The Model and Some Fundamentals

Abstract

One of the main issues in finance is to provide models which explain how agents make portfolio decisions. Moreover, by means of these models the equilibrium consequences in markets where every agent follows such decision rules can be analyzed. The Capital Asset Pricing Model (CAPM) is the most familiar of these models. It is a rich source of intuition but also the basis for many practical financial decisions. Being built around the means and covariances of the security payoffs, it has its roots in Markowitz [1952] description of the mean-variance portfolio selection problem. In its equilibrium form, the CAPM goes back to Sharpe [1964], Lintner [1965] and Mossin [1966]. The perhaps most important feature of the CAPM is that, given an assumption of “variance-aversion” on agents’ preferences, it can be shown that, for every announced price system, all agents will be satisfied with holding shares of the same two funds, the riskless asset and a price dependent portfolio [Tobin, 1958]. The latter portfolio is usually called “pricing portfolio” [Duffie, 19881 At equilibrium, the pricing portfolio can be replaced by the market portfolio, i.e. the collection of all assets available in the economy. Thus at a CAPM equilibrium all agents only hold shares in the riskless portfolio and the market portfolio. From this Mutual Fund Property a simple and linear pricing formula, which is expressed in terms of a proportionality factor—called beta coefficient—and rates of returns, can be deduced. This pricing relation says that the excess return of every asset is proportional to the excess return of the market portfolio, where the proportionality factor—the beta coefficient—is given by the covariance of the asset’s payoff and the market portfolio’s payoff per standard deviation of the market portfolio’s payoff.

Mean-variance analysis and the Sharpe-Lintner-Mossin CAPM are widely viewed as the major contributions of academic research in the post-war era.

—Jagannathan and Wang [1996]