The asset pricing problem

A central problem of the analysis of private economies is determining the prices of commodities that are risky. Almost all work on this problem takes as its starting point the extension of general equilibrium theory to uncertainty, which is due to Arrow (1963–4) and Debreu (1959). However, the Arrow–Debreu model, even when modified to take account of imperfect and heterogeneous information, can do little more than state conditions for the existence of equilibrium and the compatibility of equilibrium with various measures of efficiency. Not surprisingly, it is difficult to think of any empirical work that tests or otherwise exposes this model to data. In sharp contrast, modern theories of asset pricing offer very sharp predictions about relative asset prices; these theories have spawned hundreds of empirical papers that purport to confirm or reject various aspects of the theory. In this chapter, I will offer a critical perspective on two leading theories of asset pricing: the capital asset pricing model [henceforth CAPM, which is due toTreynor (1961), Sharpe (1964), Lintner (1965), and Mossin (1966)] and the arbitrage pricing theory (APT), which is due to Steven Ross (1976). I shall largely focus on the theoretical properties of the models. Indeed, one major purpose is to demonstrate a simple analytical structure that makes developing and comparing the two theories straightforward. Since this is an empirical subject, much of what follows is directed toward empirical work.

The plan of this essay is as follows: In the remainder of this section I set out the asset pricing problem and establish some notation.