The Paradox of Asset Pricingby Peter Bossaerts
Pub. Date: 12/28/2004
Publisher: Princeton University Press
Asset pricing theory abounds with elegant mathematical models. The logic is so compelling that the models are widely used in policy, from banking, investments, and corporate finance to government. To what extent, however, can these models predict what actually happens in financial markets? In The Paradox of Asset Pricing, a leading financial researcher/i>
Asset pricing theory abounds with elegant mathematical models. The logic is so compelling that the models are widely used in policy, from banking, investments, and corporate finance to government. To what extent, however, can these models predict what actually happens in financial markets? In The Paradox of Asset Pricing, a leading financial researcher argues forcefully that the empirical record is weak at best. Peter Bossaerts undertakes the most thorough, technically sound investigation in many years into the scientific character of the pricing of financial assets. He probes this conundrum by modeling a decidedly volatile phenomenon that, he says, the world of finance has forgotten in its enthusiasm for the efficient markets hypothesisspeculation.
Bossaerts writes that the existing empirical evidence may be tainted by the assumptions needed to make sense of historical field data or by reanalysis of the same data. To address the first problem, he demonstrates that one central assumptionthat markets are efficient processors of information, that risk is a knowable quantity, and so oncan be relaxed substantially while retaining core elements of the existing methodology. The new approach brings novel insights to old data. As for the second problem, he proposes that asset pricing theory be studied through experiments in which subjects trade purposely designed assets for real money. This book will be welcomed by finance scholars and all those mathand statistics-minded readers interested in knowing whether there is science beyond the mathematics of finance.
This book provided the foundation for subsequent journal articles that won two prestigious awards: the 2003 Journal of Financial Markets Best Paper Award and the 2004 Goldman Sachs Asset Management Best Research Paper for the Review of Finance.
Table of Contents
1. Principles of Asset-Pricing Theory
Wherein we review the basics of asset-pricing theory, starting from dynamic programming (pointing out some of the surprising simplifications when applied to portfolio analysis), introducing the notion of equilibrium,and then narrowing everything down to arrive at the Capital Asset-Pricing Model (CAPM). The emphasis is on the features that the CAPM shares with virtually all other asset-pricing models,namely, in equilibrium, prices are set so that expected excess returns are proportional to covariance with aggregate risk.
1.1 Introduction 1
1.2 Stochastic Dynamic Programming 2
1.3 An Application to a Simple Investment-Consumption Problem 8
1.4 A Nontrivial Portfolio Problem 10
1.5 Portfolio Separation 11
1.6 Toward the First Asset-Pricing Model 15
1.7 Consumption-Based Asset-Pricing Models 17
1.8 Asset-Pricing Theory: The Bottom Line 21
1.9 Arrow-Debreu Securities Pricing 22
1.10 Roll's Critique 23
1.11 Time Nonseparable Preferences 24
1.12 Existence of Equilibrium 26
1.13 Price Discovery 28
2. Empirical Methodology
Empirical tests of asset-pricing theory require the researcher to make auxiliary assumptions that are not necessarily an integral part of the theory. Most prominent is the assumption that ties ex-ante beliefs (which determine prices) to the ex-post frequencies of the payoffs, which has become known as the efficient markets hypothesis (EMH). EMH dramatically simplifies empirical methodology. We review three important types of tests that it generated: (1) Tests of the mean-variance efficiency of benchmark portfolio(s); (2)stochastic Euler equation tests; and (3) variance bounds tests.
2.1 Introduction 39
2.2 The Efficient Markets Hypothesis (EMH) 42
2.3 Violations of the Stationarity Assumption 46
2.4 Inference in a Nonstationary World 53
2.5 Testing the CAPM 55
2.5.1 A Linear Test 56
2.5.2 A Nonlinear Test 57
2.5.3 The Fama-MacBeth Procedure 58
2.5.4 Can One Condition on Less than the Entire State Vector in Tests of the CAPM? 59
2.6 Testing Consumption-Based Asset-Pricing Models 63
2.7 Diagnostics: Variance Bounds 66
3. The Empirical Evidence in a Nutshell
An anthology of the extensive literature on tests of asset-pricing models enables us to form a fairly comprehensive image of the empirical evidence. Few would be encouraged by the results.
3.1 Introduction 71
3.2 Empirical Evidence on the CAPM 72
3.3 Hansen-Jagannathan Bounds 83
3.4 GMM Tests of Consumption-Based Models 89
3.5 Cross-Sectional Tests 95
3.6 Conclusion 100
4. The Experimental Evidence
But perhaps we are demanding too much from empirical studies of historical data from field markets. What about the evidence from simple, purposely built experimental markets? Some principles emerge well and alive (e.g., the CAPM), others can be rejected outright (e.g., instantaneous equilibration). The lab also allows us to discover things that are fundamental to economic theory but difficult to detect in historical data, such as the ranking of Arrow-Debreu securities prices. At the same time, we experience how hard it is to control beliefs.
4.1 Introduction 103
4.2 A Typical Asset-Pricing Experiment 107
4.3 Theoretical Predictions 110
4.4 Experimental Results 111
4.5 Announced and Perceived Uncertainty 116
4.6 The Scale of Experimentation 122
4.7 Formal Tests 124
4.7.1 The CAPM 124
4.7.2 The Arrow-Debreu Model 126
4.8 Conclusion 128
5. From EMH to Merely Efficient Learning
Although we obviously do not yet understand how to extrapolate lab results to the giant and complex field markets, we can investigate whether our econometric methodology has not been the cause of the empirical failure of asset-pricing theory. The first suspect is EMH. The criticism will be constructive, by demonstrating that EMH is unnecessarily strong: much of the simplicity of the EMH-based empirical methodology can be retained even if one cuts out the most objectionable part. We develop a new methodology for testing asset-pricing models that allows the market to hold mistaken expectations at times, but still requires it to learn as under EMH. We will call it the hypothesis of efficiently learning markets (ELM).
5.1 Introduction 131
5.2 Bayesian Learning 137
5.3 Digital Option Prices under ELM 140
5.4 Limited Liability Security Prices under ELM 142
5.5 Revisiting an Earlier Example 147
5.6 Conclusion 151
6. Revisiting the Historical Record
Armed with new tools, we can revisit historical data. We investigate the aftermarket performance of almost five thousand U.S. initial public offerings (IPOs) in the period 1975-95. Although not perfect, we find far more support for the theory. The example suggests that we may want to substitute ELM for EMH in future studies of historical data from field markets.
6.1 Introduction 153
6.2 U.S. IPO Aftermarket Performance 154
6.3 Conclusion 162
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