYHG LQ WKH VXEPP E\ +ROODQG HW DO f $QRWKHU RI WKH DUFKHW\SHV H (UL DOVR KDV D UHVROYHG VXEPP GLVN WKDW LV FORVH WR FLUFXODU DQG PRVW OLNHO\ IDFHRQ *UHDYHV HW DO f DQG D YHU\ ORZ YVLQLf YDOXH RI NPVHF 6DDU DQG 2VWHQ f ,Q WKHLU GLVFRYHU\ SDSHU *UHDYHV HW DO f QRWH WKDW WKH DSSHDUDQFH RI WKH GLVN LV FRQVLVWHQW ZLWK LQFOLQDWLRQ HVWLPDWHV RI WKH VWHOODU SROH :H WKHUHIRUH NQRZ RI DW OHDVW IRXU H[DPSOHV LQFOXGLQJ WKUHH DUFKHW\SDO VRXUFHV ZKHUH WKH RULHQWDWLRQ RI WKH GLVN FDQ EH URXJKO\ HVWLPDWHG IURP WKH URWDWLRQDO YHORFLW\ RI WKH FHQWUDO VWDU :H EHOLHYH WKH GLVN RI +' DOVR ILWV LQWR WKLV WUHQG :KLOH WKH PHDQ YDOXH RI YVLQLnf IRU $ 9 VWDUV LV NPVHF %DFNPDQ t 3DUHVFH f +' KDV D PHDVXUHG URWDWLRQDO YHORFLW\ RI Y VLQLf s NPVHF 'XQNLQ %DUORZ t 5\DQ Df 'XQNLQ %DUORZ t 5\DQ Ef QRWH WKDW +' KDV WKH QH[W WR ORZHVW YVLQLf RI DOO RI WKH 9HJDOLNH VWDUV LQ WKHLU VDPSOH DQG VXJJHVWHG WKDW ZH PD\ EH YLHZLQJ WKLV VWDU FORVH WR SROHRQ 7KLV ZRXOG LPSO\ WKDW ZH VKRXOG VHH WKH GLVN RI +' FORVH WR IDFHRQ

PAGE 111

$QRWKHU SLHFH RI HYLGHQFH WKDW VXSSRUWV D IDFHRQ GLVN RULHQWDWLRQ LV VHHQ LQ RSWLFDO VSHFWUD RI +' 'XQNLQ %DUORZ DQG 5\DQ Ef REWDLQHG KLJK UHVROXWLRQ RSWLFDO VSHFWUD LQ WKH UHJLRQV DURXQG WKH OLQHV RI +D 1D DQG &D ,, IRU D VDPSOH RI 9HJDOLNH VWDUV ZLWK VSHFWUDO FODVVHV UDQJLQJ IURP % WR $ 7KHLU VDPSOH LQFOXGHG ERWK +' DQG +' VHH &KDSWHU f ,Q UHJDUGV WR WKH +D HPLVVLRQ RI WKHVH VRXUFHV WKH\ ILQG WKDW WZR VKRZ QR HPLVVLRQ OLQHV IRXU VKRZ GRXEOHSHDNHG HPLVVLRQ VWUXFWXUH WZR VKRZ D VLQJOHSHDNHG SURILOH DQG RQH VRXUFH KDV D VWURQJ 3 &\J SURILOH LQ LWV OLQH +' ZKLFK LV DQRWKHU RI RXU 9HJDOLNH VXUYH\ VRXUFHV DQG +' DUH WKH WZR VRXUFHV LQ WKH 'XQNLQ %DUORZ t 5\DQ VXUYH\ WKDW VKRZV D VWURQJ VLQJOHSHDNHG +D SURILOH 'XQNLQ %DUORZ t 5\DQ Ef :H DGGUHVV WKLV IDFHW RI WKH +D HPLVVLRQ DJDLQ LQ WKH QH[W VHFWLRQ ,W LV LQWHUHVWLQJ WR QRWH WKDW WKH WZR VWDUV LQ WKH 'XQNLQ %DUORZ t 5\DQ VDPSOH WKDW H[KLELW VLQJOHSHDNHG %DOPHU HPLVVLRQOLQH SURILOHV DOVR KDYH WKH ORZHVW Y VLQLnf YDOXHV RI WKH VDPSOH DQG WKH\ ERWK VKRZ 6L GHSOHWLRQ LQ WKHLU VSHFWUD 'XQNLQ %DUORZ t 5\DQ f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

PAGE 112

WRZDUG WKH =$06 :H DUH KHVLWDQW WR FDOO +' D SUHPDLQVHTXHQFH VRXUFH EHFDXVH WKLV LPSOLHV WKDW WKH VRXUFH LV D +HUELJ $H%H VWDU :H GR QRW EHOLHYH WKDW +' IXOO\ ILWV LQWR WKH +HUELJ FODVV HYHQ WKRXJK LW GRHV H[KLELW VRPH +HUELJOLNH FKDUDFWHULVWLFV ,Q WKHLU UHFHQW UHYLHZ RI 9HJDOLNH VRXUFHV /DJUDQJH HW DO f FRLQ WKH WHUP fROGSUHPDLQVHTXHQFHf 2306f VRXUFHV ZKLFK DUH VRXUFHV WKDW KDYH PRUH RU OHVV ILQLVKHG WKHLU 306 HYROXWLRQ DQG DUH QRZ PRYLQJ LQWR WKH PDLQVHTXHQFH SKDVH RI WKHLU OLYHV :H EHOLHYH WKDW +' LV DQ H[FHOOHQW H[DPSOH RI MXVW VXFK D VRXUFH 2QH SRVVLEOH VLJQDWXUH RI WKH \RXWK RI +' ZDV GLVFRYHUHG LQ WKH KLJK UHVROXWLRQ RSWLFDO VSHFWUD RI 'XQNLQ %DUORZ t 5\DQ f $ORQJ ZLWK VLQJOHSHDNHG +D HPLVVLRQ WKH\ DOVR GHWHFWHG HPLVVLRQ LQ WKH OLQH RI +H $ ,Q IDFW HPLVVLRQ LQ WKLV OLQH ZDV GHWHFWHG IRU ERWK VLQJOHSHDNHG +D VRXUFHV LQ WKHLU VDPSOH +' DQG +' f ZKLOH DEVRUSWLRQ ZDV GHWHFWHG IRU WKH GRXEOHSHDNHG +D VWDUV +' +' t +' f 7KHUH LV QR VLJQLILFDQW +H DEVRUSWLRQ RU HPLVVLRQ SUHGLFWHG WR EH SUHVHQW LQ WKH SKRWRVSKHULF VSHFWUD RI $W\SH VWDUV %RKP t &DWDOD f +RZHYHU WKH SUHVHQFH RI WKH +H $ HPLVVLRQ LQ WKH FDVH RI +' FDQ EH LQWHUSUHWHG DV D VLJQDWXUH RI RQJRLQJ DFFUHWLRQ LQ WKH V\VWHP 2QH VXJJHVWLRQ ILU WKH SUHVHQFH RI WKLV HPLVVLRQ LV WKDW WKH RULJLQ RI WKH +H HPLVVLRQ LV DW WKH LQWHUIDFH RI D ERXQGDU\ OD\HU EHWZHHQ WKH FHQWUDO VWDU DQG WKH DFFUHWLRQ GLVN ,Q WKHLU PRGHOV RI 77DXUL VWDUV +DUWPDQQ +HZHWW t &DOYHW f SURSRVH WKDW PDWHULDO LV IXQQHOHG IURP WKH VXUIDFH RI WKH LQQHUPRVW SDUWV RI WKH GLVN DORQJ WKH PDJQHWLF ILHOG OLQHV RI WKH VWDU WR HOHYDWHG ODWLWXGHV LQ ERWK KHPLVSKHUHV RI WKH FHQWUDO VRXUFH 2QH RI WKH SUHGLFWLRQV RI WKHLU PRGHOV LV WKDW GRXEOHSHDNHG %DOPHU OLQH HPLVVLRQ VKRXOG FRPH IURP V\VWHPV WKDW DUH FORVHU WR SROHRQ WKDQ HGJHRQ ZKLOH

PAGE 113

WKH VLQJOHSHDNHG +D HPLVVLRQ VKRXOG FRPH IURP HGJHRQ V\VWHPV +DUWPDQQ +HZHWW t &DOYHW f 7KLV LV H[DFWO\ RSSRVLWH RI ZKDW ZH VHH KHUH (YHQ WKRXJK WKH GHWDLOV RI WKH LQWHUDFWLRQV KDYH \HW WR EH XQFRYHUHG LW VHHPV OLNHO\ WKDW WKH SUHVHQFH RI WKH +H HPLVVLRQ LQ +' LV WUDFLQJ SKHQRPHQD RFFXUULQJ LQ WKH LQQHUPRVW UHJLRQV RI WKH VWDUGLVN V\VWHP :H LQWHUSUHW WKH SRVVLEOH DFWLYH DFFUHWLRQ LQ WKH V\VWHP DV D FOHDU VLJQDWXUH RI LWV \RXWK $QRWKHU SRZHUIXO GLDJQRVWLF WKDW ZH XVH WR LQYHVWLJDWH WKH HYROXWLRQDU\ VWDWH DQG DJH RI +' LV WKH +5 GLDJUDP ,Q )LJXUH DQG ZH SODFH +' VTXDUHf DQG WKH RWKHU HLJKW VRXUFHV LQ RXU 9HJDOLNH VXUYH\ WKDW H[KLELW QHDU,5 H[FHVV LQWR WKH +5 GLDJUDP 7KH GLDJUDP LWVHOI FRQVLVWV RI VWDUV IURP WKH +LSSDUFRV GDWDEDVH 3HUU\PDQ HW DO f DQG VKRZV D ZHOO GHILQHG PDLQVHTXHQFH DV ZHOO DV D IXOO\ SRSXODWHG JLDQW EUDQFK ,Q )LJXUH ZH KDYH WKH SUHPDLQVHTXHQFH HYROXWLRQDU\ WUDFNV IRU LQWHUPHGLDWH PDVV VWDUV IURP 3DOOD DQG 6WDKOHU f RYHUODLG RQWR WKH GLDJUDP ,Q )LJXUH WKH LVRFKURQHV RI ,EHQ f DUH SORWWHG RQ WKH GLDJUDP DORQJ ZLWK +' DQG WKH RWKHU VRXUFHV 6LQFH ZH EHOLHYH WKDW WKH HYLGHQFH VWURQJO\ VXJJHVWV WKDW +' LV DQ 2306 REMHFW WUDQVLWLRQLQJ EHWZHHQ WKH +HUELJ VWDUV DQG WKH 9HJDOLNHV ZH VXJJHVW WKDW LW LV DW D SRLQW LQ LWV HYROXWLRQ ZKHUH LW LV PRYLQJ DFURVV WKH PDLQVHTXHQFH RQWR WKH =$06 *LYHQ WKDW LWV PDVV HVWLPDWH LV 0r 0 LW LV HQFRXUDJLQJ WKDW LQVSHFWLRQ RI )LJXUH VKRZV WKDW WKH VRXUFH OLHV YHU\ FORVH WR WKH 0 WUDFN 7KH HYROXWLRQDU\ WUDFNV DOVR JLYH XV DQ DJH HVWLPDWH IRU WKH VRXUFH E\ XVLQJ WKH OHJHQG VHHQ LQ WKH ORZHU OHIW SDUW RI )LJXUH 7KH WLFNV DORQJ WKH WUDFNV FRUUHVSRQG WR WKH DJHV OLVWHG LQ WKH OHJHQG ,I +' LV IROORZLQJ WKH 0 WUDFN WKHQ ZH FDQ HVWLPDWH LWV DJH DV WR 0\U 7KH

PAGE 114

% 9 >PDJ@ )LJXUH 3RVLWLRQ RI +' LQ WKH +5 GLDJUDP VTXDUHf +' DQG WKH HLJKW RWKHU VRXUFHV LQ RXU 9HJDOLNH VXUYH\ ZLWK QHDU,5 H[FHVVHV RXU &ODVV ,OLD VWDUVf DUH SORWWHG KHUH RQ DQ +5 GLDJUDP RI VWDUV IURP WKH +LSSDUFRV FDWDORJ 2YHUODLG DUH WKH HYROXWLRQDU\ WUDFNV RI 3DOOD t 6WDKOHU f IRU LQWHUPHGLDWH PDVV VWDUV )URP WKH ULJKWPRVW WUDFN WKH FRUUHVSRQGLQJ PDVVHV RI WKH VWDUV DUH 0 7LFN PDUNV RQ WKH WUDFN FRUUHVSRQG WR WKH WLPHV OLVWV LQ WKH OHJHQG +LSSDUFRV GDWD IURP 3HUU\PDQ HW DO f

PAGE 115

‘ ‘ ‘ ‘ f ‘ ‘ % 9 >PDJ@ )LJXUH 3RVLWLRQ RI +' VTXDUHf DQG RWKHU VRXUFHV ZLWK QHDU,5 H[FHVV &ODVV ,OOEf LQ WKH +5 GLDJUDP ZLWK WKH LVRFKURQHV RI ,EHQ f RYHUODLG 7KH WLPH FRQVWDQW ORFL ZHUH GHULYHG DV GHVFULEHG LQ ,EHQ f 7KH WLPHV DSSURSULDWH IRU HDFK ORFXV DUH JLYHQ DERYH HDFK LQ \U WR 0\U DJH HVWLPDWH IRU +' LV VXEVWDQWLDWHG E\ )LJXUH +HUH ZH KDYH SORWWHG WKH LVRFKURQHV RI ,EHQ f RQWR WKH VDPH +5 GLDJUDP DV )LJXUH 2QH LPPHGLDWHO\ VHHV WKDW +' VTXDUHf IDOOV EHWZHHQ WKH [ DQG [ \U LVRFKURQHV :H EHOLHYH WKDW WKH DFFUHWLRQ K\SRWKHVLV WR DFFRXQW IRU WKH +H HPLVVLRQ DQG WKH SRVLWLRQ RI +' LQ WKH +5 GLDJUDP LV YHU\ VWURQJ HYLGHQFH WKDW LW LV D \RXQJ VRXUFH DQG PRVW OLNHO\ PRYLQJ LQWR WKH 9HJDOLNH FODVV IURP WKH +HUELJ FDWHJRU\ 7KLV LV

PAGE 116

D YHU\ LQWHUHVWLQJ WLPH LQ WKH HYROXWLRQ RI WKHVH VRXUFHV VLQFH ZH EHOLHYH WKDW LW LV WKLV GXULQJ WKLV WLPH ZKHQ WKH VRXUFHV DUH LQ WKH WR 0\U DJH UDQJH WKDW WKH DFWLYH IRUPDWLRQ RI SODQHWHVLPDOV ZLOO VWDUW WR FOHDU RXW WKH LQQHU UHJLRQV RI WKHVH GLVNV -D\DZDUGKDQD HW DO f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

PAGE 117

WUDQVLHQWO\ KHDWHG JUDLQV PRVW OLNHO\ SRO\F\FOLF DURPDWLF K\GURFDUERQV 3$+Vf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a \UV RQ WKH DJH RI +' 7KH HYROXWLRQDU\ WUDFNV IRU LQWHUPHGLDWH PDVV 306 VWDUV RI 3DOOD DQG 6WDKOHU f DQG WKH LVRFURQHV RI ,EHQ HW DO f FDQ EH XVHG WR HVWLPDWH WKH DJH RI WKH VRXUFH DW WR 0\U FRQVLVWHQW ZLWK WKH +5 $ DQDORJ\

PAGE 118

&+$37(5 .(&. ,0$*,1* 2) +' 7KLV FKDSWHU SUHVHQWV QHZ PLG,5 REVHUYDWLRQV RI WKH 9HJDOLNH VWDU +' %9Hf 7KH VWDWXV RI +' LV LQ IDFW DPELJXRXV ,W LV FODVVLILHG DV D 9HJDOLNH VWDU E\ VRPH DXWKRUV HJ 6\OYHVWHU HW DO f EXW DV D +HUELJ $H%H VWDU E\ RWKHUV HJ 9DQ GHQ $QFNHU HW DO f 7KH IDFW WKDW +' H[KLELWV FKDUDFWHULVWLFV RI ERWK D SUHPDLQVHTXHQFH DQG D PDLQ VHTXHQFH REMHFW VXJJHVWV WKDW LW PD\ EH D WUDQVLWLRQDO VWDU 9DQ GHQ $QFNHU HW DO f )RU H[DPSOH +' IXOILOOV RI WKH FULWHULD IRU D +HUELJ $H%H VWDU SXW IRUWK E\ +HUELJ LQ KLV RULJLQDO SDSHU +HUELJ f ,W KDV D VSHFWUDO W\SH HDUOLHU WKDQ ) WKHUH DUH HPLVVLRQ OLQHV SUHVHQW LQ LWV VSHFWUXP LH +D DQG 2 DW DQG ƒf DQG LW LV DVVRFLDWHG ZLWK D UHODWLYHO\ EULJKW UHIOHFWLRQ QHEXOD %\ WKHPVHOYHV WKHVH IDFWV VXJJHVW WKDW WKH VRXUFH LV D PHPEHU RI WKLV FODVV RI REMHFW +RZHYHU WKH 3DVFKHQ VHULHV LV QRW LQ HPLVVLRQ LQ +' ZKLFK LV XQXVXDO IRU D +HUELJ $H%H VWDU $QGULOODW -DVFKHN t -DVFKHN f ,Q DGGLWLRQ +' H[KLELWV QR PHDVXUDEOH SKRWRPHWULF YDULDWLRQ ZKHUHDV PRVW bf +HUELJ $H%H VWDUV VKRZ YDULDWLRQV ZLWK DPSOLWXGH PDJ $OYDUH] t 6FKXVWHU 6FKXVWHU t *XLFKDUG f )LQDOO\ WKH UDWLR RI LQIUDUHG WR VWHOODU OXPLQRVLWLHV IRU +' LV [ 2n 6\OYHVWHU HW DO f FRPSDUDEOH WR WKH YDOXH a[On IRU WKH SURWRW\SH 9HJDOLNH VWDU S 3LFWRULV EXW ORZ IRU D +HUELJ $H%H VWDU 7KHVH FRXQWHUDUJXPHQWV PDNH LW GLIILFXOW WR FODVVLI\ +' DV D +HUELJ $H%H VWDU EXW WKH\ DUH FRQVLVWHQW ZLWK LWV EHLQJ PRUH HYROYHG SRVVLEO\ PRUH WKDQ \HDUV ROG 9DQ GHQ $QFNHU HW DO f

PAGE 119

7DEOH &KDUDFWHULVWLFV RI +' 6SHFWUDO 7\SHD 'LVWDQFH % 9H ? SFf ORJ/}/#fD 0DVV 0# \Uf s NPVf ORJDJHf ORJ7HIIfD Y VLQLfE f'DWD IURP 9DQ GHQ $QFNHU HW DO fE 'DWD IURP 'XQNLQ %DUORZ DQG 5\DQ Df 7KH SRVVLEOH WUDQVLWLRQDO QDWXUH RI +' LV UHIOHFWHG LQ LWV SRVLWLRQ LQ WKH +5 GLDJUDP +' KDV D +LSSDUFRV PHDVXUHG GLVWDQFH RI SF DQG 7\FKR PDJQLWXGHV WKDW WUDQVIRUP WR JLYH %9f 6DKX HW DO f ,I ZH DVVXPH WKDW WKH %9f FRORU LV LQGLFDWLYH RI LQWHUVWHOODU UHGGHQLQJ +' KDV DQ DEVROXWH PDJQLWXGH 0Y :HLQEHUJHU HW DO f :H FDQ SODFH +' RQWR WKH +5 GLDJUDP DV VKRZQ LQ )LJXUH ZKLFK LV UHSURGXFHG IURP -XUD HW DO f 2QH FOHDUO\ VHHV WKDW +' OLHV RQ RU YHU\ FORVH WR WKH =$06 FRQVLVWHQW ZLWK LWV EHLQJ \RXQJ -XUD HW DO f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

