Multifactor Asset Pricing Models

As discussed in Chapter 2 , early empirical evidence on the CAPM by Sharpe (Journal of Finance 19: 425–442, 1964) and others using the market model to perform tests using U.S. stock returns was disappointing. The Security Market Line (SML) relating market beta risk to average stock returns was flatter with a higher intercept (or alpha) than expected. In an attempt to fix the problem, Black (Journal of Business 45:444–454, 1972) proposed the zero-beta CAPM with the zero-beta portfolio return replacing the riskless rate in the CAPM. Merton (Econometrica 41:867–887, 1973) advanced the intertemporal CAPM (ICAPM) to allow multiple periods and multiple state variables as potential asset pricing factors. Extending Merton’s pathbreaking work, a number of CAPM variants appeared in the literature that sought to enrich the model with real world assumptions and variables. Departing from the general equilibrium CAPM models, Ross (Journal of Economic Theory 13:341–360, 1976) developed the arbitrage pricing theory (APT). A very different model with no market factor, the APT simply said that arbitragers price assets using multiple long/short, zero-investment portfolios. The upshot was the later creation of multifactor models by Fama and French (Journal of Finance 47:427–465, 1992; Journal of Financial Economics 33:3–56, 1993). Supplanting the CAPM, these authors: (1) presented evidence that the CAPM did not work; and proposed the three-factor model that augments the market factor with size and value factors. These new factors are long/short, zero-investment portfolio returns that have become known as multifactors. The success of the three-factor model in terms of better fitting stock return data was impressive. Indeed, it was so impressive that other researchers began to propose a long list of multifactors. A new problem in asset pricing arose. With so many factors, Cochrane (Journal of Finance 56:1047–1108, 2011) humorously observed that a “factor zoo” existed. Which multifactors should be used in asset pricing models? What is the theoretical justification for all these factors? Asset pricing was becoming bogged down in a quagmire of factors and their myriad risks. The promising simple risk concepts of total risk by Markowitz (Journal of Finance 7:77–91, 1952; Portfolio selection: Efficient diversification of investments. Wiley, New York, NY, 1959) and beta risk by Sharpe had become complicated by a growing number of long/short multifactors. Recently, to deal with this problem, some researchers have begun using machine learning models to let the data tell us what the factors are, as opposed to researcher judgment and discretion. In this chapter, we review the APT, multifactor models, and machine learning models. At the time of this writing, multifactor models were very popular in academic research and investment practice. But as the universe of multifactors expands, it is becoming increasingly unclear how to implement them in the real world.