# The Paradox of Asset Pricing

PETER BOSSAERTS
Pages: 192
https://www.jstor.org/stable/j.ctt5hhpw2

1. Front Matter
(pp. i-iv)
(pp. v-viii)
3. PREFACE
(pp. ix-xvi)
4. CHAPTER 1 Principles of Asset-Pricing Theory
(pp. 1-38)

In this chapter, we will study the body of asset-pricing theory that is most appropriate to understanding the empirical tests that are reported later in this book. In particular, we focus on the discrete-time, stationary dynamic asset-pricing models that have been derived over the past thirty years or so. There are other classes of asset-pricing models, such as Merton’s continuous-time model (see Merton [1973]), but these have been less important in empirical analysis. The models we will consider here capture the essence of all modern asset-pricing theory, namely, that financial markets equilibrate to the point that expected returns are determined...

5. CHAPTER 2 Empirical Methodology
(pp. 39-70)

The previous chapter gathered a few core predictions that theory makes about pricing in financial markets. Central is the hypothesis that markets equilibrate (although we did mention that this is not an obvious point), and that, in equilibrium, expected excess returns will be proportional to the covariance with aggregate risk (see (1.34)).

In bringing this theory to the data, there are several issues. The most important one concerns investors’ beliefs. For the most part, we have assumed that beliefs were homogeneous (i.e., the same across investors), leaving open the possibility that these beliefs were wrong.

Intuitively, we should mean by...

6. CHAPTER 3 The Empirical Evidence in a Nutshell
(pp. 71-102)

Rather than an encyclopedic account of the numerous empirical studies of asset-pricing theory, this chapter is primarily an anthology. Enough material will be presented for the reader to get a comprehensive view of what has been tried, and how the empirical studies have produced a mixed result at best.

Virtually the entire empirical literature gathers evidence from econometric analysis of historical data from field markets. The reader who is unfamiliar with finance research may not appreciate how difficult it is to test theory on historical field data. Many auxiliary assumptions must be made for the inference to be valid. In...

7. CHAPTER 4 The Experimental Evidence
(pp. 103-130)

The central prediction of asset-pricing theory is that financial markets equilibrate to the point that expected returns become proportional to the covariance with aggregate risk. See (1.34), which is repeated here for ease of reference (the riskfree rate is pulled inside the conditional expectation):

$E[{R_n} - {R_F}\left| x \right.] = - {\mathop{\rm cov}} \left( {\frac{A}{{E[A\left| x \right.]}},{R_n}\left| x \right.} \right)$.

Specific asset-pricing models give concrete meaning to the notion of aggregate risk. The Capital Asset-Pricing Model (CAPM), for instance, associates aggregate risk with the return on the market portfolio, and the prediction is that expected excess returns are proportional to the beta with the market portfolio:

$E[{R_n} - {R_F}\left| x \right.] = {\rm{\beta }}_{n,x}^ME[{R_M} - {R_F}\left| x \right.]$.

(This is (1.26).) If markets are complete, in the sence...

8. CHAPTER 5 From EMH to Merely Efficient Learning
(pp. 131-152)

In Chapter 1, we derived the main prediction of asset-pricing theory: the market will set prices such that it expects excess returns on risky securities to be proportional to their covariance with aggregate risk. In Chapter 2, we saw how traditional empirical tests verify this theoretical prediction by comparing ex-post sample average excess returns and sample covariances. (The averages and covariances may be conditional.) The strategy implicitly assumes that (1) the market’s ex ante expectations are correct, and (2) returns and aggregate risk are stationary. Together, these two assumptions are referred to as the efficient markets hypothesis (EMH). In Chapter...

9. CHAPTER 6 Revisiting the Historical Record
(pp. 153-162)

Armed with new methodology, we are in a position to reconsider the historical field data. We are now able to test asset-pricing theory, not with EMH as the auxiliary assumption, but with ELM. That is, the market still must update its beliefs correctly (meaning that it uses Bayes’ law and the right likelihood function), but need not hold correct expectations at the beginning of each history in the dataset.

Unlike tests of asset-pricing models based on EMH, work on ELM is only in its initial stages. But the first results, some of which we will discuss here, appear promising. The...

10. REFERENCES
(pp. 163-168)
11. INDEX
(pp. 169-170)