PAGE 120

)LJXUH +' SRVLWLRQ RQ +5 GLDJUDP +5 GLDJUDP GHULYHG IURP WKH +LSSDUFRV GDWD IRU WKH $W\SH VWDUV LQ WKH
PAGE 121

,OO 6XEVHTXHQW REVHUYDWLRQV PDGH DW .HFN ,, DQG DW WKH &7,2 %ODQFR P WHOHVFRSH ZHUH XVHG WR REWDLQ PRUH DFFXUDWH IOX[ HVWLPDWHV IRU WKH VRXUFH $OO RI WKH REVHUYDWLRQV GLVFXVVHG KHUH ZHUH PDGH XVLQJ WKH 26&,5 V\VWHP +' ZDV REVHUYHG RQ WZR VHSDUDWH RFFDVLRQV DW .HFN ,, $OO REVHUYDWLRQV ZHUH PDGH XVLQJ VWDQGDUG FKRSQRG WHFKQLTXHV ZLWK DQ f FKRSSHU WKURZ LQ GHFOLQDWLRQ ,PDJHV RI +' ZHUH REWDLQHG LQ WKH 1EDQG $r SP $$ SPf DQG LQ WKH ,+: EDQG $R SP $$ SPf 7KH .HFN DXWRJXLGHU V\VWHP ZDV XVHG IRU DOO RI WKH .HFN REVHUYDWLRQV 2Q ERWK .HFN UXQV 0D\ DQG 0D\f WKH ZHDWKHU ZDV PDUJLQDO ZLWK OLJKW FLUUXV FORXGV SUHVHQW GXULQJ WKH QLJKWV +' ZDV REVHUYHG 'XULQJ SRVWSURFHVVLQJ RI WKH GDWD FKRSSHG LPDJH SDLUV WKDW ZHUH REYLRXVO\ FRPSURPLVHG E\ WKH FLUUXV ZHUH GLVFDUGHG +RZHYHU WKHUH LV VWLOO VRPH XQFHUWDLQW\ LQ WKH SKRWRPHWU\ RI WKH VRXUFH DQG WKH VWDQGDUG VWDUV ZKLFK ZH WDNH WR EH s b )RU PRVW RI WKH REVHUYDWLRQV WKLV WUDQVODWHV LQWR WKH PDMRU FRPSRQHQW RI WKH XQFHUWDLQWLHV DVVRFLDWHG ZLWK WKH IOX[ HVWLPDWHV 'HVSLWH WKH FLUUXV WKH VHHLQJ GXULQJ WKH +' REVHUYDWLRQV ZDV YHU\ JRRG 0HDVXUHPHQWV RI WKH IXOOZLGWKV DW KDOI PD[LPXP ):+0f LQWHQVLWLHV RI FRPSDULVRQ VWDUV ZHUH DSSUR[LPDWHO\ f DQG f DW DQG SP UHVSHFWLYHO\ 4XDGUDWLF VXEWUDFWLRQ RI WKH GLIIUDFWLRQ OLPLWV $'f RI f DW SP DQG f DW SP IURP WKHVH YDOXHV IURP LPSOLHV VHHLQJ RI f LQ WKH WR SP VSHFWUDO UHJLRQ 2Q WKH &7,2 %ODQFR P WHOHVFRSH 26&,5 KDV D SODWH VFDOH RI f SHU SL[HO ZLWK DQ DUUD\ ILHOG RI YLHZ RI f [ f ,PDJHV RI +' ZHUH REWDLQHG EHWZHHQ )HEUXDU\ DQG 0DUFK DQG DJDLQ RQ $XJXVW LQ WKH 1 DQG ,+: ILOWHUV DW &7,2 WR DVVLVW LQ WKH IOX[ FDOLEUDWLRQ RI WKH .HFN LPDJHV :H XVHG WKH VWDQGDUG

PAGE 122

7DEOH 26&,5 REVHUYDWLRQV RI +' 'DWH :DYHOHQJWK IOPf )OX[ P-\fDE ,QW 7LPH VHFfF 6WDQGDUG 6WDUV 7HOHVFRSH 0D\ s D %RR D &U% 9HJD .HFN 0D\ s D &U% D 6HR \ $TO W s D X 0DU s D 6HR \5HW ; 9HO &7,2 s L W 0DU s D 6HR ; 9HO X s m mm 0D\ s U_ 6JU _L 80D .HFN s L D 7KH IOX[HV ZHUH REWDLQHG E\ FHQWHULQJ D U f DSHUWXUH RQ WKH VRXUFH E 7KH HUURUV OLVWHG ZLWK WKHVH IOX[ HVWLPDWHV FRQWDLQ ERWK WKH VWDWLVWLFDO PHDVXUHPHQW HUURUV DQG WKH HUURUV LQ FDOLEUDWLRQ ,Q DOO FDVHV WKH\ DUH GRPLQDWHG E\ WKH s b XQFHUWDLQW\ LQ WKH UHSURGXFLELOLW\ RI WKH VWDQGDUG VWDU IOX[HV FDXVHG E\ QRQSKRWRPHWULF VN\ FRQGLWLRQV / 7KH LQWHJUDWLRQ WLPHV OLVWHG FRUUHVSRQG RQO\ WR WKDW KDOI RI WKH FKRSSHU F\FOH IRU ZKLFK WKH VRXUFH LWVHOI DQG QRW WKH UHIHUHQFH VN\ SRVLWLRQf ZDV SURMHFWHG RQWR WKH GHWHFWRU FKRSQRG WHFKQLTXH GXULQJ WKH &7,2 REVHUYDWLRQV ZLWK D FKRSSHU WKURZ RI f LQ GHFOLQDWLRQ 7KHVH REVHUYDWLRQV ZHUH PDGH XQGHU JHQHUDOO\ JRRG VN\ FRQGLWLRQV LH QR FLUUXVf 7DEOH VXPPDUL]HV WKH 26&,5 REVHUYDWLRQV RI +' 7DEOH VKRZV WKDW RXU SP IOX[ PHDVXUHPHQWV UDQJH IURP WR P-\ ZKLOH WKH ILP PHDVXUHPHQWV UDQJH IURP WR P-\ :H FRPELQHG DOO RI WKH PHDVXUHPHQWV IURP WKH GLIIHUHQW QLJKWV LQWR D VLQJOH IOX[ HVWLPDWH IRU HDFK ZDYHOHQJWK XVLQJ D YDULDQFHZHLJKWHG PHDQ 7KH UHVXOWLQJ IOX[ HVWLPDWHV DUH s P-\ LQ WKH 1 EDQG DQG s P-\ LQ WKH ,+: EDQG 7KHVH IOX[ HVWLPDWHV DUH VRPHZKDW ORZ FRPSDUHG WR RWKHU PHDVXUHPHQWV RI WKH VRXUFH LQFOXGLQJ WKRVH E\ 6\OYHVWHU HW DO f 2XU 26&,5 PHDVXUHPHQWV DUH b DQG b RI WKH 6\OYHVWHU HVWLPDWHV DW DQG

PAGE 123

SP UHVSHFWLYHO\ +RZHYHU WKH UDWLR RI WKH IOX[HV ) L RJ) f SUHVHQWHG KHUH LV YHU\ FRQVLVWHQW ZLWK WKH 6\OYHVWHU HW DO f IOX[ UDWLR $V ZH ZLOO VHH LQ D ODWHU VHFWLRQ LW LV SULPDULO\ WKH IOX[ UDWLR )LRV)LVLf WKDW DOORZV XV WR SODFH DQ XSSHU OLPLW RQ WKH VL]H RI WKH PLG,5 HPLWWLQJ JUDLQV DURXQG +' ,Q DGGLWLRQ WR WKH HPLVVLRQ IURP WKH GXVW WKH PHDVXUHG IOX[HV FRQWDLQ PLG,5 UDGLDWLRQ HPLWWHG E\ WKH SKRWRVSKHUH RI WKH FHQWUDO VWDU 7R UHPRYH WKLV SKRWRVSKHULF HPLVVLRQ ZH HVWLPDWHG WKH PLG,5 IOX[ GHQVLWLHV RI +' % 9Hf E\ QRUPDOL]LQJ WKH VSHFWUDO HQHUJ\ GLVWULEXWLRQ RI 9HJD $2 9f WR WKH .EDQG SPf IOX[ GHQVLW\ RI +' PHDVXUHG E\ 6\OYHVWHU HW DO f 7KLV PHWKRG LPSOLHV D SKRWRVSKHULF IOX[ GHQVLW\ RI P-\ DW SP b RI WKH WRWDO IOX[ DW WKLV ZDYHOHQJWKf $W SP WKH SKRWRVSKHUH HPLWV P-\ b RI WKH WRWDO IOX[f 7KH SKRWRVSKHUH VXEWUDFWHG YDULDQFHZHLJKWHG IOX[ HVWLPDWHV DQG DVVRFLDWHG HUURUV DUH s P-\ DW SP DQG s P-\ DW SP 6RXUFH 6L]H ,Q )LJXUH ZH SUHVHQW FRQWRXU SORWV RI +' DW DQG SP DQG D QHDUE\ FRPSDULVRQ VWDU +' f REVHUYHG WR PHDVXUH WKH SRLQWVSUHDGIXQFWLRQ 36)f $W HDFK ZDYHOHQJWK WKH ORZHVW FRQWRXU SORWWHG IRU WKH 36) VWDU UHSUHVHQWV WKH VDPH EULJKWQHVV UHODWLYH WR WKH SHDN DV WKDW SORWWHG IRU WKH SURJUDP VWDU 3DQHOV DE RI )LJXUH FRPSDUH +' DQG WKH 36) DW SP DQG SDQHOV FG FRPSDUH +' DQG WKH 36) DW SP 7KH H[WHQGHG HPLVVLRQ IURP +' LV HYLGHQW DV DQ HORQJDWLRQ RI WKH VRXUFH LQ )LJXUHV D DQG F DW 3$ r s r 7KH GLDPHWHU RI WKH ORZHVW FRQWRXU DORQJ WKH PDMRU D[LV RI WKH HPLVVLRQ LQ )LJXUH OD LV af ZKLFK

PAGE 124

, , +' PLFURQV U LWWLL L , 7 , , , , , n , n , , , L 36) VWDU PLFURQV F R F R X f Df Ef I L ,, W 0 ‘ ,W QP_O W++ W W f I f 0 f 0+ W ‘ 0 M+ + 0 f 36) VWDU PLFURQV Ff +' PLFURQV Gf W L $UFVHFRQGV )LJXUH ,PDJHV RI +' DQG D SRLQWVSUHDGIXQFWLRQ 36)f VWDU 1RUWK LV XS DQG HDVW LV WR WKH OHIW 7KH FRQWRXU SORWV KDYH EHHQ VPRRWKHG XVLQJ D *DXVVLDQ ILOWHU ZLWK ):+0 $' DQG SL[HOV IRU DQG SP UHVSHFWLYHO\f ,Q DOO SDQHOV WKH ORZHVW FRQWRXU LV DERXW WLPHV WKH VPRRWKHG QRLVH Df SP LPDJH RI +' ZLWK ORJDULWKPLF FRQWRXUV P-\ DUFVHFf VSDFHG DW 7KH VRXUFH KDV D PHDVXUHG ):+0 f Ef 3ORW RI WKH 36) VWDU DW SP QRUPDOL]HG WR DW SHDN /RJDULWKPLF FRQWRXUV KHUH DUH VSDFHG DW WKH VDPH SHUFHQWDJH OHYHOV DV SDQHO LQ Df ):+0 f Ff SP LPDJH RI +' ZLWK FRQWRXUV P-\ DUFVHFf VSDFHG OLQHDUO\ DW ):+0 f Gf 1RUPDOL]HG SORW RI WKH 36) VWDU +' DW SP /LQHDU FRQWRXU OHYHOV KHUH DUH VSDFHG DW WKH VDPH SHUFHQWDJH OHYHOV DV SDQHO LQ Ff ZLWK XQLW VWHSV ):+0 f

PAGE 125

FRUUHVSRQGV WR $8 ,Q )LJXUH OF ZH VHH WKDW WKH PD[LPXP H[WHQW RI WKH ORZHVW FRQWRXU DW SP LV f $8f ZKLFK LV DERXW b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f VKRZV WKDW WKHUH LV VWURQJ HPLVVLRQ LQ WKH SP f3$+f EDQG DQG VRPHZKDW ZHDNHU HPLVVLRQ LQ WKH SP f3$+f EDQG 2XU EURDGEDQG $; SPf IOX[ PHDVXUHPHQW DW SP LQFOXGHV D FRQWULEXWLRQ IURP WKLV 3$+ HPLVVLRQ %HORZ ZH HVWLPDWH ZKDW HIIHFW WKH SUHVHQFH RI WKLV 3$+ HPLVVLRQ FRXOG KDYH RQ RXU FRQFOXVLRQV 7KH RYHUDOO VL]H RI WKH HPLVVLRQ DURXQG +' D UDGLDO H[WHQW RI $8 DW ERWK DQG SP LV FRPSDUDEOH WR WKH VL]HV RI WKH PLG,5 HPLWWLQJ UHJLRQV RI ERWK WKH DUFKHW\SH 9HJDOLNH VRXUFH 3 3LF $9f DQG +5 $ $9f /DJDJH t 3DQWLQ

PAGE 126

1RUPDOL]HG )OX[ $UFVHFRQGV $UFVHFRQGV )LJXUH 6FDQV WKURXJK +' DQG WKH 36) VWDU ,Q DOO SORWV +' LV WKH VROLG OLQH DQG WKH 36) VWDU LV WKH GDVKHG OLQH $ JDXVVLDQ ILW WR WKH +' GDWD LV VKRZQ DV WKH GRWWHG OLQH Df 6FDQ WKURXJK WKH PDMRU D[LV 3$ rf RI +' DW SP Ef 6FDQ WKURXJK WKH PLQRU D[LV RI +' DW SP Ff 0DMRU D[LV 3$ rf VFDQ DW SP Gf 0LQRU D[LV VFDQ DW _LP f PHDVXUHG SP HPLVVLRQ IURP 3LFWRULV RXW WR $8 IURP WKH FHQWUDO VWDU 5HFHQW REVHUYDWLRQV RI WKH GLVN DURXQG +5 $ VKRZ WKDW LW WRR HPLWV ERWK DQG SP UDGLDWLRQ RXW WR D GLVWDQFH RI $8 7HOHVFR HW DO f 2XU HVWLPDWHV RI WKH VRXUFH VL]H DUH FRQVLVWHQW ZLWK VLPLODU PLG,5 LPDJHV RI WKH VRXUFH SUHVHQWHG E\ 6LOYHUVWRQH HW DO f

PAGE 127

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f 7KH PRGHO DVVXPHV WKDW WKH JUDLQV WKDW DUH VSKHULFDO 0LH SDUWLFOHV FRPSRVHG RI DVWURQRPLFDO VLOLFDWHV 'UDLQH t /HH f ZLWK GHQVLW\ S JFP 7KH WHPSHUDWXUH RI WKH GXVW SDUWLFOHV GHWHUPLQHV WKH REVHUYHG IOX[ UDWLR DQG ZH HVWLPDWH WKH JUDLQ VL]H E\ PDWFKLQJ WKH REVHUYHG IOX[ UDWLR WR WKH IOX[ UDWLR FDOFXODWHG IRU JUDLQV RI GLIIHUHQW GLDPHWHUV ORFDWHG DW D GLVWDQFH RI $8 IURP WKH VWDU 7KH UHVXOWV RI WKH PRGHO VKRZ WKDW VSKHULFDO 0LH SDUWLFOHV FRPSRVHG RI DVWURQRPLFDO VLOLFDWHV ZLWK D

PAGE 128

WHPSHUDWXUH DQG D GLDPHWHU RI ILP ILW WKH REVHUYHG PLG,5 IOX[ UDWLR 0RUH GHWDLOHG PRGHOV RI +' SURGXFHG E\ 6\OYHVWHU t 6NLQQHU f LQGLFDWH D FRPSDUDEOH YDOXH IRU WKH XSSHU OLPLW WR WKH FKDUDFWHULVWLF JUDLQ VL]H 0RGHOLQJ RI WKH GLVN RI +5 $ LQ :\DWW HW DO f DQG 7HOHVFR HW DO f VKRZV WKDW ZLWK WKH DVVXPSWLRQ WKDW WKH\ DUH VSKHULFDO 0LH SDUWLFOHV WKH PLGLQIUDUHG HPLWWLQJ GXVW JUDLQV LQ WKDW GLVN DUH DOVR DSSUR[LPDWHO\ >LP LQ VL]H 0LG,5 DSHUWXUH SKRWRPHWU\ DQG VSHFWURSKRWRPHWULF REVHUYDWLRQV RI 3LFWRULV 7HOHVFR HW DO 7HOHVFR t .QDFNH $LWNHQ HW DO f LPSOLHV WKH SUHVHQFH RI SP JUDLQV LQ WKDW GLVN 9DQ GHU %OLHN HW DO f UHDQDO\]HG WKH ,5$6 GDWD RQ 9HJD DQG SURSRVHG WKDW WKH GRPLQDQW JUDLQV LQ WKDW DUFKHW\SDO GLVN DUH RQ WKH RUGHU RI _LP LQ VL]H 7KH PLG,5 VSHFWUXP RI +' E\ 6\OYHVWHU HW DO f VKRZV WKDW WKHUH LV HPLVVLRQ LQ WKH PLG,5 f3$+f EDQGV WKDW FRQWULEXWHV WR RXU LP IOX[ HVWLPDWH 7R LQYHVWLJDWH KRZ RXU GHGXFHG JUDLQ VL]H HVWLPDWHV FKDQJH GXH WR WKLV FRQWDPLQDWLRQ ZH UDQ WKH PRGHOV DVVXPLQJ WKDW QRQH b DQG b RI WKH LP IOX[ ZDV HPLWWHG E\ 3$+ JUDLQV 2XU JUDLQ VL]H HVWLPDWHV UDQJHG IURP _LP QR FRQWDPLQDWLRQf WR _LP b FRQWDPLQDWLRQf (YHQ ZLWK PRVW RI WKH IOX[ FRPLQJ IURP WKH 3$+ JUDLQV WKH GHULYHG JUDLQ VL]HV HVWLPDWHV DUH FRQVLVWHQW ZLWK WKRVH LQ RWKHU GHEULV GLVNV 7KH IDFW WKH +' PD\ KDYH GXVW RI WKLV VL]H KDV LPSRUWDQW LPSOLFDWLRQV IRU RXU XQGHUVWDQGLQJ RI WKH HYROXWLRQ RI WKH GLVN %\ FRQVLGHULQJ WKH UDWLR RI WKH UDGLDWLRQ IRUFH WR WKH JUDYLWDWLRQDO IRUFH RQ D SDUWLFOH FDOOHG 3f ZH FDQ LQYHVWLJDWH WKH HIIHFWV RI WKH VWHOODU UDGLDWLRQ RQ WKHVH SDUWLFOHV $V VXPPDUL]HG LQ $UW\PRZLF] f 3 4SU! /r0rf 5 S

