Arbitrage Pricing Theory (APT), founded upon the work of Ross (1976,1977), aims to analyze the equilibrium relationship between assets’ risk and expected return just as the CAPM does. The two key CAPM assumptions of perfectly competitive and efficient markets and homogeneous expectations are maintained. Moreover, in line with the CAPM, the APT assumes that portfolios are sufficiently diversified, so that the contribution to the total portfolio risk of assets’ unique (unsystematic) risk is approximately zero.

The APT’s two main differences from the CAPM are: (a) the explicit modeling of several factors affecting assets’ actual and expected returns, as opposed to the CAPM’s focus on the market portfolio, and (b) the fact that the equilibrium relationship is only approximate and is derived based on a no-arbitrage assumption. The two are in fact interrelated, as market equilibrium in the CAPM rests on the observability and efficiency of the market portfolio.

With regard to the first difference, recall from lecture 3 that the CAPM was essentially derived from a single-index (single-factor) model, i.e. from a process generating asset returns which was only a function of returns unique to the asset (predictable and unpredictable) and returns on two factors, the market portfolio itself and the riskless asset, or the zero-beta portfolio. The sensitivity of the asset’s returns to the market’s was defined as the asset’s beta, measuring systematic (market) risk, while the unsystematic (unique) risk of the asset (portfolio) tended to zero through diversification.

APT can then be seen as a multi-index (multi-factor) model, i.e. one in which the
returns generating process of the portfolio is a function of several factors, generally
excluding the market portfolio. The factors are not specified a priori and their choice depends on the question at hand. Possible factors may include particular sector-specific influences, such as price-dividend ratios, as well as aggregate macroeconomic variables such as inflation and interest rate spreads. The covariance of each factor with the portfolio then leads to a natural extension of measuring risk by the beta attached to each factor. In the context of arbitrage pricing models the betas are often referred to as the factor loadings. The fact that identification of the market portfolio is not required is a big
advantage of the APT--however, its general specification is a mixed blessing because it
gives no guidance as to which factors should be considered. It is, consequently, easy to misprice assets by including the wrong (i.e. irrelevant) risk factors. Moreover, in principle one always gains in explanatory power by including more factors, even if they seem economically irrelevant.

The second difference between the CAPM and the APT has to do with the equilibrium notion. In contrast to the CAPM’s assumption of an efficient market portfolio which every investor desires to hold, the APT relies on the absence of free arbitrage opportunities. In particular, two portfolios with the same risk cannot offer different expected returns, because that would present an arbitrage opportunity with a net
investment of zero. An investor could then guarantee a riskless positive expected return
by short-selling one portfolio and holding an equal and opposite long position in the other. As such free arbitrage cannot persist, equilibrium in the APT specifies a linear
relationship between expected returns and the betas of the corresponding risk factors.

The short-selling assumption is crucial to the equilibrium, as it constitutes one side of the arbitrage portfolio. Equally important is the requirement that the proceeds from short-selling are immediately available. However, despite its shortcomings--especially the difficulties associated with empirical testing of its validity--the APT has caught on in financial practice as it allows for a more detailed and custom-made approach to portfolio risk management than the CAPM. This has become more relevant with the wide-spread use of derivative instruments and their particular types of risk.