Larger Stocks Earn Higher Returns !

Controlling for idiosyncratic volatility, large stocks earn higher returns than small stocks. Idiosyncratic volatility is positively related to return, but negatively related to size. Failure to control for idiosyncratic volatility generates a downward omitted variable bias, leading to the widely documented negative size-return relation. We explain the two contrasting sizereturn relations in a general equilibrium model that incorporates three empirical regularities: individual investors are under-diversified; small stocks have higher idiosyncratic volatilities; large stocks, relative to their size, have fewer investors. To clear the markets, large stocks offer higher expected returns to induce their relatively fewer investors to allocate more wealth.