PAGE 129

ZKHUH 5 LV WKH SDUWLFOH UDGLXV S LV LWV GHQVLW\ 4SUf LV WKH UDGLDWLRQ SUHVVXUH HIILFLHQF\ DYHUDJHG DFURVV WKH VWHOODU VSHFWUDO HQHUJ\ GLVWULEXWLRQ DQG /r0r LV WKH UDWLR RI WKH VWHOODU OXPLQRVLW\ DQG PDVV 8VLQJ WKH VWHOODU SDUDPHWHUV IRU +' IURP 7DEOH ZH KDYH FDOFXODWHG 3 DV D IXQFWLRQ RI SDUWLFOH VL]H IRU DVWURQRPLFDO VLOLFDWH 0LH VSKHUHV ZLWK GHQVLW\ S JFP )RU SP GLDPHWHU SDUWLFOHV ZH LQIHU D YDOXH RI 3 3DUWLFOHV ZLWK 3 DUH RQ XQERXQG K\SHUEROLF RUELWV DQG ZLOO EH UHPRYHG IURP WKH V\VWHP LQ D YHU\ VKRUW WLPH ,Q WKH FDVH RI +' WKLV LV RQ WKH RUGHU RI D IHZ KXQGUHG WR D WKRXVDQG \HDUV GHSHQGLQJ RQ ZKHUH LQ WKH GLVN WKH KLJK 3 SDUWLFOHV ZHUH IRUPHG 7KH PRGHOV VKRZ WKDW WKH YDOXH RI 3 UHPDLQV DERYH XQLW\ IRU SDUWLFOHV VPDOOHU WKDQ SP LQ GLDPHWHU &RQVHTXHQWO\ ZH FRQFOXGH WKDW WKH PLG,5 HPLWWLQJ SDUWLFOHV ZLOO EH UHPRYHG IURP WKH V\VWHP YHU\ TXLFNO\ HYHQ LI RXU XSSHU OLPLW XQGHUHVWLPDWHV WKH JUDLQ VL]H E\ D IDFWRU RI WZR RU PRUH 6LQFH WKH UHPRYDO WLPH RI WKH JUDLQV IURP WKH GLVN LV PXFK OHVV WKDQ WKH DVVXPHG DJH RI WKH V\VWHP \Uf ZH FRQFOXGH WKDW WKH PLG,5 HPLWWLQJ JUDLQV DUH QRW SULPRUGLDO DQG KDYH EHHQ UHSOHQLVKHG WKURXJK VRPH PHFKDQLVP 2QH SRVVLEOH VFHQDULR IRU WKH UHSOHQLVKPHQW RI WKHVH SDUWLFOHV LV WKURXJK FROOLVLRQV RI ODUJHU ERGLHV DV LV DSSDUHQWO\ WKH FDVH IRU 3 3LFWRULV $UW\PRZLF] f DQG +5 $ :\DWW HW DO 7HOHVFR HW DO f &RPSDULVRQ WR 1,&026 ,PDJHV :HLQEHUJHU HW DO f PDGH FRURQDJUDSKLF REVHUYDWLRQV RI +' DW SP ZLWK 1,&026 7KH\ XVHG D f GLDPHWHU VSRW EXW LQVWUXPHQWDO HIIHFWV UHQGHUHG GDWD

PAGE 130

ZLWKLQ f RI WKH FHQWUDO VWDU XQXVDEOH 7KHLU LPDJHV VKRZ ZKDW DSSHDUV WR EH DQ DOPRVW IDFHRQ FLUFXPVWHOODU GLVN 7KH QHDU,5 IOX[ ZKLFK LV SUREDEO\ OLJKW IURP WKH VWDU VFDWWHUHG E\ GXVW LQ WKH GLVN H[WHQGV RXW WR D UDGLXV RI f $8f :HLQEHUJHU HW DO f 7KH SRVLWLRQ DQJOH RI WKH PDMRU D[LV RI WKH QHDU,5 GLVN LV HTXDO WR WKDW RI WKH PLG ,5 HPLVVLRQ 7KH 1,&026 LPDJH DOVR VKRZV HYLGHQFH IRU D JDS LQ WKH GXVW DW D UDGLXV RI f $V VXJJHVWHG E\ :HLQEHUJHU HW DO f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t :ROVWHQFURIW f ILW D EODFNERG\ WR WKH IDU,5 DQG SPf ,5$6 IOX[HV IRU WKLV VRXUFH +RZHYHU WKH SP ,5$6 SRLQW ZDV FRQVSLFXRXVO\ KLJK FRPSDUHG WR WKH RWKHUZLVH JRRG ILW 7KLV LPSOLHV WKDW WKHUH PD\ EH D VHFRQG SRSXODWLRQ RI GXVW DW D WHPSHUDWXUH KLJKHU WKDQ WKDW LV UHVSRQVLEOH IRU WKH SP H[FHVV LQ WKH VRXUFH 7KH PLG,5 FRQWRXUV LQ )LJXUH SUREDEO\ LQGLFDWH WKH ORFDWLRQ RI WKRVH ZDUPHU JUDLQV 7KH 26&,5 t 1,&026 GDWD VKRZQ LQ )LJXUH PD\ EH GLUHFW REVHUYDWLRQDO HYLGHQFH IRU WZR VHSDUDWH SRSXODWLRQV RI GXVW JUDLQV 7KH LQQHU ZDUPHU JUDLQV ZKLFK

PAGE 131

)LJXUH 1,&026 LPDJH DQG 26&,5 FRQWRXUV RI +' _LP FRQWRXUV RYHU D SP LPDJH IURP :HLQEHUJHU HW DO f &RQWRXUV LQ P-\ DUFVHFf DUH VSDFHG OLQHDUO\ DW DQG 7KH ORZHVW FRQWRXU OHYHO LV DERXW WLPHV WKH VPRRWKHG QRLVH 7KH PLG,5 FRQWRXUV ZHUH UHJLVWHUHG WR WKH VWHOODU SRVLWLRQ LQ WKH QHDU,5 LPDJH HPLW WKH PLG,5 DQG SPf UDGLDWLRQ DQG WKH PRUH GLVWDQW JUDLQV WKDW DUH UHVSRQVLEOH IRU WKH VFDWWHUHG QHDU,5 IOX[ VHHQ LQ WKH 1,&026 LPDJH DQG WKH IDU,5 DQG SPf HPLVVLRQ GHWHFWHG E\ ,5$6 7KH VWURQJ 3$+ HPLVVLRQ VHHQ LQ WKH VSHFWUXP RI WKLV VRXUFH 6\OYHVWHU f LQGLFDWH WKDW WKLV SURSRVHG fLQQHU SRSXODWLRQf FDQQRW VLPSO\ EH ZDUP VLOLFDWHV 7KH 3$+ JUDLQV LQ WKH LQQHUPRVW UHJLRQV RI WKH GLVN PD\

PAGE 132

LQGHHG EH PL[HG ZLWK VLOLFDWHV IRU ZKLFK WKHUH LV QRW \HW GLUHFW HYLGHQFH (YHQ LI WKH PLG ,5 HPLWWLQJ JUDLQV ZHUH EODFNERGLHV WKH\ ZRXOG FRQWULEXWH D YHU\ WLQ\ IUDFWLRQ RI WKH DQG SP H[FHVV DQG P-\ UHVSHFWLYHO\f DQG WKHUHIRUH WKH ORQJHU ZDYHOHQJWK H[FHVV PXVW FRPH IURP RWKHU JUDLQV 7KLV VLWXDWLRQ LV VLPLODU WR WKDW IRU 3LFWRULV ZKHUH WKH PLG,5 HPLVVLRQ FRPHV IURP D UHODWLYHO\ VPDOO LQQHU UHJLRQ RI WKH WRWDO GLVN ,PDJHV LQ WKH YLVLEOH DQG QHDU,5 E\ %XUURZV t .ULVW f .DODV DQG -HZLWW f DQG 6PLWK DQG 7HUULOH f VKRZ WKDW WKH GLVN DURXQG 3LFWRULV H[WHQGV RXW WR DW OHDVW D UDGLXV RI f $8f IURP WKH VWDU LQ WKH QHDU,5 DQG PXFK IDUWKHU WKDQ WKDW LQ WKH YLVLEOH &RQFOXVLRQV $ERXW WKH 'LVN RI +' 2XU PLG,5 LPDJHV PDGH ZLWK 26&,5 RQ .HFN VKRZ H[WHQGHG HPLVVLRQ DURXQG WKH % 9HJDOLNH VWDU +' DW DQG SP 7KH HPLVVLRQ LV GHWHFWHG RXW WR D UDGLXV RI f $8f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

PAGE 133

7KH YDOXH RI WKH UDWLR RI WKH UDGLDWLRQ IRUFH WR WKH JUDYLWDWLRQDO IRUFH RQ D SDUWLFOH IRU WKHVH SDUWLFOHV LV a 3DUWLFOHV ZLWK D YDOXH RI DUH RQ XQERXQG K\SHUEROLF RUELWV DQG ZLOO EH UHPRYHG IURP WKH V\VWHP RQ D YHU\ VKRUW WLPH VFDOH ,Q WKH FDVH RI +' WKH UHPRYDO WDNHV SODFH LQ D IHZ KXQGUHG \HDUV :H WKHUHIRUH FRQFOXGH WKDW LI WKH\ DUH VLOLFDWH 0LH VSKHUHV WKH JUDLQV UHVSRQVLEOH IRU WKH PLG,5 HPLVVLRQ DUH QRW SULPRUGLDO 7KH\ KDYH EHHQ UHSOHQLVKHG E\ VRPH PHFKDQLVP SHUKDSV WKURXJK FROOLVLRQV RI ODUJHU ERGLHV DV LV DOVR DSSDUHQWO\ WKH FDVH IRU +5 $ 7KH ODUJH H[WHQW RI WKLV GLVN LWV RULHQWDWLRQ DQG LWV UHODWLYHO\ KLJK VXUIDFH EULJKWQHVV PDNH WKLV VRXUFH DQ H[FHOOHQW FKRLFH IRU IXUWKHU VWXG\ :LWK RQO\ D IHZ H[DPSOHV RI WKLV FODVV RI GLVN NQRZQ WKH GLVN RI +' ZLOO PRVW OLNHO\ EH VWXGLHG LQWHQVHO\ IRU WKH IRUHVHHDEOH IXWXUH ,Q SDUWLFXODU GHHS PLG,5 LPDJLQJ ZLWK D WHOHVFRSH VXFK DV *HPLQL ZRXOG DOORZ XV WR WU\ WR GHWHFW DQ\ WKHUPDO HPLVVLRQ HYHQ IDUWKHU DZD\ IURP WKH FHQWUDO VWDU 7KH V\PPHWULF 36) RI *HPLQL ZRXOG PDNH UHPRYDO RI WKH HPLVVLRQ IURP WKH FHQWUDO PXFK HDVLHU WKXV JLYLQJ XV D EHWWHU FKDQFH RI VHHLQJ VWUXFWXUH LQ WKH GLVN ,QVWUXPHQWV WKDW DUH QRZ EHLQJ EXLOW WR EH XVHG RQ WKH QHZ FODVV RI PHWHU WHOHVFRSHV DUH EHLQJ HTXLSSHG ZLWK VXLWHV RI QDUURZEDQG PLG,5 ILOWHUV ZKLFK ZLOO EH H[WUHPHO\ YDOXDEOH LQ WKH VWXG\ RI WKH f3$+f EDQGV DQG HPLVVLRQ IHDWXUHV %\ LPDJLQJ VRXUFHV OLNH +' ZLWK ILOWHUV WKDW DUH LQ DQG RXW RI WKHVH IHDWXUHV ZH ZLOO EH DEOH WR PDS ZKHUH WKH HPLVVLRQ IURP WKHVH PROHFXOHV DUH DQG EHWWHU PRGHO WKH SDUWLFOH GLVWULEXWLRQ LV WKHVH GLVNV

PAGE 134

&+$37(5 6$2 $ 48(67,21 2) &/$66,),&$7,21 7KLV FKDSWHU GLVFXVVHV .HFN REVHUYDWLRQV RI WKH VRXUFH 6$2 7KH XQXVXDO QDWXUH RI 6$2 +' f ZDV ILUVW UHFRJQL]HG E\ WKH ,5$6 VDWHOOLWH ZKHQ LW GHWHFWHG D ODUJH ,5 H[FHVV DW DOO ZDYHOHQJWKV ORQJHU WKDQ SP IRU WKH VRXUFH 7KH FKDUDFWHULVWLFV RI WKH H[FHVV ILW WKH FULWHULD RI :DONHU DQG :ROVWHQFURIW f >::@ DQG WKH\ LQFOXGHG WKH REMHFW RQ WKHLU OLVW RI 9HJDOLNH VRXUFHV ,QGHHG 6$2 ORRNV OLNH DQ H[FHOOHQW GLVN FDQGLGDWH 7KH RYHUDOO EULJKWQHVV RI WKH VRXUFH DQG WKH VKDSH RI LWV 6(' ERWK VHHP WR LPSO\ WKHUH LV D ODUJH DPRXQW RI GXVW DURXQG WKH VRXUFH $GGLWLRQDOO\ 6$2 KDV RQH RI WKH KLJKHVW >@ >@ FRORUV LQ WKH VDPSOH RI :: DQG WKH VRXUFH ZDV PDUNHG DV H[WHQGHG DW DQG SP LQ WKH ,5$6 :RUNLQJ 6XUYH\ 'DWDEDVH ::f 7KH QDWXUH RI WKH H[FHVV LWV RYHUDOO PDJQLWXGH DQG WKH HYLGHQFH IRU H[WHQVLRQ PDGH 6$2 DQ H[FHOOHQW FDQGLGDWH IRU IXUWKHU REVHUYDWLRQ 6\OYHVWHU HW DO f LQFOXGHG 6$2 LQ WKHLU IROORZXS VXUYH\ RI WKH :: VRXUFHV DQG REVHUYHG WKH VRXUFH IURP WKH RSWLFDO WR WKH PLOOLPHWHU 6NLQQHU HW DO f DOVR REVHUYHG 6$2 IURP WKH QHDU,5 WR WKH PLOOLPHWHU ILOOLQJ LQ JDSV LQ WKH 6\OYHVWHU HW DO f REVHUYDWLRQV DQG SUHVHQWHG D SP 1EDQGf LPDJH RI WKH VRXUFH WKDW VKRZV ZKDW DSSHDUV WR EH D KLJKO\ LQFOLQHG GLVN VXUURXQGLQJ WKH VWDU $ERXW WKH VDPH WLPH WKH 6NLQQHU HW DO f UHVXOW ZDV SXEOLVKHG D SDSHU E\ =XFNHUPDQ HW DO f SUHVHQWHG D OLVW RI OXPLQRVLW\ FODVV ,,, VWDUV ZLWK IDU,5 H[FHVV HPLVVLRQ $OWKRXJK 6$2 ZDV QRW LQFOXGHG LQ WKH WKLV RULJLQDO OLVW RI VRXUFHV WKH =XFNHUPDQ HW DO f SDSHU ZDV SHUKDSV WKH ILUVW WR GLVFXVV WKH LGHD RI D FODVV RI JLDQW

PAGE 135

VWDUV ZLWK GXVW RUELWLQJ WKHP )HNHO HW DO f SUHVHQWHG HYLGHQFH WKDW 6$2 LV LQ IDFW D PHPEHU RI WKH OXPLQRVLW\ FODVV ,,, VWDUV ZLWK IDU,5 H[FHVVHV 7KH OXPLQRVLW\ FODVV ,,, GHVLJQDWLRQ LV DW RGGV ZLWK WKH ZRUN RI 0LURVKQLFKHQNR HW DO f ZKR DUJXH WKDW 6$2 LV LQ IDFW D GZDUI VWDU OXPLQRVLW\ FODVV 9f EXW ZLWK D ODWHU VSHFWUDO W\SH .f WKDQ WKDW DVVXPHG E\ 6NLQQHU HW DO f DQG 6\OYHVWHU HW DO f ,Q ZH DGGHG RXU RZQ IROORZXS REVHUYDWLRQV WR WKH VWXG\ RI WKH VRXUFH ZKHQ ZH LPDJHG 6$2 DV SDUW RI RXU 9HJDOLNH VXUYH\ DW .HFN 7KH 'HWHFWLRQ DQG 1RQGHWHFWLRQ RI WKH 6$2 'LVN 3UHYLRXV 2EVHUYDWLRQV 7KH ILUVW LQIUDUHG REVHUYDWLRQV RI 6$2 ZHUH PDGH ZLWK WKH ,5$6 VDWHOOLWH 7KH VRXUFH ZDV PDUNHG DV H[WHQGHG LQ WKH WKUHH ORQJ ZDYHOHQJWK ,5$6 EDQGV DQG SPf DQG ZDV WKXV ZDV HDUPDUNHG DV DQ H[FHOOHQW FDQGLGDWH IRU IROORZXS REVHUYDWLRQV ,Q 6NLQQHU HW DO SUHVHQWHG LPDJLQJ RI 6$2 WKDW SUHVXPDEO\ VKRZHG D QHDUO\ HGJHRQ GLVN DW SP 7KHLU SP 1EDQGf LPDJH ZDV FRQVLVWHQW ZLWK WKH GXVW EHLQJ FRQILQHG WR D GLVN DW 3$ r ZLWK ):+0 f DQG DQ LQFOLQDWLRQ DQJOH RI r 6NLQQHU HW DO f 7KH PLG,5 LPDJLQJ ZDV REWDLQHG DV SDUW RI DQ H[WHQVLYH VXLWH RI REVHUYDWLRQV PDGH E\ WKH JURXS IURP WKH QHDU,5 WR WKH PLOOLPHWHU UHJLPH ,Q WKH SDSHU WKDW SUHVHQWHG WKH PLG,5 LPDJLQJ WKH\ DOVR SXEOLVKHG QHDU,5 SKRWRPHWU\ D PLG,5 VSHFWUD DQG DQ XSSHU OLPLW IRU WKH IOX[ RI WKH VRXUFH DW SP 6NLQQHU HW DO f $OO RI WKHLU REVHUYDWLRQV H[FHSW WKH SP XSSHU OLPLW ZHUH REWDLQHG RQ WKH P 8QLWHG .LQJGRP ,QIUDUHG 7HOHVFRSH 8.,57f RQ 0DXQD .HD XQGHU JRRG REVHUYLQJ FRQGLWLRQV XVLQJ WKH %HUNHOH\/LYHUPRUH PLG,5 FDPHUD

PAGE 136

%HUNFDPf 6LQFH RXU 26&,5 UHVXOWV DUH DW RGGV ZLWK WKH REVHUYDWLRQV RI 6NLQQHU HW DO f ZH OLVW D IHZ RI WKH PRVW UHOHYDQW FKDUDFWHULVWLFV RI %HUNFDP KHUH %HUNFDP FRQWDLQV D [ DUUD\ RI ZKLFK D [ VHFWLRQ ZDV XVHG WR LPDJH WKH VRXUFH 7KH SL[HO VL]H RI %HUNFDP LV f SHU SL[HO 6NLQQHU HW DO .HWR HW DO f 7KH 6NLQQHU HW DO f REVHUYDWLRQV ZHUH PDGH XVLQJ WKH VWDQGDUG fFKRSQRGf WHFKQLTXH RI PLG,5 REVHUYLQJ VHH $SSHQGL[ $f $ QHDUE\ VWDQGDUG VWDU 3 *HPf ZDV XVHG DV D SKRWRPHWULF VWDQGDUG DQG DV D 36) VWDU IRU WKHLU REVHUYDWLRQV ,W LV LQWHUHVWLQJ WR QRWH LV WKDW WKH 6,0%$' VHUYLFH FDOFXODWHV WKDW S *HP LV r IURP 6$2 2XU H[SHULHQFH KDV VKRZQ WKDW WKLV LV D UDWKHU ODUJH GLVWDQFH EHWZHHQ D SURJUDP REMHFW DQG 36) VWDU )RU RXU 9HJDOLNH VXUYH\ DOO RI WKH 36) VWDUV ZHUH ZLWKLQ r RI WKH WDUJHW WR PLQLPL]H V\VWHPDWLF HUURUV OLNH WHOHVFRSH IOH[XUH 7KH EURDG EDQG 1 LPDJH RI 6$2 SUHVHQWHG LQ 6NLQQHU HW DO f KDV ):+0 s f LQ ULJKW DVFHQVLRQ DQG ):+0 s f LQ GHFOLQDWLRQ 7KHLU LPDJH VKRZHG D SRVLWLRQ DQJOH IRU WKH H[WHQGHG HPLVVLRQ RI r 3KRWRPHWU\ RI WKH VRXUFH JDYH D IOX[ GHQVLW\ RI )1 -\ FRQVLVWHQW ZLWK WKH ,5$6 SP SRLQW DQG RXU 1EDQG IOX[ HVWLPDWH RI -\ 7KH 6NLQQHU HW DO f SDSHU DOVR GLVFXVVHG WKH SRVVLEOH JUDLQ SRSXODWLRQV WKDW ZRXOG H[LVW LQ VXFK D GLVN ,Q D ODWHU VHFWLRQ ZH VKRZ KRZ RXU PRGHOLQJ RI WKH JOREDO JUDLQ SURSHUWLHV DJUHH ZLWK WKHLUV +RZHYHU GXH WR WKH QHZ VL]H OLPLWV ZH SODFH RQ WKH VRXUFH ZH EHOLHYH WKDW WKHLU GLVFXVVLRQ RI VSDWLDO VWUXFWXUH LQ WKH GLVN DQG KRZ WKDW PD\ FKDQJH WKH LQWHUSUHWDWLRQ RI WKHLU PRGHOV PXVW EH WUHDWHG ZLWK WKH XWPRVW RI FDXWLRQ

