Ambiguity Aversion and the Arbitrage Pricing Theory

Abstract

We consider a linear factor APT model and assume that agents are ambiguity averse with respect to payoffs of arbitrage portfolios. In contrast to the standard result, pricing errors need not converge to zero in the limit as the number of assets goes to infinity. Even in the case of exact factor structure, pricing errors may be nonzero and would not be eliminated by ambiguity averse arbitragers. This is because ambiguity about factor loadings and/or expected returns remains even in pure factor portfolios. Moreover, when there is ambiguity about factor sensitivities, strict arbitrage is impossible and pricing errors need not be bounded at all. Replacing a strict no-arbitrage requirement with one which imposes bounds on mean-standard deviation ratios for portfolio returns implies a bound on the pricing error which depends on the maximum admissible mean-standard deviation ratio, ambiguity about the coefficients in the return generating process (RGP), and factor volatilities. We also consider a case when agents can learn the RGP from the data using the framework of Epstein and Schneider (2007, REStud.). We show that pricing errors induced by ambiguity about RGP are quantitatively significant after accounting for the effects of learning. The results have empirical implications for tests of APT, market efficiency (anomalies) and pricing of idiosyncratic risk.