An analysis of some issues in asset price behaviour

(1)

AUSTRALIAN NATIONAL UNIVERSITY LIBRARY

The persons whose signatures appear below have consulted this thesis by Vladimir Pavlov and are aware that it is available for study only and that no quotations, or substantive information not otherwise available, may be published therefrom without the consent of the author and of

Name (PRINT & Sign) Date Name (PRINT & Sign)

Permission is given

1111.'

,i'fl..-to the University Librarian or his representative to allow persons other than students or members of staff of the University to consult my thesis only for the purposes of private study and research.

(2)

An Analysis of Some Issues in Asset Price

Behaviour

Vladimir Pavlov

A thesis submitted for the degree of

Doctor of Philosophy of

The Australian National University

(3)

(4)

DECLARATION

The work contained in this thesis has not been previously submitted for a

degree or diploma at any other education institution. To the best of my

knowledge and belief, the thesis contains no material previously published

or written by another person except where due reference is made.

Signed

--~

...

:71 ...

k ... .

~/

1 . 1

Date

(5)

ACKNOWLEDGEMENTS

First and foremost, I would like to acknowledge the help and support of

my supervisor, Adrian Pagan, whose commitment and patience have been

an inspiration to me and shaped my views on what it is to be a real

academic and a professional. I am also grateful to Simon Grant for his

support and comments on various parts of the thesis. Since I joined QUT,

Stan Hurn has been a friend, a mentor and a constant source of

encouragement. I would also like to thank all of my family and friends for

their support (and constant nagging on the topic of getting it over and

done with).

(6)

ABSTRACT

The equity premium puzzle, described by Mehra and Prescott in 1985, has

baffled financial economists for almost two decades and still lacks a

satisfactory resolution. For an area of economics, whose main focus is on

measuring risks and rewards for risk taking, not being able to explain the

difference in expected returns between two major classes of financial assets

- equity and bonds - is a major challenge. We examine some of the issues

associated with the equity premium and related puzzles. The mam

contribution of the thesis is in establishing that a representative agent

model can be used to approximate the solutions of an over

lapping-generations economy when markets are conditionally complete and then

using this approximation to examine age-related liquidity restrictions as

possible explanations for the puzzle. We conclude that such restrictions by

themselves can not explain the equity premium puzzle.

(7)

/3,

T Using Australian Data ... 19

1.4 SOURCES OF THE PUZZLES ... 23

1.4.1 Equity Premium Puzzle ... 23

1.4.2 Risk-Free Rate Puzzle ... 27

1.5 CONCLUSION ... 29

~A REVIEW OF ASSET PRICING PUZZLES ... 30

2.2 MOVEMENTS IN EXPECTED RETURNS AND THE EQUITY PREMIUM ... 31

2.3 ALTERNATIVE UTILITY SPECIFICATIONS ... 41

2. 3.1 Habit Formation Preferences ... 42

2.3.2 Relative Consumption ... 43

2.3.3 Non-Expected Utility ... 45

2.4 CREDIT MARKET EXPLANATION ... 50

2.5 LIQUIDITy ... 56

2.6 INCOMPLETE MARKETS ... 61

2.5.1 The Effect of Transaction Costs ... 66

(8)

2.5.2 Persistence of Individual Income Shocks ... 68

;LAS SET PRICING IN OLG MODELS ... 73

3.2 CDM ~IODEL ... 76

3.3 CDM CALIBRATION ... 79

3.4 EXTENTIONS TO CDM ... 86

U,LFinancial Structure ... .... 87

~ OLG versus Representative Agent .... ... 93

3.4.3 Simple Equilibria ... 96

;:LCALIBRATION AND EQUILIBRIUM ... 103

4.1 IN1'RODUCTION ... 103

4.2 EQUILIBRIUM WITH LOGARITHMIC PREFERENCES ... 103

4.3 CALIBRATION AND SCALING ... 107

4.3.1 Aggregate Dynamics ... 108

4.3.2 Markov Chain Approximation ... 110

4.3.3 Scaling ... 116

4.3.4 Distribution of Wages ... ... 117

4.4 SOLUTION TO THE REPRESENTATIVE AGENT PROBLEM ... 119

4.5 PRICES IN OLG AND REPRESENTATIVE AGENT ECONOMIES ... 120

4.6 ASSET RETURNS IN RESTRICTED AND UNRESTRICTED ECONOMIES ... 123

!LSOLVING ASSET PRICING MODELS ... 128

5.2 SOLUTIONS ... 129

(9)

5.2.1 Discretisation (DA) ... 130

5.2.2 Parameterized Expectations (PE) ... 132

5.2.3 Direct Approximations (A A) ... 134

5.2.3 A Simple Solution Algorithm when G is Linear in Z (LA) ... 137

5.2.4 Recursive Algorithm (RAJ ... 138

5.3 EXAMPLES ... 142

REFEREN CES ... 150

(10)

PREFACE

In an article published in 1985 Mehra and Prescott argued that the equity

premium in the US appears too high to be explained by a consumption

asset-pricing model (CAPM). The growth of aggregate consumption is too

smooth and not sufficiently correlated with the equity premium to

generate the observed level of the average excess return on equities over

risk-free bonds for a reasonable level of risk aversion. This observation,

termed the equity premium puzzle, has been a subject of much research

since the Mehra and Prescott publication but, despite a number of

important contributions, the equity premium puzzle is still unresolved.

On the other hand, finance in general has been an extraordinarily

successful field of modern economics. Factor pricing models, in particular,

have found numerous practical applications in areas such as capital

budgeting, performance evaluation, investment analysis, risk management,

etc. The failure to find a satisfactory economic explanation of the equity

premium puzzle means that these models, and business tools derived from

them, are built on shaky theoretical grounds, as all factor models and

economic intuition about these models are, in fact, based on Lucas's {1978}

(11)

consumption pncmg model and its generalizations. As Cochrane (2001)

points out:

IIThis is a point worth remembering: all factor models are

derived as specializations of the consumption-based models.

Many authors of factor model papers disparage the

consumption-based model, forgetting that their factor model

is the consumption-based model plus extra assumptions that

allow one to proxy for marginal utility growth from some

other variables. "

Understanding the fundamental economic factors driving the equity

premium is vastly important. Grant and Quiggin (1998), for example,

argue that, if a large portion of the observed equity premium is the result

of market frictions, then the common practice of using equity market

returns to evaluate the value of public projects can lead to under-financing

of such projects and create inefficiencies.

This thesis exammes some of the issues associated with the equity

premmm and related puzzles. Chapter 1 formulates the puzzles and the

main empirical features of the data that generate it. Chapter 2 provides a

brief overview of the main contributions to the literature. An important

explanation for the puzzles emerged recently and is based around the effect

of liquidity restrictions on asset pricing in models that take into account

(12)

life-cycle considerations. The mam body of the thesis examines this

explanation under an alternative market structure. Chapter 3 shows that

asset prices in such a model can be approximated using an appropriately

calibrated Lucas model. Chapter 4 uses this approximation in the context

of a calibrated economy to examine the effect of liquidity restrictions on

asset pricing and the equity premium. Chapter 5 concludes with a

discussion of various algorithms used to obtain equilibrium solutions for

asset pricing models.