PAGE 137

1HZ .HFN ,PDJLQJ ZLWK 26&,5 :H REWDLQHG QHDU GLIIUDFWLRQOLPLWHG LPDJHV RI 6$2 XVLQJ 26&,5 RQ .HFN ,, LQ 0D\ 2EVHUYDWLRQV ZHUH PDGH LQ WKH SP 1%DQGf DQG LP ,+:f EDQGV RQ DQG 0D\ XQGHU JRRG REVHUYLQJ FRQGLWLRQV 2XU REVHUYDWLRQV VKRZ 6$2 WR EH DQ XQUHVROYHG SRLQW VRXUFH ZLWK ):+0 RI f DW SP DQG ):+0 RI f DW SP 2XU REVHUYDWLRQDO VWUDWHJ\ XVHG IRU WKH 6$2 REVHUYDWLRQV ZDV VLPLODU WR WKRVH XVHG IRU WKH 9HJDOLNH VXUYH\ 7KH VHTXHQFH RI REVHUYDWLRQV PDGH RQ HDFK QLJKW ZDV REVHUYDWLRQV RI D QHDUE\ 36) VWDU DW DQG SP GHHS LQWHJUDWLRQV RQ 6$2 DW DQG SP DQRWKHU VHW RI 36) VWDU REVHUYDWLRQV DQG ILQDOO\ REVHUYDWLRQV RI DQ ,5 VWDQGDUG VWDU IRU SKRWRPHWULF FDOLEUDWLRQ 7KH 36) VWDU XVHG IRU DOO 6$2 REVHUYDWLRQV ZDV 330 .9f ZKLFK LV DW D GLVWDQFH RI r IURP WKH VRXUFH 7KH ,5 VWDQGDUG VWDUV D /\U D &U% DQG D %RR ZHUH XVHG IRU DEVROXWH IOX[ FDOLEUDWLRQ VHH 7DEOH IRU VWDQGDUG VWDU IOX[ GHQVLWLHVf 7KH .HFN DXWRJXLGHU V\VWHP ZDV XVHG IRU DOO RI WKH REVHUYDWLRQV 2XU H[SHULHQFH ZLWK WKH DXWRJXLGHU V\VWHP VKRZV WKDW WKHUH LV D SL[HO fMLWWHUf DVVRFLDWHG ZLWK WKH JXLGLQJ FRUUHFWLRQV ZKLFK FRUUHVSRQGV WR f RQ .HFN &ORVH LQVSHFWLRQ RI WKH GDWD VKRZV WKDW WKH VHHLQJ ZDV PRVWO\ VWDEOH RQ WKH QLJKWV RI WKH REVHUYDWLRQV DQG WKDW WKH SULPDU\ OLPLW WR WKH UHVROXWLRQ RI WKH GDWD LV GLIIUDFWLRQ $OO RI WKH 26&,5 REVHUYDWLRQV ZHUH PDGH XVLQJ WKH VWDQGDUG fFKRSQRGf WHFKQLTXH 7KH FKRSSHU WKURZ ZDV f LQ GHFOLQDWLRQ DW D IUHTXHQF\ RI +] 7KH WHOHVFRSH ZDV QRGGHG HYHU\ VHFRQGV $OO RI WKHVH SDUDPHWHUV DUH ZHOO ZLWKLQ WKH VSHFLILFDWLRQV RI WKH V\VWHP DQG WKHUH ZHUH QR SUREOHPV HYLGHQW GXULQJ WKH REVHUYDWLRQV 26&,5 XVHV D [SL[HO GHWHFWRU DQG WKH HQWLUH ILHOG RI YLHZ ZDV XVHG IRU WKH 6$2

PAGE 138

REVHUYDWLRQV 2Q .HFN 26&,5 KDV D SODWH VFDOH RI f SHU SL[HO D IDFWRU RI WLPHV ILQHU WKDQ WKDW RI %HUNFDP RQ 8.,57 7KH FKRSSHG LQWHJUDWLRQ WLPH RI HDFK RI RXU 6$2 REVHUYDWLRQV ZDV PLQXWHV LH PLQXWHV RQVRXUFHf 2XU H[SHULHQFH DW .HFN KDV VKRZQ WKDW WKH 36) GRHV H[KLELW VRPH YDULDWLRQ WKURXJKRXW D VLQJOH QLJKW VHH )LJXUH f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f DW SP DQG ):+0 f DW SP 7KH ORZHVW FRQWRXU LQ WKH 6$2 REVHUYDWLRQV LV DW D OHYHO RI DSSUR[LPDWHO\ WLPHV WKH VPRRWKHG QRLVH LQ WKH LPDJH 'XH WR WKH UHODWLYHO\ KLJK EULJKWQHVV RI WKH VRXUFH DQG WKH IDFW WKDW WKH VRXUFH LV XQUHVROYHG ZH VHH WKH HIIHFWV RI GLIIUDFWLRQ LQ )LJXUH 7KHVH HIIHFWV DUH DSSDUHQW DV WKH EURDG ORZHVW OHYHO FRQWRXU LQ HDFK SDQHO

PAGE 139

)LJXUH &RQWRXU SORWV RI 6$2 DQG D QHDUE\ 36) VWDU DW DQG SP 1RUWK LV XS DQG (DVW LV OHIW $ SL[HO *DXVVLDQ VPRRWK ):+0 ff KDV EHHQ DSSOLHG WR DOO LPDJHV 7KH ORZHVW FRQWRXU LQ WKH 6$2 SDQHOV LV DSSUR[LPDWHO\ WLPHV WKH VPRRWKHG QRLVH LQ WKH LPDJH Df 1EDQG LPDJH RI 6$2 &RQWRXUV VSDFHG OLQHDUO\ DW P-\ DUFVHFnf Ef 1EDQG LPDJH RI 36) VWDU 330 f &RQWRXUV SODFHG DW VDPH UHODWLYH EULJKWQHVV OHYHOV DV LQ SDQHO Df Ff ,+: LPDJH RI 6$2 &RQWRXUV VSDFHG OLQHDUO\ DW P-\ DUFVHFff Gf ,+: LPDJH RI 36) VWDU &RQWRXUV SODFHG DW VDPH UHODWLYH EULJKWQHVV OHYHOV DV LQ SDQHO Ff RI )LJXUH 7KH DV\PPHWU\ VHHQ LQ WKH ORZ OHYHO FRQWRXUV RI WKH SP LPDJHV LV GXH WR WKH IDFW WKDW WKH REVHUYHG GLIIUDFWLRQ ULQJ ZDV fEURNHQf WKDW LV QRW D]LPXWKDOO\ V\PPHWULF 7KH DV\PPHWU\ LV PRUH VXEWOH LQ WKH SP LPDJHV EXW LV VWLOO SUHVHQW DV WKH fEXPSf YLVLEOH RQ WKH 6 : TXDUWHU RI WKH VHFRQG FRQWRXU RI ERWK SDQHOV ,Q )LJXUH ZH VKRZ QRUWKVRXWK VFDQV RI 6$2 DQG D QHDUE\ SRLQW VSUHDGIXQFWLRQ 36)f VWDU DW SP DQG SP ZKLFK VKRZ WKDW WKHUH LV QR

PAGE 140

$UFVHHRQGV )LJXUH 1RUPDOL]HG 1RUWKVRXWK VFDQV WKURXJK 6$2 DQG D QHDUE\ 36) VWDU 330 f WRSf 6FDQV DW >LP ERWWRPf 6FDQV DW SP 7KHVH VFDQV DUH DSSUR[LPDWHO\ DORQJ WKH SRVLWLRQ D[LV RI WKH GLVN UHSRUWHG E\ 6NLQQHU HW DO f DQG VKRZ 6$2 WR EH XQUHVROYHG DW D KLJK OHYHO RI FRQILGHQFH 1R VPRRWKLQJ KDV EHHQ DSSOLHG WR WKH GDWD DSSUHFLDEOH GLIIHUHQFH EHWZHHQ WKH UDGLDO SURILOH RI 6$2 DQG WKH 36) VWDU 7KH VPDOO GLIIHUHQFH LQ ZLGWKV RI WKH VFDQV VHHQ DW ORZ OHYHOV DW SP LV PRVW OLNHO\ GXH WR WKH IDFW WKH ZH REVHUYHG 6$2 IRU PXFK ORQJHU WKDQ WKH 36) VWDU DQG WKH DFFXPXODWHG HIIHFW RI VHHLQJ RQ WKH VFLHQFH REMHFW VOLJKWO\ EURDGHQHG LWV SURILOH ,W LV YHU\

PAGE 141

LQIRUPDWLYH WR FRPSDUH )LJXUH ZLWK )LJXUHV DQG LQ WKLV GLVVHUWDWLRQ 6XFK D FRPSDULVRQ VKRZV WKH GLIIHUHQFHV EHWZHHQ VFDQV WKURXJK DQ XQUHVROYHG VRXUFH OLNH 6$2 DQG VRXUFHV WKDW DUH VRXUFHV WKDW DUH UHVROYHG +' +' f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f RU KLJK UHVROXWLRQ RSWLFDO VSHFWUD HJ )HNHO HW DO f $V ZH ZLOO VHH WKHVH REVHUYDWLRQV KHOS HDFK FDPS PDNH VWURQJ FODLPV WR WKH FODVVLILFDWLRQ RI WKH VRXUFH $GGLWLRQDOO\ WKHVH REVHUYDWLRQV KDYH UHILQHG WKH IXQGDPHQWDO SDUDPHWHUV RI WKH FHQWUDO VWDU ZKLFK DUH VKRZQ LQ 7DEOH ,Q WKH IROORZLQJ VHFWLRQV ZH GHWDLO WKH FKDUDFWHULVWLFV WKDW SODFH LW LQFRQJUXRXVO\ LQ ERWK OXPLQRVLW\ FODVV 9 DQG OXPLQRVLW\ FODVV ,,, DQG ZH VSHFXODWH RQ WKH QDWXUH RI WKH VRXUFH DIWHU SUHVHQWLQJ D QHZ SLHFH RI HYLGHQFH WKDW PD\ KHOS WKH FODVVLILFDWLRQ TXHVWLRQ

PAGE 142

&?, 3W+ :DYHOHQJWK Pf )LJXUH 6(' RI 6$2 7KLV RSWLFDO WR PP 6(' LV FRPSULVHG RI WKH SKRWRPHWU\ RI 6NLQQHU HW DO f 7KH 6(' VKRZV WKH ,5 H[FHVV RI WKH VRXUFH IRU ; _LP 6$2 H[KLELWV QR QHDU,5 H[FHVV ZKLFK LV GLIIHUHQW WKDQ WKH VRXUFH +' 7KLV ODFN RI QHDU,5 H[FHVV HPLVVLRQ PD\ EH D ZD\ WR KHOS SODFH 6$2 LQ WKH FRUUHFW OXPLQRVLW\ FODVV /XPLQRVLW\ &ODVV 9 $ 0DLQ6HTXHQFH 'ZDUI )RU WKLV ZRUN WKH VWRU\ RI 6$2 VWDUWV ZLWK WKH LQFOXVLRQ RI WKH VRXUFH RI WKH OLVW RI 9HJDOLNH VRXUFHV SUHVHQWHG E\ :DONHU DQG :ROVWHQFURIW LQ 8VLQJ ,5$6 GDWD DV D GLDJQRVWLF :: SODFHG 6$2 RQ WKHLU SULPDU\ f$ff OLVW RI GLVN FDQGLGDWHV 7KH :: OLVW LV FRPSULVHG RI VRXUFHV WKDW KDYH VLPLODU FKDUDFWHULVWLFV DV WKH DUFKHW\SDO 9HJDOLNH VRXUFHV 7KRVH VRXUFHV LQ WKH f$f VHFWLRQ RI WKH :: OLVW ZHUH VLQJOHG RXW DV PRVW UHVHPEOLQJ WKH DUFKHW\SHV DQG WKHUHIRUH OLNHO\ WR KDYH UHVROYHG GLVNV 7KH ILUVW VHW RI IROORZXS REVHUYDWLRQV WKDW UHODWH GLUHFWO\ WR RXU VWXG\ RI 6$2 ZHUH WKRVH RI 6\OYHVWHU HW DO f ZKHQ WKH\ SXEOLVKHG DQ H[WHQVLYH VHW RI

PAGE 143

SKRWRPHWULF REVHUYDWLRQV RI WKH VRXUFH LQ WKH RSWLFDO 8 % 9 5 ,f DQG WKH QHDU,5 + / 0f 7KH\ DOVR REVHUYHG 6$2 LQ WKH PP UHJLPH DQG REWDLQHG DQ XSSHU OLPLW WR WKH IOX[ RI WKH VRXUFH 8VHG LQ FRQMXQFWLRQ ZLWK WKH SUHYLRXVO\ SXEOLVKHG ,5$6 GDWD DQ DFFXUDWH 6(' RI WKH VRXUFH ZDV FRQVWUXFWHG ZKLFK LV VKRZQ LQ )LJXUH 4XDOLWDWLYHO\ WKH 6(' RI 6$2 ORRNV YHU\ VLPLODU WR WKH 6(' RI D 9HJDOLNH VRXUFH 7KH ,5 H[FHVV RI WKH VRXUFH LV VHHQ IRU DOO ZDYHOHQJWKV ORQJHU WKDQ DSSUR[LPDWHO\ SP DQG WKH H[FHVV SHDNV DURXQG SP %RWK RI WKHVH FKDUDFWHULVWLFV DUH VLPLODU WR D QXPEHU RI VRXUFHV RQ WKH :: OLVW LQFOXGLQJ WKH DUFKHW\SHV :RUNLQJ ZLWK FRORU FRUUHFWHG ,5$6 IOX[ GHQVLWLHV :: IRXQG WKDW D VLQJOH WHPSHUDWXUH EODFNERG\ ZLWK 7 ILW WKH H[FHVV ZHOO 7R WU\ WR ILW 6$2 LQWR WKH EURDGHU FODVV RI 9HJDOLNH VRXUFHV ZH FDQ FRPSDUH LWV 6(' WR RWKHU PHPEHUV RI WKH FODVV ,W LV LQIRUPDWLYH WR FRPSDUH )LJXUH ZLWK )LJXUH WKH 6(' RI +' $V ZH GLVFXVVHG ZH EHOLHYH WKDW +' LV D WUDQVLWLRQ REMHFW EHWZHHQ D +HUELJ $H%H VWDU DQG D 9HJDOLNH VRXUFH :H WKHUHIRUH EHOLHYH WKDW LW LV PRYLQJ GRZQ DFURVV WKH PDLQVHTXHQFH WRZDUG WKH =$06 ,I 6$2 ZHUH LQ WKH VDPH VWDJH RI LWV HYROXWLRQ ZH FRXOG UHDVRQDEO\ H[SHFW LW DQG LWV 6(' WR KDYH VLPLODU FKDUDFWHULVWLFV $ FDUHIXO FRPSDULVRQ RI )LJXUH DQG )LJXUH VKRZV WKDW WKHUH LV D PDMRU GLIIHUHQFH LQ WKH 6('V RI WKH WZR VRXUFHV :KLOH +' H[KLELWV VWURQJ QHDU,5 H[FHVV WKH H[FHVV RI 6$2 GRHV QRW EHJLQ XQWLO DURXQG SP 7KLV ODFN RI QHDU,5 H[FHVV HPLVVLRQ LV D VWURQJ SLHFH RI HYLGHQFH DJDLQVW WKH VRXUFH EHLQJ SUHPDLQVHTXHQFH UDWKHU LW VHHPV WR LPSO\ WKDW 6$2 LV PRUH HYROYHG

PAGE 144

/LWKLXP $EXQGDQFH 2QH RI WKH UHDVRQV WKDW 6$2 LV VR GLIILFXOW WR FODVVLI\ LV WKDW LW H[KLELWV D YHU\ VWURQJ /L OLQH DW ƒ )HNHO HW DO f 7KH HTXLYDOHQW ZLGWK RI WKH OLQH LV Pƒ ZKLFK \LHOGV D OLWKLXP DEXQGDQFH RI H/Lf a XVLQJ WKH FRQYHUVLRQV RI 6RGHUEORP HW DO f DQG &DUOVVRQ HW DO f 7KLV OHYHO RI /L LV HTXDO WR WKDW IRXQG LQ \RXQJ 3RSXODWLRQ VWDUV ZKRVH OLWKLXP KDV QRW EHHQ VLJQLILFDQWO\ PL[HG RU GHVWUR\HG E\ QXFOHDU SURFHVVHV &DUOVVRQ HW DO f 7KLV YHU\ VWURQJ OLWKLXP HPLVVLRQ DUH FRQVLVWHQW ZLWK 6$2 EHLQJ D \RXQJ GZDUI KRZHYHU LI LW LV D \RXQJ VRXUFH WKHQ WKHUH VKRXOG DOVR EH VWURQJ FKURPRVSKHULF HPLVVLRQ VHHQ LQ LWV VSHFWUXP DV SUHGLFWHG E\ 6NLQQHU HW DO f 7R ORRN IRU VLJQDWXUHV RI VXFK DFWLYLW\ )HNHO HW DO f SUHVHQW WZR VSHFWUD RI 6$2 WKH ILUVW VSDQQLQJ WKH &D ,, + t OLQHV DQG WKH VHFRQG WKH +D UHJLRQ )HNHO HW DO f ILQGV WKDW WKHUH LV FDOFLXP HPLVVLRQ SUHVHQW LQ WKH 6$2 VSHFWUXP EXW XQOLNH RWKHU GZDUIV VXFK DV +' )HNHO HW DO f DQG +' 6WUDVVPHLHU HW DO f WKH HPLVVLRQ IHDWXUH RI 6$2 LV YHU\ ZHDN DQG FRPHV QR ZKHUH QHDU WKH OHYHO RI WKH UHODWLYH FRQWLQXXP 7KH HTXLYDOHQW ZLGWKV RI WKH + t OLQHV DUH $ R DQG $ UHVSHFWLYHO\ 7KHVH YDOXHV DUH YHU\ ORZ IRU D GZDUI EXW DUH ZHOO ZLWKLQ WKH UDQJH RI YDOXHV WKRVH IRXQG IRU DFWLYH JLDQWV WKDW URWDWH UDSLGO\ 6WUDVVPHLHU HW DO f :LWK UHJDUGV WR WKH VHFRQG )HNHO HW DO f VSHFWUXP VSHFWURVFRSLF VWXGLHV RI 7 7DXUL VWDUV KDYH VKRZQ WKDW WKH\ H[KLELW D ZLGH UDQJH RI +D SURILOHV IURP DEVRUSWLRQ WR VWURQJ HPLVVLRQ :DOWHU HW DO f +RZHYHU HYHQ WKH GHHSHVW +D DEVRUSWLRQ OLQH RI WKH 306 .VWDUV VWXGLHG E\ :DOWHU HW DO f KDV D ORZ HTXLYDOHQW ZLGWK LQGLFDWLQJ WKDW LW LV VLJQLILFDQWO\ ILOOHG ZLWK HPLVVLRQ 7KLV LV UHOHYDQW WR 6$2 VLQFH WKH VSHFWUXP RI )HNHO HW DO f FOHDUO\ VKRZV WKDW WKH +D SURILOH RI WKH VRXUFH LV QRW

