Forecast Dispersion and the Cross-section of Expected Returns

Recent work by Diether, Malloy, and Scherbina (2002) has established a negative relationship between stock returns and the dispersion of analysts’ earnings forecasts. I offer a simple explanation for this phenomenon based on the interpretation of dispersion as a proxy for unpriced information risk arising when asset values are unobservable. The relationship then follows from a general options-pricing result: For a levered firm, expected returns should always decrease with the level of idiosyncratic asset risk. This story is formalized with a straightforward model. Reasonable parameter values produce large effects, and the theory’s main empirical prediction is supported in cross-sectional tests. In an intriguing recent article, Diether, Malloy, and Scherbina (2002) (hereafter DMS) document a new anomaly in the cross-section of returns: Firms with more uncertain earnings (as measured by the dispersion of analysts’ forecasts) do worse. The finding is important in that it directly links asset returns with a quantitative measure of an economic primitive – information about fundamentals – but the sign of the relationship is apparently wrong. Rather than discounting uncertainty, investors appear to be paying a premium for it. This would seem to pose a formidable challenge to usual notions of efficiently functioning markets. This article argues that the challenge can be met. In fact, a simple, standard asset pricing model implies the DMS effect even when there is no cross-sectional relationship between dispersion of beliefs and fundamental risk. The logic relies on two elements. First, when fundamentals are unobservable, dispersion may proxy for idiosyncratic parameter risk. Second, for a levered firm, expected equity returns will in general decrease with the level of idiosyncratic asset risk due to convexity. I formalize this in a straightforward way. The story has some direct and distinguishing testable implications, which I take to the data. The empirical evidence is remarkably supportive. The theory offered here contrasts sharply with the explanation suggested by DMS. They view the negative relationship between forecast dispersion and subsequent returns as supportive of a story in which costly arbitrage leads to mispricing when agents have differing beliefs. With short-sales constraints, the argument goes, the most optimistic investors will bid prices up too high (assuming they don’t adjust for the winner’s curse). Hence the more views differ, the more stocks may become overpriced. This intuition may well be valid. Short-sales constraints, heterogeneous information, and investor biases are certainly important features of real markets that undoubtedly affect price formation. However, this paper demonstrates that they need not be necessary to explain the return puzzle.