Idiosyncratic RiskMatters

This paper takes a new look at the predictability of stock market returns with risk measures.We ¢nd a signi¢cant positive relation between average stock variance (largely idiosyncratic) and the return on the market. In contrast, the variance of the market has no forecasting power for the market return. These relations persist after we control for macroeconomic variables known to forecast the stock market. The evidence is consistent with models of time-varying risk premia based on background risk and investor heterogeneity. Alternatively, our ¢ndings can be justi¢ed by the option value of equity in the capital structure of the ¢rms. MOSTASSETPRICINGMODELS, starting withMerton’s (1973) ICAPM, suggest a positive relation between risk and return for the aggregate stock market.There is a long empirical literature that has tried to establish the existence of such a tradeo¡ between risk and return for stock market indices.1 Unfortunately, the results have been inconclusive. Often the relation between risk and return has been found insigni¢cant, and sometimes even negative. The innovation in this paper is to look at average stock risk in addition to market risk.We measure average stock risk in each month similarly to Campbell et al. (2001; hereafter CLMX), as the cross-sectional average of the variances of all the stocks traded in that month.We then run predictive regressions of market returns on this variance measure as well as the variance of the market. Consis-tent with some previous studies, we ¢nd that market variance has no forecasting power for the market return. However, we do ¢nd a signi¢cant positive relation between average stock variance and the return on the market