PAGE 145

VLJQLILFDQWO\ ILOOHG 'LUHFW FRPSDULVRQ ZLWK SURILOHV RI RWKHU VRXUFHV VKRZV WKDW WKH SURILOH PRVW UHVHPEOHV WKDW RI D JLDQW RU VXSHUJLDQW /LQH UDWLR DQDO\VLV E\ )HNHO HW DO f GLVFRXQWV WKH K\SRWKHVLV WKDW 6$2 LV D VXSHUJLDQW ZKLFK DOORZV XV WR UHDVRQDEO\ LQWHUSUHW WKH +D SURILOH LQ WKH FRQWH[W RI D OXPLQRVLW\ FODVV ,,, JLDQW XQGHUJRLQJ VRPH PDVV ORVV 8S WR WKLV SRLQW ZH KDYH VKRZQ WKDW IURP DP HPLVVLRQ IHDWXUH VWDQGSRLQW LW LV OLNHO\ WKDW 6$2 LV D OXPLQRVLW\ FODVV ,,, VWDU EXW ZH KDYH \HW WR DQVZHU WKH TXHVWLRQ RI LWV KLJK OLWKLXP DEXQGDQFH ZKLFK LV QRUPDOO\ DVVRFLDWHG ZLWK YHU\ \RXQJ REMHFWV RI WKLV PDVV 7R H[SODLQ WKLV ZH WXUQ WR WKH PRGHO RI GH OD 5H]D HW DO f $Q LPSRUWDQW DVSHFW RI WKLV PRGHO LV WKDW LQYRNHV D FLUFXPVWHOODU GXVW VKHOO WR H[SODLQ WKH SUHVHQFH RI WKH LQIUDUHG H[FHVV DVVRFLDWHG ZLWK WKH VRXUFH 7KH PDLQ FKDUDFWHULVWLFV RI WKH PRGHO VFHQDULR DUH VXPPDUL]HG LQ GH OD 5H]D HW DO f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f VWRSV WKLV PDWHULDO GHWDFKHV DQG LV HMHFWHG LQWR WKH VXUURXQGLQJ UHJLRQ 7KH EHVW YDOXHV IRU WKH FLUFXPVWHOODU VKHOO VHH GH OD 5H]D HW DO f JLYH DQ H[SDQVLRQ YHORFLW\ RI NPVHF DQG D PDVV ORVV UDWH RI WR [ n 0\U ZKLFK LV WLPHV WKH PDVV ORVV RI DQ RUGLQDU\ JLDQW 7KH QHZ /L WKDW KDV QRW EHHQ HMHFWHG LQWR WKH VXUURXQGLQJ UHJLRQ VWD\V LQ WKH SKRWRVSKHUH 7KLV OLWKLXP LV GHSOHWHG RQ D WLPHVFDOH WKDW LV OHVV WKDQ WKH FLUFXPVWHOODU GXVW DQG JDV HMHFWLRQ HSLVRGH WKDW PD\ H[SODLQ WKH SUHVHQFH RI JLDQWV ZLWKRXW KLJK /L DV REVHUYHG E\ )HNHO HW DO f

PAGE 146

7KH REVHUYHG FKDUDFWHULVWLFV RI 6$2 DUH ZHOO H[SODLQHG LQ WKH FRQWH[W RI WKLV PRGHO ,Q IDFW GH OD 5H]D HW DO f XVH 6$2 DV DQ H[DPSOH RI D VXFFHVV VWRU\ IRU WKHLU PRGHO 8VLQJ RXU REVHUYDWLRQV LQ FRQMXQFWLRQ ZLWK WKLV PRGHO ZH FDQ SODFH D WLJKWHU FRQVWUDLQW RQ WKH H[SDQVLRQ YHORFLW\ WKH HMHFWHG FLUFXPVWHOODU PDWHULDO )HNHO HW DO f UHSRUW WKDW WKH HMHFWHG VKHOO IRU 6$2 LV \HDUV ROG ,I WKH VRXUFH LV DW D GLVWDQFH RI SF DV SURSRVHG E\ )HNHO HW DO f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

PAGE 147

3DUDPHWHU /XPLQRVLW\ &ODVV 9 /XPLQRVLW\ &ODVV ,,, 6SHFWUDO 7\SH WR .r %9f r r 'LVWDQFH SFr SFr 7HII .r // r 00p V 55H L f§f§f§ f§f§ i r VHTXHQFH LV VSDUVHO\ SRSXODWHG DW EHVW 5HFDOO WKDW 6$2 H[KLELWV QR PHDVXUDEOH QHDU,5 H[FHVV 3KRWRPHWU\ LQ WKH + DQG EDQGV LV HQWLUHO\ FRQVLVWHQW ZLWK SKRWRVSKHULF HPLVVLRQ RQO\ 6NLQQHU HW DO f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f 8VLQJ KLJK UHVROXWLRQ RSWLFDO VSHFWURPHWU\ LQ FRQMXQFWLRQ ZLWK +LSSDUFRV GDWD -DVQLHZLF] HW DO

PAGE 148

% 9 >PDJ@ )LJXUH 3RVVLEOH SRVLWLRQV RI 6$2 LQ WKH +5 GLDJUDP 7KH FLUFOH PDUNV WKH SRVLWLRQ WKDW 6$2 ZRXOG RFFXS\ DVVXPLQJ WKH VWDU LV /XPLQRVLW\ FODVV 9 ZLWK D GLVWDQFH RI SF DV VXJJHVWHG E\ 0LURVKQLFKHQNR HW DO f 7KH VTXDUH GHQRWHV ZKHUH WKH VWDU ZRXOG OLH DVVXPLQJ D GLVWDQFH RI SF LQ DFFRUGDQFH ZLWK )HNHO HW DO f 7KH JUD\ ER[ RXWOLQHV D UHJLRQ WKDW FRQWDLQV OLWKLXP ULFK JLDQW VWDUV IURP WKH OLVW RI -DVQLHZLF] HW DO f 7KH %9f YDOXH IURP 0LURVKQLFKHQNR HW DO f +LSSDUFRV +5 GLDJUDP IURP 3HUU\PDQ HW DO f f GHWHUPLQHG DFFXUDWH IXQGDPHQWDO SDUDPHWHUV IRU OLWKLXP ULFK JLDQWV IURP WKH OLVW RI =XFNHUPDQ HW DO f 8VLQJ WKHVH UHILQHG SDUDPHWHUV QHZ LQWULQVLF OXPLQRVLWLHV IRU WKH VRXUFHV ZHUH FDOFXODWHG DQG WKH\ ZHUH SORWWHG RQ WKH +5 GLDJUDP ,W LV FOHDU WKDW 6$2 UHVLGHV ZHOO ZLWKLQ WKH UHJLRQ RI WKH RWKHU VRXUFHV :H EHOLHYH WKDW WKH SUR[LPLW\ RI WKHVH RWKHU VRXUFHV WR WKH SRVLWLRQ RI 6$2 LV VWURQJ HYLGHQFH WKDW WKH

PAGE 149

PRGHO RI GH OD 5H]D f GRHV GHVFULEH WKLV VRXUFH DQG WKDW LW LV PRVW OLNHO\ QRW 9HJDn OLNH EXW LV D OXPLQRVLW\ FODVV ,,, JLDQW 6XPPDU\ DQG &RQFOXVLRQV :H KDYH SUHVHQWHG QHZ DQG SP LPDJHV RI 6$2 PDGH ZLWK 26&,5 RQ .HFN ,, 8VLQJ RXU QHZ REVHUYDWLRQV LQ FRQMXQFWLRQ ZLWK SUHYLRXV GDWD ZH PDNH WKH IROORZLQJ FRQFOXVLRQV DERXW 6$2 2XU PDLQ FRQFOXVLRQ LV WKDW 6$2 LV XQUHVROYHG LQ WKH PLG,5 DW WKH KLJKHVW UHVROXWLRQ FXUUHQWO\ SRVVLEOH DW WKHVH ZDYHOHQJWKV :H PHDVXUH WKH VRXUFH WR KDYH D ):+0 OHVV WKDQ f DW ERWK SP DQG SP 7KH SP VL]H LV LQFRQVLVWHQW ZLWK SUHYLRXV REVHUYDWLRQV WKDW VKRZHG ZKDW DSSHDUHG WR EH D KLJKO\ LQFOLQHG GLVN ZLWK ):+0 f 7KH IDFW WKDW WKHUH LV QR GLVNOLNH VWUXFWXUH VHHQ DURXQG WKH VRXUFH ZHDNHQV WKH WKHRU\ WKDW 6$2 LV D PHPEHU RI WKH 9HJDOLNH FODVV RI REMHFWV DQG VWUHQJWKHQV WKH LGHD WKDW WKH VRXUFH KDV /XPLQRVLW\ &ODVV ,,, :H EHOLHYH WKH IDFW WKDW 6$2 LV XQUHVROYHG LQ WKH PLG,5 LV VWURQJ FLUFXPVWDQWLDO HYLGHQFH WKDW WKH VWDU LV QRW D FODVVLFDO 9HJDOLNH VRXUFH &RXSOHG ZLWK HYLGHQFH SUHVHQWHG LQ RWKHU ZRUNV HJ )HNHO HW DO f DQG GH OD 5H]D HW DO ff RXU QHZ PLG,5 LPDJHV VXSSRUW WKH FODVVLILFDWLRQ RI 6$2 DV D OXPLQRVLW\ FODVV ,,, JLDQW :H DOVR SUHVHQW HYLGHQFH VXSSRUWLQJ WKLV FODVVLILFDWLRQ LQ WKH IRUP RI WKH +5 GLDJUDP 7R GHILQLWLYHO\ SODFH WKH VRXUFH LQ RQH OXPLQRVLW\ FODVV RU WKH RWKHU PRUH GLDJQRVWLF REVHUYDWLRQV DUH QHHGHG ,Q SDUWLFXODU D UREXVW GLVWDQFH PHDVXUHPHQW ZRXOG DQVZHU WKH TXHVWLRQ RI ZKHUH 6$2 LV LQ LWV HYROXWLRQ

PAGE 150

&+$37(5 ,167580(17$7,21 $&7,9,7,(6 7+( 26&,5 6<67(0 $QRWKHU DVSHFW RI WKH UHVHDUFK GRQH IRU WKLV GLVVHUWDWLRQ LV FHQWHUHG RQ WKH FRPPLVVLRQLQJ XVH DQG VXSSRUW RI WKH 26&,5 FDPHUD V\VWHP 26&,5 LV D PLGLQIUDUHG WR SPf FDPHUDVOLW VSHFWURPHWHU V\VWHP EXLOW E\ WKH 8QLYHUVLW\ RI )ORULGD ,QIUDUHG $VWURSK\VLFV *URXS ,$*f 26&,5 LV EXLOW DURXQG D [ 6L$V +) EORFNHG LPSXULW\EDQG %,%f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a P WDOO DQG DUH DSSUR[LPDWHO\ FP LQ GLDPHWHU 7KH GHZDU ZHLJKV a NJ ZKHQ IXOO\ SUHSDUHG IRU REVHUYLQJ 7KLV LQFOXGHV WKH ZHLJKW RI WKH DWWDFKHG FRPSRQHQWV DQG WKH FU\RJHQV 2ULJLQDOO\ SODQQHG IRU H[FOXVLYH XVH RQ WKH 1$6$ ,57) 26&,5 KDV HYROYHG LQWR D VHOIFRQWDLQHG WUDYHOLQJ V\VWHP WKDW KDV EHHQ DGDSWHG IRU XVH RQ RWKHU WHOHVFRSHV 6LQFH FRPPLVVLRQLQJ LQ ODWH 26&,5 KDV EHHQ XVHG SURGXFWLYHO\ DW IRXU PDMRU REVHUYDWRULHV WKH ,57) WKH &7,2 P .HFN ,, DQG *HPLQL 1RUWK 7DEOH

PAGE 151

VXPPDUL]HV WKH REVHUYLQJ UXQV WKDW 26&,5 KDV EHHQ XVHG RQ $V D EDVLF PHDVXUH RI WKH V\VWHP SURGXFWLYLW\ ZH GHWHUPLQHG WKH QXPEHU RI fXVHDEOHf QLJKWV RQ HDFK REVHUYLQJ UXQ ZKHUH D XVHDEOH QLJKW LV GHILQHG DV D QLJKW LQ ZKLFK DQ\ GDWD ZDV REWDLQHG &OHDUO\ WKLV LV QRW DQ DFFXUDWH PHDVXUH RI D QLJKWV TXDOLW\ RU WKH TXDOLW\ RI WKH GDWD REWDLQHG RQ WKDW QLJKW +RZHYHU LW GRHV LOOXVWUDWH WKH IDFW WKDW ZKHQ DOO WKH H[WHUQDO UHTXLUHPHQWV ZHUH PHW LH ZHDWKHU WHOHVFRSH RSHUDWLRQf 26&,5 ZDV UHDG\ WR REVHUYH 2I WKH RIILFLDO QLJKWV WKDW KDYH EHHQ DZDUGHG WR 26&,5 GDWD ZDV REWDLQHG RQ RI WKHP $SSUR[LPDWHO\ RI WKH UHPDLQLQJ QLJKWV ZHUH ORVW WR 26&,5 UHODWHG SUREOHPV DQG RI WKRVH QLJKWV ZHUH ORVW RQ WKH SUHFRPPLVVLRQLQJ UXQ 7KHVH QXPEHUV VKRZ WKDW 26&,5 KDV EHHQ D YHU\ UHOLDEOH DQG UREXVW V\VWHP IRU LWV HQWLUH H[LVWHQFH 7DEOH DOVR KLQWV DW WKH WHQDFLW\ RI WKH 26&,5 REVHUYHUV DV WKHUH ZHUH FHUWDLQO\ GDWD REWDLQHG RQ fXVHDEOHf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

PAGE 152

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f PRQLWRU WKDW ZLOO EH VKRUWO\ XSJUDGHG WR

PAGE 153

)LJXUH +LJKOHYHO VFKHPDWLF RI WKH 26&,5 LQVWUXPHQW 7KH WKUHH VXEV\VWHPV DUH ODEHOHG LQ EROG 0DMRU FRQQHFWLRQV EHWZHHQ WKH VXEV\VWHPV DQG WKH GLUHFWLRQ RI FRPPXQLFDWLRQ DORQJ WKHP DUH DOVR VKRZQ /DEHOHG FRPSRQHQWV DUH DV IROORZV $ %LDVOHYHO VKLIWHU ER[ % 3UHDPSOLILHU & 7HPSHUDWXUH DQG VWHSSHU PRWRU FRQWUROOHUV /LQHDU SRZHU VXSSOLHV IRU %LDV ER[ DQG 3UHDPS ( /RZHU ILEHU ERDUG ) 5$3725 IUDPH JUDEEHU FDUG ,'/ VRIWZDUH HQYLURQPHQW 7KH FDEOHV ODEHOHG f&ORFNVf DUH DQDORJ ULEERQ FDEOHV f$QDORJf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

PAGE 154

7KH 'HZDU 7KH GHZDU LV WKH VXEV\VWHP RI WKH LQVWUXPHQW WKDW LV PRVW RIWHQ LGHQWLILHG DV fWKH FDPHUDf ,W LV D ODUJH DOXPLQXP F\OLQGHU WKDW FRQWDLQV WKH RSWLFV DQG GHWHFWRU DV ZHOO DV WKH FU\RJHQLF IOXLGV XVHG WR FRRO WKHP 7KH GHZDU DQG WKH 90( FUDWHf UHVLGHV RQ WKH WHOHVFRSH $W *HPLQL 1RUWK WKH ,57) DQG &7,2 WKH GHZDU LV PRXQWHG RQ WKH WHOHVFRSH DW FODVVLFDO &DVVHJUDLQ IRFXV DW .HFN ,, LW ZDV XVHG DW D fEHQWf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n P7RUU 7KH SXPSV DUH QRUPDOO\ OHIW RQ WKH GHZDU IRU DSSUR[LPDWHO\ KRXUV 2QFH WKH GHZDU LV HYDFXDWHG WR WKLV OHYHO WKH FU\RJHQV DUH DGGHG 26&,5 XVHV OLTXLG QLWURJHQ /1f DQG OLTXLG KHOLXP /+Hf WR FRRO WKH GHWHFWRU DQG RSWLFV WR DFFHSWDEOH WHPSHUDWXUHV 7KH WZR VWRUDJH YHVVHOV LQVLGH WKH GHZDU HDFK KROG ILYH OLWHUV RI OLTXLG 7KH QRPLQDO WHPSHUDWXUH RI OLTXLG QLWURJHQ LV

PAGE 155

/1 'HZDU:LQGRZ /+H 6OLW :KHH 7HOHVFRSH )RFDO 3, 'HZDU &DVH )LOWHU :KHHO *UDWLQJ 0LUURU 7XUUHW )LJXUH YLHZ RI WKH 26&,5 GHZDU 7KH YDFXXP MDFNHW LV WKH RXWHUPRVW OD\HU DQG VXUURXQGV DOO RI WKH RSWLFDO FRPSRQHQWV RI WKH V\VWHP DV ZHOO DV WKH YHVVHOV IRU WKH /1 DQG /+H 7KH EHDP SDWK WKURXJK WKH V\VWHP LV VKRZQ LQ GDUN JUD\ $OO RI WKH RSWLFDO FRPSRQHQWV DUH ODEHOHG f)f GHVLJQDWHV D IODW PLUURU f3f LV D SRZHUHG FRPSRQHQW 7KHUH DUH IROGV LQ WKH 26&,5 EHDP DIWHU LW HQWHUV WKH YDFXXP MDFNHW $OVR VKRZQ DUH WKH WKUHH LQWHUQDO FRPSRQHQWV WKDW DUH PRYHG YLD WKH H[WHUQDO VWHSSHU PRWRUV ILOWHU ZKHHO VOLW ZKHHO JUDWLQJPLUURU WXUUHWf

PAGE 156

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f LV FRROHG WR QLWURJHQ WHPSHUDWXUH .f RU FRROHU 2I WKLV DSSUR[LPDWHO\ NJ LV WDNHQ GRZQ WR KHOLXP WHPSHUDWXUH .f ,W WDNHV OLWHUV RI /+H DQG OLWHUV RI /1 WR FRRO 26&,5 WR LWV QRPLQDO RSHUDWLQJ WHPSHUDWXUH UDQJH RI WR 1RUPDOO\ LW WDNHV DERXW KRXUV IRU WKH GHWHFWRU WR UHDFK HTXLOLEULXP ZLWK WKH /+H DW a 2QFH WKH GHWHFWRU LV FROG LI ZH QHHG WR EULQJ WKH V\VWHP EDFN WR URRP WHPSHUDWXUH LW LV ZDUPHG XS VORZO\ RYHU D SHULRG RI KRXUV RU VR 7KLV SUHYHQWV GDPDJH IURP WKHUPDO H[SDQVLRQ WR WKH GHWHFWRU DQG RWKHU VXVFHSWLEOH FRPSRQHQWV DV WKH V\VWHP ZDUPV 8QGHU H[WUHPH FLUFXPVWDQFHV WKH GHZDU KDV EHHQ fFROGF\FOHGf LH JRQH IURP FU\RJHQLF WHPSHUDWXUHV WR URRP WHPSHUDWXUH DQG EDFN WR FU\RJHQLF WHPSHUDWXUHf LQ DURXQG KRXUV 26&,5 DQG LWV SHHUV ZLOO PRVW OLNHO\ EH WKH ODVW PLG,5 LQVWUXPHQWV WR XVH OLTXLG FU\RJHQV %HFDXVH RI WKH WURXEOH DQG H[SHQVH RI WUDQVSRUWLQJ WKHVH VXEVWDQFHV WR WKH UHPRWH REVHUYLQJ VLWHV WKH ODWHU JHQHUDWLRQV RI

PAGE 157

LQVWUXPHQWV ZLOO EH HTXLSSHG ZLWK FORVHGF\FOH FRROHUV 7KHVH DUH PHFKDQLFDO FRROHUV WKDW FDQ FRRO ODUJH DPRXQWV RI PDWHULDO WR KHOLXP WHPSHUDWXUHV ZLWKRXW DQ\ OLTXLG FU\RJHQV 7KH FORVHGF\FOH FRROHU WKDW ZLOO EH XVHG ZLWK 75H&6 D ILUVW JHQHUDWLRQ LQVWUXPHQW IRU *HPLQL 6RXWK FDQ FRRO NJ RI PHWDO WR LQ a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

PAGE 158

)LJXUH .HFN DUWLILFLDO DQG REVHUYHG 36) (DFK LPDJH LV f [ f %RWK LPDJHV KDYH EHHQ QRUPDOL]HG WR RQH DW WKHLU SHDN Df $]LPXWKDOO\ V\PPHWULF PRGHO 36) IRU .HFN ,, DW D ZDYHOHQJWK RI SP Ef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b SHU VXUIDFHf (YHQ ZLWK WKH JROG FRDWLQJ ZH ORVH D PLQLPXP RI b RI WKH OLJKW HQWHULQJ WKH GHZDU ^ff ` 7KH RSWLFV FXUUHQWO\ LQ 26&,5 KDYH EHHQ WKHUH VLQFH WKH FRPPLVVLRQLQJ RI WKH GHZDU DQG ZLOO EH XVHG IRU WKH UHPDLQGHU RI 26&,5fV VFLHQWLILF DQG HQJLQHHULQJ XVH 7KH RSWLFDO SHUIRUPDQFH RI 26&,5 LV H[FHOOHQW 26&,5 KDV GHPRQVWUDWHG GLIIUDFWLRQOLPLWHG SHUIRUPDQFH DW ERWK DQG SP DW WKH ,57) &7,2 DQG .HFN )LJXUH VKRZV DQ H[DPSOH RI WKH SHUIRUPDQFH RQ .HFN ,, 6LQFH WKH ZDYHOHQJWKV WKDW 26&,5 REVHUYHV LQ DUH UHODWLYHO\ ORQJ DV FRPSDUHG WR WKH YLVXDO WKH HIIHFWV RI GLIIUDFWLRQ DUH FRUUHVSRQGLQJO\ HDVLHU WR VHH LQ 26&,5 GDWD 6XEWOH PLUURU IRUP SUREOHPV WKDW DUH

