ریسک ویژه و سطح مقطع بازده سهام: مرتون (1987) مطابق با میلر (1977)

Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predicts that idiosyncratic risk should be priced when investors hold sub-optimally diversified portfolios, and cross-sectional stock returns should be positively related to their idiosyncratic risk. However, the literature generally finds a negative relationship between returns and idiosyncratic risk, which is more consistent with Miller's [1977. Risk, uncertainty, and divergence of opinion. Journal of Finance 32, 1151–1168] analysis of asset pricing under short-sale constraints. We examine the cross-sectional effects of idiosyncratic risk while explicitly recognizing the confounding effects that dispersion of beliefs and short-sale constraints produce in the Merton framework. We find strong support for Merton's [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] model among stocks that have low levels of investor recognition and for which short selling is limited. For these stocks, the relation between idiosyncratic risk and expected returns is positive, as predicted by Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510].

Merton (1987) presents an “IRH” which extends the standard CAPM model under the assumption that investors only hold securities whose risk and returns characteristics they are familiar with. Because these investors hold under-diversified portfolios, they demand compensation for idiosyncratic risk. Accordingly, ex post returns are positively related to firms’ idiosyncratic risk. Direct tests of Merton's predicted positive correlation between idiosyncratic risk and returns are relatively rare. Those which have been undertaken have concluded that stocks with high idiosyncratic volatility have “abysmally low average returns”, an opposite conclusion to the implications of Merton (1987). Previous studies have noted that the low returns to idiosyncratic risk seem to be more consistent with the predictions of Miller (1977). Miller theorized that short-sale constraints will result in poor returns for stocks with high dispersion of investor opinion, an attribute known to be positively correlated with trading volatility. We hypothesize that these previous tests of Merton (1987) fail to find that idiosyncratic risk is priced for two reasons. First, Merton's hypothesis applies only to stocks with low visibility (those stocks not “recognized” by investors). Prior studies have not explicitly controlled for visibility. Second, firms with high levels of short-selling are likely either to have high dispersion of investor opinion such that the conditions for Miller's hypothesized overvaluation are present, or to have negative information that is not yet incorporated in prices. Our tests control for both visibility and short-selling activities. Using low institutional holdings as a proxy for low visibility, we examine firms that also have relatively low short-sales activity. These firms are unlikely to possess Miller's requisite dispersion of beliefs and are also unlikely to have negative information that is not immediately priced. Using the calendar-time portfolio approach, we compare the returns of high volatility firms against firms with low volatility. We find idiosyncratic risk is priced for the least-shorted half of stocks belonging to the lowest three quartiles of IO. In other words, idiosyncratic risk appears to be priced for an economically significant fraction of U.S. stocks. These findings are robust to alternative asset pricing model specifications, alternative portfolio weighting methods, alternative rebalancing frequencies, and alternative investment horizons. Each of these findings is qualitatively replicated when we consider the lack of sell-side analyst coverage, rather than low IO, as the indicator of low visibility. For robustness, we also conduct a set of cross-sectional Fama–MacBeth regressions of monthly portfolio returns using alternative visibility metrics. Consistent with the calendar-time approach, the Fama–MacBeth regressions reveal that idiosyncratic risk is priced for low visibility firms that are not subject to high levels of short selling, again with high levels of statistical significance. The regression results hold whether visibility is proxied using IO or the lack of analyst coverage. Thus, except where firms possess high visibility (inconsistent with Merton's assumptions) or where firms have high short selling (consistent with Miller's requisite dispersion of beliefs), we find that idiosyncratic risk is priced in accordance with the IRH forwarded by Merton (1987).