PAGE 159

LPSRVVLEOH WR VHH ZKHQ REVHUYLQJ LQ WKH YLVLEOH DUH RIWHQ HDVLO\ GLVFHPDEOH LQ 26&,5 LPDJHV :H KDYH LQ WKH SDVW XVHG DV\PPHWULHV DQG GLVWRUWLRQV LQ 26&,5 GDWD WR SUHGLFW DQG GLDJQRVH SUREOHPV ZLWK WHOHVFRSH V\VWHPV ,W LV VDIH WR VD\ WKDW DW HDFK WHOHVFRSH 26&,5 KDV EHHQ XVHG DW WKLV IRUP RI fLPDJHf HQJLQHHULQJ KDV KHOSHG ZLWK WKH RYHUDOO RSHUDWLRQ RI WKH IDFLOLW\ 7R DFKLHYH WKH EHVW IRFXV RI WKH V\VWHP ZH IRFXV XVLQJ WKH ILOWHU ,Q WKLV UHJLPH 26&,5 LV QRUPDOO\ QRW GLIIUDFWLRQ OLPLWHG DQG ILQH DGMXVWPHQWV WR WKH IRFXV FDQ EH PDGH ([SHULHQFH ZLWK 26&,5 XQGHU REVHUYLQJ FRQGLWLRQV KDV VKRZQ WKDW WKH WHOHVFRSH FDQ EH ZHOO RXW RI IRFXV EHIRUH WKHUH LV DQ\ QRWLFHDEOH GLIIHUHQFH LQ D SP VWHOODU LPDJH +RZHYHU EHLQJ RXW RI IRFXV GRHV KDV D GHWULPHQWDO HIIHFW RQ WKH REVHUYDWLRQV :KHQ WKH WHOHVFRSH LV VOLJKWO\ RXW RI IRFXV SRZHU IURP WKH FRUH LV SXPSHG LQWR WKH ZLQJV RI WKH SDWWHUQ $ VLJQLILFDQW DPRXQW RI SRZHU FDQ EH SXPSHG LQWR WKH ILUVW DLU\ ULQJ EHIRUH WKHUH LV DQ\ QRWLFHDEOH GHJUDGDWLRQ RI WKH LPDJH YLVXDOO\ 'XH WR GLIIUDFWLRQ WKH DSSDUHQW VL]H HJ IXOO ZLGWK DW KDOIPD[LPXP LQWHQVLW\f RI D VWHOODU LPDJH LV QRW D JRRG PHDVXUH RI WKH TXDOLW\ RI IRFXV 7KH SHDN LQWHQVLW\ RU 6WUHKO UDWLR ZKHQ QRUPDOL]HG E\ WKH WKHRUHWLFDO SHDNf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

PAGE 160

(QWUDQFH :LQGRZ DQG )LOWHUV 1RW DOO RI WKH RSWLFDO FRPSRQHQWV LQ 26&,5 DUH UHIOHFWLYH %RWK WKH GHZDU HQWUDQFH ZLQGRZ DQG WKH ILOWHU FRPSOHPHQW DUH PDGH RI LQIUDUHG WUDQVPLWWLQJ PDWHULDOV 6LQFH QRUPDO JODVVHV EHFRPH RSDTXH LQ WKH QHDU DQG PLG,5 WKH\ DUH LQDSSURSULDWH IRU XVH LQ D PLG,5 V\VWHP OLNH 26&,5 )RU WKH PLG,5 D YDULHW\ RI FU\VWDOOLQH VXEVWDQFHV DUH XVHG LQVWHDG 1DWXUDO FU\VWDOV OLNH FHVLXP LRGLGH &VOf DQG EDULXP IOXRULGH %D)f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b WKURXJKRXW WKH PLG,5 UHJLPH 7KLV LV FRPSDUHG WR D WUDQVPLVVLRQ RI b IRU D VLPLODU VL]HG SLHFH RI .56 0DQ PDGH PDWHULDOV OLNH .56 DQG RWKHUV DOVR KDYH WKH GLVDGYDQWDJH RI EHLQJ WR[LF DQG WKHUHIRUH GDQJHURXV WR ZRUN ZLWK 2Q WKH RWKHU KDQG WKH PDQ PDGH PDWHULDOV DUH H[WUHPHO\ VWURQJ DQG DUH PRVWO\ LPSHUYLRXV WR ZDWHU )RU PRVW RI 26&,5fV VFLHQWLILF XVH WKH DGYDQWDJH RI RYHUDOO GXUDELOLW\ RXWZHLJKHG WKH JDLQ LQ WKURXJKSXW DQG D .56 HQWUDQFH ZLQGRZ ZDV XVHG ,Q )LJXUH WKH .56 ZLQGRZ LV VKRZQ 7KLV ZLQGRZ KDV EHHQ UHPRYHG IURP WKH GHZDU DQG UHSODFHG ZLWK D FXVWRP ZLQGRZ DVVHPEO\ IRU XVH RI 26&,5 DW *HPLQL 1RUWK 7KH FXVWRP HQWUDQFH ZLQGRZ DVVHPEO\ FXUUHQWO\ LQVWDOOHG RQ 26&,5 LV FRPSULVHG RI WZR &VO OHQVHV ZKLFK KDYH EHHQ DQWLUHIOHFWLRQ $5f FRDWHG DQG KDYH D ZDWHUSURRI FRDWLQJ DSSOLHG RQ WRS RI WKH $5 FRDWLQJ WR SURWHFW WKH FU\VWDO VXUIDFH 7KLV

PAGE 161

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n OD\HU LQWHUIHUHQFH ILOWHUV 7KHVH ILOWHUV DUH GHVLJQHG WR SDVV RQO\ D FHUWDLQ UDQJH RI ZDYHOHQJWKV $OO RWKHU ZDYHOHQJWKV DUH H[FOXGHG SDUWO\ E\ WKH LQWHUIHUHQFH SURSHUWLHV RI WKH ILOWHUV WKHPVHOYHV EXW DOVR E\ WKH RYHUDOO WUDQVPLVVLRQ SURSHUWLHV RI WKH FRDWLQJV DQG WKH ILOWHU VXEVWUDWH PDWHULDOV 7KH WUDQVPLVVLRQ RI DQ LQWHUIHUHQFH ILOWHU ZLWKLQ WKH SDVVEDQG LV QRUPDOO\ EHWZHHQ WR b DQG WKH ILOWHUV LQ 26&,5 EHDU WKLV RXW )LJXUH VKRZV WKH SDVVEDQGV RI WKH 26&,5 EURDGEDQG 1 DQG ,+: ,QWHUQDWLRQDO +DOOH\ :DWFKf ILOWHUV 7KHVH DUH WKH WZR ILOWHUV WKDW KDYH VR IDU EHHQ WKH ILOWHUV XVHG WKH PRVW E\ ERWK WHDP PHPEHUV DQG YLVLWLQJ VFLHQWLVWV 7KHVH DUH DOVR WKH ILOWHUV XVHG IRU DOO RI WKH REVHUYDWLRQV LQ WKLV GLVVHUWDWLRQ )LJXUH VKRZV D VLPLODU SORW IRU WKH QDUURZEDQG VLOLFDWH ILOWHUV LQVWDOOHG LQ 26&,5 7KH VHYHQ ILOWHUV DUH FDOOHG WKH fVLOLFDWHf ILOWHUV VLQFH

PAGE 162

26&,5 3OORUD )LJXUH 26&,5 EURDGEDQG 1 DQG ,+: ILOWHU WUDQVPLVVLRQ SORWV 7KHVH WUDQVPLVVLRQ SORWV ZHUH PDGH ZKHQ WKH ILOWHUV ZHUH DW URRP WHPSHUDWXUH 7KH SDVVEDQG RI HDFK VKLIWV DSSUR[LPDWHO\ b WR VKRUWHU ZDYHOHQJWKV ZKHQ WKH ILOWHUV DUH DW RSHUDWLQJ WHPSHUDWXUH .f WKHLU SDVVEDQGV VSDQ WKH WR SP DWPRVSKHULF ZLQGRZ ZKHUH WKHUH LV D SURPLQHQW VLOLFDWH IHDWXUH VHHQ LQ VRPH DVWURQRPLFDO REMHFWV $ORQJ ZLWK WKH 1 DQG ,+: ILOWHUV WKH VLOLFDWH ILOWHUV KDYH EHHQ WKH PDLQ RQHV XVHG LQ 26&,5 VLQFH LWV FRPPLVVLRQLQJ $OO RI WKH ILOWHUV LQ 26&,5 DUH LQ H[FHOOHQW FRQGLWLRQ ([FHSW IRU D VOLJKW fJKRVWf LQ WKH 1EDQG ILOWHU ZKHQ REVHUYLQJ H[WUHPHO\ EULJKW VWDUV WKHUH DUH QR VWUD\ OLJKW SUREOHPV ZLWK WKH V\VWHP 7KHUH LV D VLJQLILFDQW LPDJH VKLIW ZKHQ XVLQJ WKH SP VLOLFDWH ILOWHU WKRXJK ,Q WKLV ILOWHU WKH LPDJH LV VKLIWHG SL[HOV DORQJ WKH KRUL]RQWDO GHWHFWRU D[LV DQG SL[HOV LQ WKH YHUWLFDO GHWHFWRU D[LV :H EHOLHYH WKLV VKLIW LV GXH WR D VOLJKW ZHGJH VKDSH WR WKH ILOWHU 7KLV NQRZQ HIIHFW LV FRPSHQVDWHG IRU ZKLOH REVHUYLQJ

PAGE 163

26 2,5 6LOEDWR 6RW )LOWRUV )LJXUH 26&,5 VLOLFDWH ILOWHU WUDQVPLVVLRQ SORWV 7KHVH WUDQVPLVVLRQ SORWV ZHUH PDGH ZKHQ WKH ILOWHUV ZHUH DW URRP WHPSHUDWXUH 7KH SDVVEDQG RI HDFK VKLIWV DSSUR[LPDWHO\ b WR VKRUWHU ZDYHOHQJWKV ZKHQ WKH ILOWHUV DUH DW RSHUDWLQJ WHPSHUDWXUH .f 26&,5 DOVR FRQWDLQV WZR VKRUW ZDYHOHQJWK DQG D VXLWH RI QHZO\ LQVWDOOHG ORQJ ZDYHOHQJWK ILOWHUV 7KH SPf DQG 0 SPf ILOWHUV DUH QRUPDOO\ XVHG IRU HQJLQHHULQJ DQG VHWXS SXUSRVHV OLNH IRFXVLQJ 7KHUH KDYH DOVR EHHQ D IHZ VFLHQFH REVHUYDWLRQV PDGH WKURXJK WKHVH ILOWHUV EXW WKH ORZ V\VWHP VHQVLWLYLW\ OLPLWV WKHP WR YHU\ EULJKW REMHFWV 2EVHUYLQJ LQ WKH WR SP UHJLRQ ZLWK 26&,5 LV DOVR QRW UHFRPPHQGHG EHFDXVH WKHUH LV QR EDFNJURXQG UDGLDWLRQ WR KHOS ILOO WKH ZHOOV RI WKH GHWHFWRU DQG WKH REVHUYDWLRQV EHFRPH UHDGQRLVH OLPLWHG (YHQ IUDPHWLPHV DV ORQJ DV WR PV GR QRW JHW WKH ZHOO GHSWK DERYH b ,Q WKH WKHUPDO ,5 WKH ZHOOV ILOO WR b LQ PV LQ WKH EURDGEDQG 1 ILOWHU

PAGE 164

7KH ORQJ ZDYHOHQJWK ILOWHUV ZHUH LQVWDOOHG LQ SUHSDUDWLRQ IRU WKH FRPPLVVLRQLQJ UXQ RQ *HPLQL 1RUWK $OO RI WKH IRXU QHZ ORQJ ZDYHOHQJWK ILOWHUV KDYH D FHQWUDO ZDYHOHQJWK ORQJHU WKDQ WKDW RI WKH +: ILOWHU :LWK WKH DGGLWLRQ RI WKHVH ILOWHUV 26&,5 ZLOO EH WKH RQO\ FDPHUD LQ IXOO RSHUDWLRQ RQ 0DXQD .HD ZLWK ILOWHUV WKDW KDYH SDVVEDQGV LQ WKH SP UDQJH 6LQFH WKH DWPRVSKHULF ZLQGRZ LQ WKLV UHJLPH LV ULGGOHG ZLWK + DQG & DEVRUSWLRQ EDQGV WKH XVH RI WKHVH ILOWHUV ZLOO EH KHDYLO\ GHSHQGHQW RQ WKH TXDOLW\ RI WKH DWPRVSKHUH ,Q SDUWLFXODU WKH 4ZLGH ILOWHU ZKLFK LV WKH ORQJ ZDYHOHQJWK HTXLYDOHQW RI WKH 1 EDQG ZLWK D EDQGZLGWK RI SP ZLOO RQO\ EH DEOH WR EH XVHG RQ H[WUHPHO\ JRRG QLJKWV ,I WKHUH LV DQ\ VLJQLILFDQW ZDWHU LQ WKH DWPRVSKHUH WKH EDFNJURXQG LV WRR KLJK WR XVH WKLV ILOWHU VLQFH ZH FDQQRW UHDG RXW WKH GHWHFWRU IDVW HQRXJK WR SUHYHQW VDWXUDWLRQ :H DUH SDUWLFXODUO\ HDJHU WR REVHUYH ZLWK WKH QHZ + ILOWHU ZKLFK KDV WKH ORQJHVW FHQWUDO ZDYHOHQJWK DW SP 7KLV ILOWHU ZLOO EH H[WUHPHO\ XVHIXO LQ H[WHQGLQJ RI WKH UHVHDUFK SUHVHQWHG KHUH 7DEOH OLVWV VRPH UHOHYDQW ILOWHU FKDUDFWHULVWLFV 'HWHFWRU 7KH UHFHQW HYROXWLRQ RI WKH GHWHFWRU WHFKQRORJ\ LV DUJXDEO\ WKH VLQJOH PRVW LPSRUWDQW GHYHORSPHQW LQ WKH DUHD RI LQIUDUHG DVWURQRP\ LQ WKH ODVW \HDUV ,QVWUXPHQWV KDYH UDSLGO\ PRYHG IURP EHLQJ VLQJOH HOHPHQW GHWHFWRUV WR VPDOO ERORPHWHU DUUD\V WR WKH GHWHFWRU DUUD\V WKDW DUH QRZ FRPPRQ LQ DOO IURQWOLQH LQVWUXPHQWDWLRQ :KLOH LW KDV EHHQ FRPPRQ IRU YLVLEOH OLJKW &&' FDPHUDV WR KDYH LQ H[FHVV RI RQH PLOOLRQ SL[HOV IRU WKH ODVW GHFDGH WKH VL]H RI WKH ELJJHVW PLG,5 DUUD\V QRZ LQ FRPPRQ XVH KDYH DURXQG SL[HOV 7KH UHDVRQ IRU WKLV ODUJH GLVFUHSDQF\ LQ WKH VL]H RI WKH DUUD\V OLHV LQ WKH IDFW WKDW WKH PLG,5 REVHUYLQJ UHJLPH UHTXLUHV WRWDOO\ GLIIHUHQW GHWHFWRU WHFKQRORJ\ IURP WKH

PAGE 165

7DEOH &KDUDFWHULVWLFV RI WKH 26&,5 ILOWHU VHW )LOWHU &HQWUDO :DYHOHQJWK SPf %DQGZLGWK SPf f D 0 f D 1 f ,+: f 4ZLGH f D 4 f /3) f D + D D $SSUR[LPDWH EDQGZLGWKV $FFXUDWH WR s SP YLVLEOH ,Q SDUWLFXODU WKH VLOLFRQ EDVHG GHWHFWRUV IRU WKH YLVLEOH DUH QRUPDOO\ XVHG IRU UHODWLYHO\ ORQJ H[SRVXUHV DQG FDQ XVH FRQYHQWLRQDO VKLIWFRXQWHU UHDGRXW WHFKQRORJLHV 7KLV LV QRW SRVVLEOH IRU PLG,5 GHWHFWRUV VLQFH WKH GHWHFWRUV QHHG WR EH UHDG RXW DW PXFK KLJKHU UDWHV WR FRPEDW WKH KLJK EDFNJURXQGV DQG DYRLG VDWXUDWLRQ 26&,5 XVHV D 5RFNZHOO%RHLQJ [ +) EORFNHG ,PSXULW\ EDQG %,%f GHWHFWRU 7KH GHWHFWRU LQ 26&,5 VHULDO QXPEHU +)f KDV EHHQ IXOO\ FKDUDFWHUL]HG E\ WKH 26&,5 WHDP DQG PXFK HIIRUW KDV EHHQ SXW LQWR RSWLPL]LQJ LWV SHUIRUPDQFH IRU XVH LQ JURXQG EDVHG DVWURQRP\ 7KH EORFNHG LPSXULW\ EDQG WHFKQRORJ\ ZDV ERP IURP WKH 6WDU :DUV 'HIHQVH SURJUDP RI WKH V ,W LV DQ fH[WULQVLFf VHPLFRQGXFWRU DV RSSRVHG WR D &&' ZKLFK LV DQ fLQWULQVLFf VHPLFRQGXFWRU $Q LQWULQVLF VHPLFRQGXFWRU LV PDGH IURP D

PAGE 166

7DEOH 26&,5 'HWHFWRU FKDUDFWHULVWLFV $UUD\ VL]H 3L[HO 6L]H )XOOZHOO FDSDFLW\ 08; UHDGQRLVH [ [ >LP a [ HOHFWURQV HOHFWURQV [ HVHF QRPLQDO GHWHFWRU ELDVf 'DUN &XUUHQW SXUH VHPLFRQGXFWLQJ PDWHULDO WKDW FDQ LQWHUDFW ZLWK KLJKHU HQHUJ\ SKRWRQV 7KH VLOLFRQ LQ D &&' DUUD\ LQWHUDFWV ZLWK DQ RSWLFDO SKRWRQ FDXVLQJ HOHFWURQV LQ WKH VHPLFRQGXFWRUfV YDOHQFH EDQG WR EH H[FLWHG WR WKH FRQGXFWLRQ EDQG 7KH HOHFWURQV LQ WKH FRQGXFWLRQ EDQG DUH WKHQ IUHH WR FRQGXFW HOHFWULFLW\ DQG WKLV FKDUJH FDQ EH UHDG RXW +RZHYHU VLOLFRQ E\ LWVHOI GRHV QRW HIIHFWLYHO\ LQWHUDFW ZLWK SKRWRQV RI ORZHU HQHUJ\ VXFK DV PLGLQIUDUHG SKRWRQV ,QVWHDG H[WULQVLF VHPLFRQGXFWLQJ PDWHULDOV DUH FUHDWHG VXFK DV VLOLFRQ RU JHUPDQLXP WKDW KDYH DWRPV LQ WKHLU FU\VWDOOLQH VWUXFWXUH GHOLEHUDWHO\ UHSODFHG ZLWK RWKHU DWRPV D SURFHVV UHIHUUHG WR DV fGRSLQJf 7KHVH fLPSXULWLHVf RU fGRSDQWVf DUH DWRPV WKDW FDQ EH H[FLWHG E\ ORQJHU ZDYHOHQJWK SKRWRQV KHQFH SURYLGLQJ HOHFWURQV IRU WKH FRQGXFWLRQ EDQG 7KH SUREOHP ZLWK GRSHG SKRWRFRQGXFWRUV LV WKDW WKHLU TXDQWXP HIILFLHQF\ LV GHSHQGHQW XSRQ WKH FRQFHQWUDWLRQ RI GRSDQW +RZHYHU WRR PXFK GRSDQW FDXVHV fWXQQHOLQJf RU fKRSSLQJf DFURVV WKH YDOHQFH EDQG DQG WKLV FDQ OHDG WR ODUJH GDUN FXUUHQWV 7KH RQO\ RWKHU FKRLFH LV WR PDNH WKH SKRWRFRQGXFWLQJ PDWHULDO OLJKWO\ GRSHG EXW YHU\ WKLFN ZKLFK OHDGV WR PDQ\ RSHUDWLRQDO SUREOHPV $ ZD\ RI RYHUFRPLQJ WKLV LV WR XVH D fEORFNLQJ EDQGf %\ SODFLQJ D OD\HU RI SXUH VLOLFRQ EHWZHHQ WKH GRSHG PDWHULDO DQG WKH UHDGRXW FRQWDFW HOHFWURQV FDQQRW KRS DFURVV WKH PDWHULDO DQG RXW WKH FRQWDFW WKXV UHGXFLQJ WKH GDUN FXUUHQW ,Q WKLV ZD\ WKH LQIUDUHG UHDFWLYH PDWHULDO FDQ EH KHDYLO\ GRSHG WR LQFUHDVH TXDQWXP HIILFLHQF\ DQG WKH UHDG RXW WKURXJK WKH FRQWDFW ZLOO RQO\ EH IURP

PAGE 167

)LJXUH 26&,5 GHWHFWRU XQGHU XQLIRUP 1%DQG LOOXPLQDWLRQ ,PDJH RI 26&,5 GHWHFWRU XQGHU XQLIRUP 1EDQG LOOXPLQDWLRQ 7KH a GHDG SL[HOV DUH WKH VPDOO EODFN VSRWV 7KH YLJQHWWLQJ LV LQ WKH ORZHU ULJKW FRPHU 7KH IHZ ZKLWH VSRWV DUH fKRWf SL[HOV WKDW DUH DOLYH EXW ZLWK VLJQLILJDQWO\ GLIIHUHQW UHVSRQVH WKDQ WKH RWKHUV $OO RI WKH VWUXFWXUH KHUH LV fIL[HGSDWWHUQf DQG LV UHPRYHG LQ WKH FKRSQRG SURFHVV HOHFWURQV WKDW ZHUH H[FLWHG LQWR WKH FRQGXFWLRQ EDQG E\ LQWHUDFWLRQ ZLWK D PLGLQIUDUHG SKRWRQ 7KH GHWHFWRU XVHG LQ 26&,5 KDV H[FHOOHQW FRVPHWLF TXDOLW\ )LJXUH VKRZV DQ LPDJH RI WKH GHWHFWRU XQGHU XQLIRUP LOOXPLQDWLRQ 7KHUH DUH RQO\ a GHDG SL[HOV GLVWULEXWHG DFURVV WKH DUUD\ $OWKRXJK WKHUH LV D VPDOO DPRXQW RI YLJQHWWLQJ LQ WKH ORZHU ULJKW FRUQHU RI WKH DUUD\ WKH UHVSRQVH RI WKH DUUD\ LV LQ JHQHUDO YHU\ IODW DQG WKH IODWILHOG

PAGE 168

YDULHV E\ sb 7KH VWUXFWXUH VHHQ RQ WKH DUUD\ LV fIL[HGf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

PAGE 169

)LJXUH 'HWDLO RI 90( FUDWH DQG FRPPXQLFDWLRQ OLQNV LQFOXGLQJ FORFNLQJ SDWWHUQV IRU WKH GHWHFWRU DUH VHQW IURP WKH 90( FUDWH WR WKH GHZDU 7KH GHZDU VHQGV RXWSXW VLJQDOV DV ZHOO DV WKH GDWD VWUHDP EDFN WR WKH FUDWH 8QGHU QRUPDO REVHUYLQJ FRQGLWLRQV WKH GDWD VWUHDP PRYLQJ IURP WKH GHZDU LQWR WKH 90( FUDWH LV DSSUR[LPDWHO\ 0%VHF :H JLYH D KLJKOHYHO RYHUYLHZ RI WKH GDWD SDWK WKURXJK WKLV VXEV\VWHP KHUH 7KH VLJQDOV IURP WKH GHZDU DUULYH DORQJ DQDORJ OLQHV ZKLFK FRPH GLUHFWO\ IURP WKH SUHDPSOLILHU RQ WKH GHZDU 7KHVH VLJQDOV HQWHU WKH 90( FUDWH LQWR IRXU DQDORJWRGLJLWDO $'&f FRQYHUWHU ERDUGV (DFK RI WKH IRXU $'& ERDUGV KDQGOHV IRXU FKDQQHOV IURP WKH GHWHFWRU 7KH $'& ERDUGV DUH UHVSRQVLEOH IRU FRQYHUWLQJ WKH DQDORJ VLJQDOV IURP WKH GHZDU LQWR GLJLWDO VLJQDOV WKH UHVW RI WKH V\VWHP FDQ ZRUN ZLWK 7KLV FRQYHUVLRQ LV GRQH LV VL[WHHQ $'& XQLWV RQ WKH IRXU ERDUGV RQH IRU HDFK FKDQQHO 7KH

PAGE 170

GDWD LV GLJLWL]HG DW D UHVROXWLRQ RI ELWV XVLQJ D 0+] VDPSOH UDWH 2QFH D VLJQDO LV GLJLWL]HG WKH UHVXOW LV VWRUHG LQ RQERDUG 5$0 XQWLO WKH SURSHU QXPEHU RI IUDPH FRDGGV LV FRPSOHWHG 2QFH WKH FRDGGV DUH ILQLVKHG WKH ILQDO VWDFN RI GDWD LV WUDQVIHUUHG DFURVV WKH 90( EDFNSODQH WR WKH XSSHU ILEHU FRPPXQLFDWLRQ ERDUG 7KH GDWD LV WUDQVIHUUHG IURP WKH XSSHU ILEHU ERDUG WKURXJK D 0%VHF RSWLFDO ILEHU FDEOH WR WKH ORZHU ILEHU ERDUG ZKLFK LV ORFDWHG LQ WKH FRQWURO URRP FORVH WR WKH FRQWURO FRPSXWHU 7KH GDWD LV VWRUHG LQ 5$0 LQ WKH ORZHU ILEHU ERDUG XQWLO WKH FRQWURO FRPSXWHU LV UHDG\ WR DFFHSW LW LQWR WKH 5$3725 IUDPH JUDEEHU FDUG UHVLGHQW LQ WKH FRQWURO FRPSXWHU 2QFH WKH GDWD LV WUDQVIHUUHG WR WKH 5$3725 FDUG LW LV DFFHVVLEOH WR WKH FRQWURO FRPSXWHU DQG FDQ EH EURXJKW LQWR WKH 26&,5 VRIWZDUH LQWHUIDFH ZKLFK LV ZULWWHQ LQ ,'/ 7KH ,'/ VRIWZDUH HQYLURQPHQW LV WKH ODVW VWHS RI WKH GDWD SDWK )URP KHUH WKH GDWD LV ZULWWHQ WR GLVN LQ D VWDQGDUG DOEHLW D GLPHQVLRQDO ),76 ILOH DQG GLVSOD\HG WR WKH REVHUYHUV LQ D JUDSKLFDO XVHU LQWHUIDFH ZULWWHQ XVLQJ ,'/ ZLGJHWV 7KH &38 LQ WKH 90( FUDWH LV D 0RWRUROD FKLS ,W LV UHVSRQVLEOH IRU FRRUGLQDWLQJ DOO RI WKH DFWLYLWLHV LQ WKH 90( FUDWH ,Q SDUWLFXODU WKH &38 LV UHVSRQVLEOH IRU PDNLQJ VXUH WKDW WKH FRUUHFW FORFNLQJ SDWWHUQV DQG VHWWLQJV DUH ORDGHG LQWR WKH ;LOLQ[ SURJUDPPDEOH JDWH DUUD\ 7KH YDULRXV FORFNLQJ SDWWHUQV DUH VWRUHG LQ VWDWLF PHPRU\ 3520Vf RQ WKH &38 ERDUG LQ WKH FUDWH 7KH SDWWHUQ JHQHUDWRU ERDUG FRQWDLQV D ;LOLQ[ SURJUDPPDEOH JDWH DUUD\ 3*$f PLFURSURFHVVRU ,W LV LQ WKH ;LOLQ[ FKLS WKDW WKH FORFNLQJ VLJQDOV DUH JHQHUDWHG 7KLV FKLS DOVR REWDLQV YDULRXV GHWHFWRU VHWWLQJV LH ELDV LQIRUPDWLRQf IURP WKH FRPPDQG FRPSXWHU WR WUDQVODWH DQG VHQG WKH GHWHFWRU 6LQFH WKHUH DUH GLIIHUHQW PRGHV RI RSHUDWLRQ WKDW DUH XVHG ZLWK 26&,5 LH FKRS RQO\ QRG RQO\ VWDUH DQG FKRSQRGf WKHUH DUH GLIIHUHQW VHWV RI FRPPDQGV DQG VHWWLQJ WKDW QHHG WR EH VHQW

PAGE 171

WR DQG IURP WKH &38 WKH GHWHFWRU DQG WKH ;LOLQ[ FKLS (DFK RI WKH DSSUR[LPDWHO\ GLIIHUHQW fF\FOH W\SHVf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f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

PAGE 172

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fSLFNXSf &RQWURO &RPSXWHU 7KH FRQWURO FRPSXWHU LV WKH ILQDO VXEV\VWHP RI WKH 26&,5 LQVWUXPHQW 7KH GDWD LV WUDQVIHUUHG IURP WKH 90( FUDWH WR WKH FRPSXWHU WKURXJK WKH RSWLFDO ILEHU DQG WKH XSSHU DQG ORZHU ILEHU ERDUGV 7KH FXUUHQW LQFDUQDWLRQ RI WKH FRQWURO FRPSXWHU LV D 0+] 3HQWLXP ,,, 3& ZLWK 0% 5$0 DQG *% VWRUDJH VSDFH ,W XVHV D f PRQLWRU WR GLVSOD\ WKH 26&,5 VRIWZDUH LQWHUIDFH 7KH RQO\ QRQVWDQGDUG SLHFH RI KDUGZDUH LQ WKH FRQWURO FRPSXWHU LV WKH SUHYLRXVO\ PHQWLRQHG 5$3725 IUDPHJUDEEHU FDUG 7KLV FDUG fJUDEVf WKH IUDPHV WKDW DUH RXWSXW IURP WKH ORZHU ILEHU ERDUG DQG VWRUHV WKHP LQ RQERDUG PHPRU\ XQWLO WKH 26&,5 VRIWZDUH LQWHUIDFH QHHGV WR DVVHVV WKH GDWD IUDPHV WR VWRUH WKHP WR GLVN DQG SUHVHQW WKHP YLVXDOO\ WR WKH REVHUYHU $ VHFRQG FRQWURO FRPSXWHU LV NHSW RQn VLWH ZLWK WKH 2&,5 V\VWHP DQG FDQ EH XVHG LQ FDVH RI IDLOXUH RI WKH SULPDU\ FRPSXWHU )RU PRVW RI 26&,5fV XVH WKH FRQWURO FRPSXWHU ZDV XVHG WR EDFNXS WKH GDWD DW WKH HQG RI HDFK REVHUYLQJ QLJKW 7KH GDWD ZDV WUDQVIHUUHG WR RSWLFDO GLVNV DW WKH WHOHVFRSH IRU HYHQWXDO

PAGE 173

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f 7KH PDMRULW\ RI WKH LQWHUIDFH LV ZULWWHQ LQ WKH ,'/ VRIWZDUH HQYLURQPHQW 7KH JUDSKLFDO XVHU LQWHUIDFH *8,f RI WKH VRIWZDUH XVHV ,'/ ZLGJHWV WR SUHVHQW WKH REVHUYHU ZLWK DQ HDV\ DQG HIILFLHQW ZD\ WR FRPPXQLFDWH ZLWK WKH V\VWHP DV D ZKROH $OO FRPPXQLFDWLRQ EHWZHHQ WKH REVHUYHU DQG WKH GHZDU SDVV WKURXJK WKH YDULRXV ZLQGRZV WKDW PDNH XS WKH *8, DQG WKH REVHUYHU FDQ DFFHVV WKH GDWD LQ DOPRVW UHDOWLPH WKURXJK WKH VDPH ZLQGRZV 7KLV QHDU UHDOWLPH GDWD DFFHVV LV PDGH SRVVLEOH ZLWK D VXLWH RI fTXLFNORRNf GDWD DQDO\VLV WRROV WKDW DUH EXLOW LQWR WKH *8, 7KHVH WRROV DOORZ WKH REVHUYHU WR GLVSOD\ WKH GDWD WKDW ZDV MXVW REWDLQHG E\ WKH V\VWHP DQG SHUIRUP EDVLF DQDO\VLV RQ WKH GDWD YHU\ TXLFNO\ 7KLV LV H[WUHPHO\ XVHIXO LQ DVVHVVLQJ WKH TXDOLW\ RI DQ REVHUYDWLRQ DQG JLYHV WKH XVHUV LPPHGLDWH IHHGEDFN RQ WKH RYHUDOO VWDWXV RI WKH REVHUYDWLRQDO SURJUDP 7KHVH WRROV ZHUH XVHG H[WHQVLYHO\ LQ WKH GDWD UHGXFWLRQ DQG DQDO\VLV RI WKH REVHUYDWLRQ SUHVHQWHG LQ WKLV GLVVHUWDWLRQ

PAGE 174

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

PAGE 175

$33(1',; 0,',5 $6752120< $ 6+257 &2856( 3RRU DWPRVSKHULF WUDQVPLVVLRQ KLJKO\ YDULDEOH VN\ FRQGLWLRQV DQG LQFUHGLEO\ KLJK EDFNJURXQG OHYHOV KDYH PDGH LW LPSRVVLEOH WR ZRUN LQ WKLV UHJLPH XQWLO UHODWLYHO\ UHFHQWO\ 7KH ILUVW PDMRU REVWDFOH IRU WKH PLGLQIUDUHG OLJKW IURP D VRXUFH WR KXUGOH LV JHWWLQJ WKURXJK WKH HDUWKfV DWPRVSKHUH 7KHUH DUH WZR XVHIXO fZLQGRZVf LQ WKH DWPRVSKHUH EHWZHHQ WKH ZDYHOHQJWKV RI WR SP 7KH ILUVW LV D UHODWLYHO\ KLJK WUDQVPLVVLRQ ZLQGRZ EHWZHHQ DQG SP ZKLFK FRQWDLQV DQ DEVRUSWLRQ IHDWXUH DW SP GXH WR R]RQH %HWZHHQ DQG SP WUDQVPLVVLRQ GURSV WR QLO GXH WR & +RZHYHU DIWHU SP LV WKH VHFRQG ZLQGRZ ZKLFK FRQWLQXHV XQWLO DERXW SP 7KLV ZLQGRZ LV ULGGOHG ZLWK ZDWHU YDSRU DEVRUSWLRQ IHDWXUHV EXW HQRXJK PLGLQIUDUHG UDGLDWLRQ FDQ SHQHWUDWH WKURXJK WKH DWPRVSKHUH DW WKHVH ZDYHOHQJWKV WR EH XVHIXO )LJXUH $f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

PAGE 176

$WPRVSKHULF 7UDQVPLVVLRQ 0DXQD .HD DOWLOXGH P DLUPDVV SZY PP 5 f )LJXUH $O $75$1 PRGHO RI DWPRVSKHULF WUDQVPLVVLRQ IRU 0DXQD .HD 7KH SP ZLQGRZ FDQ EH VHHQ FOHDUO\ DV ZHOO DV WKH VKRUWHU ZDYHOHQJWK QHDU,5 ZLQGRZV 7KH DEVRUSWLRQ IHDWXUH DW SP LV GXH WR DWPRVSKHULF R]RQH WKH RSDTXH EDQG DW SP LV IURP &2 /RQJHU ZDYHOHQJWK ILOWHUV WDNH DGYDQWDJH RI WKH SP ZLQGRZ ZKLFK KDV PDQ\ DEVRUSWLRQ IHDWXUHV FDPHUD 7KHVH VRXUFHV RI fEDFNJURXQG UDGLDWLRQf FDQ EH UHPRYHG DV ZLOO EH GLVFXVVHG LQ WKH QH[W VHFWLRQ 2QFH WKH PLGLQIUDUHG UDGLDWLRQ IURP WKH DVWURQRPLFDO VRXUFH SDVVHV WKURXJK WKH HQWUDQFH ZLQGRZ LQ WR WKH FDPHUD V\VWHP RI 26&,5 )LJXUH f LW XQGHUJRHV YHU\ OLWWOH DWWHQXDWLRQ EHIRUH KLWWLQJ WKH GHWHFWRU 7KLV LV EHFDXVH H[FHSW IRU WKH ILOWHUV DQG WKH FDPHUD HQWUDQFH ZLQGRZ 26&,5 LV DQ HQWLUHO\ UHIOHFWLYH V\VWHP $OO RI WKH PLUURUV LQ WKH RSWLFDO SDWK RI 26&,5 DUH JROGFRDWHG WR WDNH DGYDQWDJH RI WKH ORZ HPLVVLYLW\ JROG KDV LQ WKH PLGLQIUDUHG )XUWKHUPRUH WKH HQWUDQFH ZLQGRZ LV WKH RQO\ FRPSRQHQW LQ WKH FDPHUD WKDW LV QRW FU\RJHQLFDOO\ FRROHG %\ FRROLQJ WKH RSWLFDO FRPSRQHQWV LQ WKLV ZD\

PAGE 177

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fVWRSf LV SODFHG QHDU WKH SXSLO LPDJH RI WKH VHFRQGDU\ PLUURU ZKHUH LW FDQ UHMHFW VWUD\ OLJKW IURP RXWVLGH WKH EHDP 7KLV VWRS LV ORFDWHG LQWHUQDOO\ ZKHUH LW FDQ EH FU\RJHQLFDOO\ FRROHG FDOOHG D fFROGf VWRSf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f DQG WKH UHODWLYHO\ VWDWLF UDGLDWLRQ IURP WHOHVFRSH RSWLFV DQG FDPHUD HQWUDQFH ZLQGRZ LH UDGLDWLYH RIIVHWf ,Q IDFW WKLV EDFNJURXQG UDGLDWLRQ GRPLQDWHV REVHUYDWLRQV

PAGE 178

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f§ ’ SKRWRQV FP V *LYHQ WKH KLJK TXDQWXP HIILFLHQF\ RI WKH GHWHFWRU DQG D ZHOO GHSWK RI ’ HOHFWURQV WKH ZHOOV RI WKH GHWHFWRU ILOO WR b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fFKRSQRGf WHFKQLTXH ,Q WKLV WHFKQLTXH WKH WHOHVFRSH LV SRLQWHG DW DQ REMHFW RI LQWHUHVW WKH fSURJUDP REMHFWff DQG WKH FDPHUD DFTXLUHV D VHW RI LPDJHV $Q LPDJH FRQVLVWV RI VLJQDO IURP WKH SURJUDP REMHFW VXSHUSRVHG RQ WKH PXFK ODUJHU VLJQDO IURP WKH EDFNJURXQG 7KH VHFRQGDU\ PLUURU RI WKH WHOHVFRSH LV WKHQ PRYHG VOLJKWO\ DZD\ IURP WKH QRPLQDO SRVLWLRQ VR WKDW WKH SURJUDP REMHFW PRYHV

PAGE 179

1RG 3RVLWLRQ $ 1RG 3RVLWLRQ % 1HW 6RXUFH 6LJQDO 2Q6RXUFH 2Q6RXUFH &KRSSHG 'LIIHUHQFH &KRSSHG 'LIIHUHQFH )LJXUH $ 6FKHPDWLF RI fFKRSQRGf REVHUYLQJ 7KH WRS IRXU LPDJHV DUH WKH UDZ FRDGGHG GDWD WUDQVIHUUHG IURP WKH 90( FUDWH WR WKH FRQWURO FRPSXWHU DW a +] 7KH PLGGOH OHYHO VKRZV WKH fGLI f IUDPHV WKDW DUH FRQVWUXFWHG IURP WKH GLIIHUHQFH RI WKH WZR IUDPHV DERYH LW +HUH WKH SDWWHUQ RI UDGLDWLYH RIIVHW LV FOHDUO\ YLVLEOH 7KH ERWWRP LPDJH LV WKH VXP RI WKH fGLIVf )LQDOO\ ZH VHH WKH DVWURQRPLFDO VRXUFH ,Q WKLV FDVH WKH QXFOHXV RI WKH VWDUEXUVW JDOD[\ 1*& 'DWD WDNHQ DW WKH ,57) RXW RI WKH ILHOG RI YLHZ RI WKH FDPHUD $QRWKHU VHW RI LPDJHV LV DFTXLUHG E\ WKH FDPHUD 7KLV SURFHGXUH FDOOHG D fFKRSf F\FOH LV UHSHDWHG PDQ\ WLPHV DW W\SLFDOO\ D +] UDWH PRYLQJ EDFN DQG IRUWK EHWZHHQ fRQVRXUFHf DQG fRIIVRXUFHf SRVLWLRQV $ fFKRS GLIIHUHQFHGf VLJQDO LV IRUPHG E\ WDNLQJ WKH GLIIHUHQFH EHWZHHQ WKH RQVRXUFH DQG RII VRXUFH LPDJHV :KLOH WKLV UDSLG PRYHPHQW RI WKH VHFRQGDU\ PLUURU DOORZV VXEWUDFWLRQ RI D VSDWLDOO\ XQLIRUP EDFNJURXQG WKDW LV YDU\LQJ LQ WLPH DW IUHTXHQFLHV EHORZ WKH FKRS

PAGE 180

IUHTXHQF\ LW XVXDOO\ JHQHUDWHV D VSXULRXV VLJQDO ZKLFK PD\ VWLOO EH VLJQLILFDQWO\ ODUJHU WKDQ WKH VRXUFH VLJQDO 7KLV VSXULRXV VLJQDO WHUPHG WKH fUDGLDWLYH RIIVHWf UHVXOWV IURP WKH IDFW WKDW WKH HPLVVLRQ SDWWHUQ RI WKH WHOHVFRSH DV VHHQ E\ WKH FDPHUD GHSHQGV RQ WKH RSWLFDO FRQILJXUDWLRQ RI WKH WHOHVFRSH 0RYHPHQW RI WKH VHFRQGDU\ PLUURU FKDQJHV WKLV FRQILJXUDWLRQ UHVXOWLQJ LQ WZR GLIIHUHQW HPLVVLRQ SDWWHUQV 7KH GLIIHUHQFH LQ WKHVH HPLVn VLRQ SDWWHUQV VKRZV XS LQ WKH FKRSGLIIHUHQFHG VLJQDO ,Q RUGHU WR UHPRYH WKH UDGLDWLYH RIIVHW WKH HQWLUH WHOHVFRSH LV PRYHG DIWHU D VKRUW SHULRG RI WLPH W\SLFDOO\ RQ WKH RUGHU RI WHQV RI VHFRQGVf VR WKDW WKH VRXUFH QRZ DSSHDUV LQ ZKDW ZDV SUHYLRXVO\ WKH RIIVRXUFH SRVLWLRQ RI WKH VHFRQGDU\ PLUURU 7KLV PRYHPHQW RI WKH WHOHVFRSH LV WHUPHG D fEHDP VZLWFKf RU fQRGf &KRSGLIIHUHQFHG IUDPHV DUH WKHQ IRUPHG ZLWK WKLV QHZ RQVRXUFH DQG RIIVRXUFH FRQILJXUDWLRQ $ OLWWOH WKRXJKW VKRZV WKDW LQ WKLV QHZ FRQILJXUDWLRQ WKH UDGLDWLYH RIIVHW ZLOO KDYH FKDQJHG VLJQ DQG ZLOO FDQFHO LGHQWLFDOO\ ZKHQ WKH QHZ FKRSGLIIHUHQFHG GDWD LV DGGHG WR WKH ROG FKRSGLIIHUHQFHG GDWD SURYLGHG WKH WHOHVFRSH HPLVVLRQ KDV QRW FKDQJHG LQ WKH WLPH EHWZHHQ EHDP VZLWFKLQJf )LJXUH $ GHPRQVWUDWHV WKH DFTXLVLWLRQ RI GDWD LQ WKH VWDQGDUG fFKRSQRGf PRGH 7KH LPDJHV VKRZQ KHUH ZHUH REWDLQHG ZLWK 26&,5 DW WKH ,57) 7KH WRS URZ RI IRXU LPDJHV VKRZV WKH UDZ GDWD IUDPHV IURP WKH WZR VHFRQGDU\ PLUURU SRVLWLRQV DW HDFK RI WKH WZR QRG SRVLWLRQV FDOOHG f1RG 3RVLWLRQ $f DQG f1RG 3RVLWLRQ %ff RI WKH WHOHVFRSH 7KHVH LPDJHV DUH GRPLQDWHG E\ IL[HGSDWWHUQ RIIVHWV GXH WR SL[HOWRSL[HO YDULDWLRQV DQG RIIVHWV EHWZHHQ WKH FKDQQHOV RI WKH DFTXLVLWLRQ HOHFWURQLFV 7KH EDFNJURXQG FRXQWV LQ WKHVH UDZ LPDJHV FRUUHVSRQG WR [ HV (DFK UDZ LPDJH FRQVLVWV RI a PLQXWHV RI WRWDO LQWHJUDWLRQ WLPH LH IUDPHV FRDGGHG XVLQJ D PV IUDPH LQWHJUDWLRQ WLPH DQG WKH 1EDQG ILOWHUf REWDLQHG LQ WKH FKRSQRG VHTXHQFH DV GHVFULEHG DERYH 7KH VHFRQG

PAGE 181

URZ RI WZR LPDJHV VKRZV WKH fFKRSGLIIHUHQFHGf GDWD GHULYHG IURP WKH VXEWUDFWLRQ RI WKH RQVRXUFH DQG RIIVRXUFH GDWD LQ WKH WZR QRG SRVLWLRQV RI WKH WHOHVFRSH 1RWH WKDW WKH GRPLQDQW SDWWHUQ SULQFLSDOO\ D JUDGLHQW DORQJ WKH GLDJRQDO FRQQHFWLQJ WKH ORZHUOHIW WR XSSHUULJKW FRPHUV RI WKH LPDJHVf KDV FKDQJHG VLJQ EHWZHHQ WKH WZR FKRSGLIIHUHQFHG IUDPHV +RZHYHU VLQFH WKH VXEWUDFWLRQ LV DOZD\V GRQH DV fRQVRXUFH PLQXV RIIVRXUFHf WKH VRXUFH VLJQDO UHPDLQV SRVLWLYH LQ ERWK FKRSGLIIHUHQFHG IUDPHV 7KH VLJQDO OHYHOV LQ WKHVH GLIIHUHQFHG IUDPHV UDQJH s[O HV ZKLFK LV b RI WKH UDZ EDFNJURXQG VLJQDO )LQDOO\ WKH ERWWRP URZ VKRZV WKH QHW VLJQDO REWDLQHG E\ DGGLQJ WRJHWKHU WKH WZR FKRSGLIIHUHQFHG IUDPHV VKRZQ LQ WKH PLGGOH URZ QRWH WKDW QR RWKHU SURFHVVLQJ KDV EHHQ GRQH WR WKH GDWD RWKHU WKDQ WKH DGGLWLRQV DQG VXEWUDFWLRQV DV GHVFULEHG DERYHf 7KH GHWHFWHG VRXUFH LV WKH QXFOHDU UHJLRQ RI WKH VWDUEXUVW JDOD[\ 1*& 7KH QHW VLJQDO LV WKH UHVXOW RI D WRWDO H[SRVXUH RI PLQXWHV LQ ZKLFK KDOI WKDW WLPH LV DFWXDOO\ VSHQW LPDJLQJ WKH RIIVRXUFH fUHIHUHQFHf SRVLWLRQ 7KH VLJQDO OHYHO DW WKH fWDLOf RI WKLV VRXUFH QHDU WKH PLGGOH RI WKH IUDPH LV [ HV 7KLV LV DERXW IRXU RUGHUV RI PDJQLWXGH EHORZ WKH EDFNJURXQG OHYHO VKRZQ LQ WKH UDZ IUDPH ,Q IDFW WKH VLJQDOWRQRLVH UDWLR DW WKLV OHYHO LQ HDFK SL[HO LV DERXW VHYHQ VR WKDW WKH HIIHFWLYH EDFNJURXQG VXEWUDFWLRQ LV PRUH QHDUO\ ILYH RUGHUV RI PDJQLWXGH EHORZ WKH EDFNJURXQG

PAGE 182

/,67 2) 5()(5(1&(6 $LWNHQ 0RRUH 7 7 5RFKH 3 ) 6PLWK & + t :ULJKW & 0 015$6 / $OOHQ & : LQ $OOHQfV $VWURSK\VLFDO 4XDQWLWLHV )RXUWK (GLWLRQ HG $ 1 &R[ 6SULQJHU 9HUODJf $OYDUH] 0 t 6FKXVWHU : 5HY 0H[ $VWURQ $QGUH 3 LQ 7KH &ROG 8QLYHUVH HG 7 0RQWPHUOH t & /DGD 6SULQJHU 9HUODJf $QGUH 3 :DUG7KRPSVRQ t %DUVRQ\ 0 $S$QGULOODW < -DVFKHN 0 t -DVFKHN & $t$ $UW\PRZLF] 3 $S/ $UW\PRZLF] 3 $QQX 5HY (DUWK 3ODQHW 6FL $XJHUHDX & /DJUDQJH $ 0 0RXLOOHW 3DSDORL]RX & % t *URURG 3 $ $t$ $XPDQQ + + 3$63 $XPDQQ + + %HLFKPDQ & $ *LOOHW ) & GH -RQJ 7 +RXFN 5 /RZ ) 1HXJHEDXHU :DONHU 5 t :HVVHOLXV 3 5 $S/ %DFNPDQ ( *LOOHWW ) & t :LWWHUERP ) & $S%DFNPDQ ( t 3DUHVFH ) LQ 3URWRVWDUV DQG 3ODQHWV ,,, HG ( + /HY\ /XQLQH t 0 6 0DWWKHZV 7XVFRQ8QLYHUVLW\ RI $UL]RQD 3UHVVf %DUUDGR < 1DYDVFXHV 6WDXIIHU 5 6RQJ t &DLOODXOW -3 $S/ %OLW] / LQ 7KH 3K\VLFV RI 6WDU )RUPDWLRQ DQG (DUO\ 6WHOODU (YROXWLRQ HG & /DGD t 1' .\ODILV 'RUGUHFKW .OXZHUf %RKP 7f t &DWDOD & $t$

PAGE 183

%RKUHQ &) t +XIIPDQ 5 $EVRUSWLRQ DQG 6FDWWHULQJ RI /LJKW E\ 6PDOO 3DUWLFOHV 1HZ
PAGE 184

*UHDYHV 6 +ROODQG : 6 0RULDUW\6FKLHYHQ -HQQHVV 7 'HQW : 5 ) =XFNHUPDQ % 0F&DUWK\ & :HEE 5 $ %XWQHU + 0 *HDU : t :DONHU + $S*XVWDIVRQ % $ 6 $QQ 5HY (DUWK 3ODQHW 6FL +DQQHU 0 6 7RNXQDJD $ 7 9HHGHU t $f+HDP 0 ) $+DUWPDQQ / +HZHWW 5 t &DOYHW 1 $S+HDS 6 5f /LQGOHU t :RRGJDWH % %$$6 +HLQULFKVHQ :DONHU + t .ODDV 8 015$6 / +HUELJ + $S-6 +ROODQG : 6 *UHDYHV 6 =XFNHUPDQ % :HEE 5 $ 0F&DUWK\ & &RXOVRQ 0 :DOWKHU 0 'HQW 5 ) *HDU : t 5REVRQ 1DWXUH ,EHQ $S,EHQ t 7DOERW 5 $S-DVQLHZLF] 3DUWKDVDUDWK\ 0 GH /DYHUQ\ 3 t 7KHYHQLQ ) $t$ -D\DZDUGKDQD 5 )LVKHU 5 6 +DUWPDQQ / 7HOHVFR & 0 3LD 5 t )D]LR $S-D\DZDUGKDQD 5 )LVKHU 5 6 7HOHVFR & 0 3LD 5 %DUUDGR \ 1DYDVFXHHV +DUWPDQQ / t )D]LR $SDFFHSWHG -XUD 0 0DONDQ 0 :KLWH 5 7HOHVFR & 3LD 5 t )LVKHU 5 6 $S.DODV 3f t -HZLWW $.HWR ( -HPLJDQ %DOO 5 $UHQV ) t 0HL[QHU 0 $S/ .QDFNH 5 ) )DMDUGR$FRVWD 6 % 7HOHVFR & 0 +DFNZHOO $ /\QFK t 5XVVHOO 5 : $S.RHPHU : 5HVVOHU 0 ( :HUQHU 0 : t %DFNPDQ ( $S/ /DGD & LQ 6WDU )RUPLQJ 5HJLRQV ,$8 6\PSRVLXP HG 0 3HLPEHUW DQG -XJDNX .OXZHQ'RUGUHFKWf

PAGE 185

/DJDJH 3 t 3DQWLQ ( 1DWXUH /DJUDQJH $0 %DFNPDQ t $UW\PRZLF] 3 LQ 3URWRVWDUV DQG 3ODQHWV ,9 HG 9 0DQQLQJV $ 3 %RVV t 6 6 5XVVHOO 7XVFRQ8QLYHUVLW\ RI $UL]RQD 3UHVVf /DRU $ t 'UDLQH % 7 $S/HLQHUW & t *ULLQ ( LQ 6SDFH DQG 6RODU 3K\VLFV 9RO 3K\VLFV DQG &KHPLVWU\ LQ 6SDFH 3K\VLFV RI WKH ,QQHU +HOLRVSKHUH HG 5 6FKZHHQ t ( 0DUVFK %HUOLQ6SULQJHUf 0DQQLQJV 9 t %DUORZ 0 $S0DOIDLW %RJDHUW ( t :DHONHQV & $t$ 0DUF\ :f t %XWOHU 5 3 %$$6 0DULDV 1 7HOHVFR & 0 3LD 5 )LVKHU 5 6 t :\DWW 0 & $$6 0 0RXLOOHW /DUZRRG 3DSDORL]RX & % t /DJUDQJH $ 0 015$6 2VLS 3LD 5 7HOHVFR & 0 )LVKHU 5 6 t +DQQHU 0 6 ,$8& &RPHW & +DOH%RSSf 3DOOD )f t 6WDKOHU 6 : $S3HUU\PDQ 0 $ & 3HUU\PDQ 0 $ & /LQGHJUHQ / .RYDOHYVN\ 7XUQ & +RHJ ( *UHQRQ 0 6FKULMYHU + %HUQDFFD 3 / &UH]H 0 'RQDWL ) (YDQV : )DOLQ / )URHVFKOH 0 *RPH] $ *UHZLQJ 0 YDQ /HHXZHQ ) YDQ GHU 0DUHO + 0LJQDUG ) 0XUUD\ & $ 3HQVWRQ 0 3HWHUVHQ & /H 3RROH 5 6f :DOWHU + $t$ 3H]]XWR 6 6WUDIHOOD ) t /RUHQ]HWWL $S3RORPVNL ( ) 7HOHVFR & 0 3LD 5 t )LVKHU 5 6 $3 3UDWR / *KH] $ 0 3LD 5 7HOHVFR & 0 )LVKHU 5 6 :L]LQRZLFK 3 /DL 2 $FWRQ 6 t 6WRPVNL 3 $$6 6DDU 5 $ t 2VWHQ 6 + 015$6

PAGE 186

6DKX 0 6 %ODGHV & +H / +DUWPDQQ %DUORZ 0 t &UDZIRUG $ $S6FKQHLGHU 6PLWK % $ %HFNOLQ ( ( .RHPHU : 0HLHU 5 +LQHV & /RZUDQFH 3 7HUULOH 5 7KRPSVRQ 5 t 5HLNH 0 $S/ 6FKXVWHU : t *XLFKDUG 5HY 0H[ $VWURQ 6KX ) + $GDPV ) & t /L]DQR 6 $5$$ 6LOYHUVWRQH 0 %$$6 6NLQQHU & 6\OYHVWHU 5 *UDKDP 5 %DUORZ 0 0HL[QHU 0 .HWR ( $UHQV ) t -HPLJDQ $S6PLWK % $ t 7HUULOH 5 6FLHQFH 6RGHUEORP 5 -RQHV % ) %DODFKDQGUDQ 6 6WDXIHU 5 'XQFDQ )HGHOH 6 % t +XGRQ $6WDXIIHU 5 +DUWPDQQ / : t 1DYDVFXHV % $S6WHQFHO 5 ( t %DFNPDQ ( $S/6 6WUDVVPHLHU )HNHO ) & %RSS % : 'HPSVH\ 5 & t +HQU\ : $S-6 6\OYHVWHU 5 %DUORZ 0 t 6NLQQHU & $St66 6\OYHVWHU 5 t 6NLQQHU & 015$6 6\OYHVWHU 5 6NLQQHU & t %DUORZ 0 015$6 6\OYHVWHU 5 6NLQQHU & %DUORZ 0 t 0DQQLQJV 9 015$6 7HOHVFR & 0 'HFKHU 5 %HFNOLQ ( ( t :ROVWHQFURIW 5 1DWXUH 7HOHVFR & 0 )LVKHU 5 6 3LfD 5 .QDFNH 5 ) 'HUPRWW 6 ) :\DWW 0 & *URJDQ +ROPHV ( *KH] $ 0 3UDWR / +DUWPDQQ / : t -D\DZDUGKDQD 5 $S7HOHVFR & 0f t .QDFNH 5 ) $S/ YDQ GHQ $QFNHU 0 ( GH :LQWHU t 7MLQ $ 'MLH + 5 ( $t$

PAGE 187

YDQ GHU %OLHN 1 6 3UXVWL 7 t :DWHUV / % ) 0 $t$ :DONHU + t +HLQULFKVHQ ,FDUXV :DONHU + t :ROVWHQFURIW 5 3$63 :DOWHU ) 0 %URZQ $ 0DWKLHX 5 0\HUV 3 & t 9UED ) $:HLQEHUJHU $ %HFNOLQ ( ( 6FKQHLGHU 6PLWK % $ /RZUDQFH 3 6LOYHUVWRQH 0 =XFNHUPDQ % t 7HUULOH 5 $S/ :\DWW 0 & 3K' WKHVLV 8QLYHUVLW\ RI )ORULGD :\DWW 0 & 'HUPRWW 6 ) 7HOHVFR & 0 )LVKHU 5 6 *URJDQ +ROPHV ( t 3LD 5 $S;X
PAGE 188

%,2*5$3+,&$/ 6.(7&+ ZDV UDLVHG LQ WKH WRZQ RI 0DSOHWRQ 'HSRW 3HQQV\OYDQLD XQWLO DJH $IWHU PLGGOH VFKRRO LQ 3$ PRYHG WR )ORULGD DQG ILQLVKHG KLJK VFKRRO LQ /HHVEXUJ VSHQW WKUHH VHPHVWHUV DW D FRPPXQLW\ FROOHJH WKHUH DQG HDUQHG DQ $$ GHJUHH WKHQ ZDV DZDUGHG D &RQJUHVV%XQGHVWDJ
PAGE 189

, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 3/f§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

PAGE 190

, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 5RJHU ) .QDFNH 'LUHFWRU 6FKRRO RI 6FLHQFH 3HQQ 6WDWH (ULH FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 3DXO $YHU\ 3URIHVVRU RI 3K\VLFV 7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH *UDGXDWH )DFXOW\ RI WKH 'HSDUWPHQW RI $VWURQRP\ LQ WKH &ROOHJH RI /LEHUDO $UWV DQG 6FLHQFHV DQG WR WKH *UDGXDWH 6FKRRO DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXLUHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ $XJXVW 'HDQ *UDGXDWH 6FKRRO

PAGE 191

/' 2) 81,9(56,7< 2) )/25,'$


xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID ECPI6PRK0_QJ0RBB INGEST_TIME 2013-11-15T23:33:23Z PACKAGE AA00014222_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES