Size and Return: A New Perspective - FU, Fangjian (Institutional Knowledge at Singapore Management University, 2012)
We document robust empirical evidence that, after controlling for idiosyncratic volatility, large stocks earn significantly higher returns than small stocks. Our empirical results indicate that idiosyncratic volatility is positively related to return, but negatively related to size. Hence, failure to control for idiosyncratic volatility generates a downward omitted variable bias and leads to the widely documented negative relation between size and return. We explain the two contrasting size-return relations, with and without the control for idiosyncratic volatility, in a parsimonious equilibrium model that incorporates three empirical regularities: some individual investors are under-diversified; small stocks have higher idiosyncratic volatilities than large stocks; and large stocks, relative to their size, are held by fewer investors than small stocks. Investors follow mean-variance optimization to allocate wealth among their stocks. To clear the markets, large stocks have to o er higher expected returns to induce their relatively smaller number of investors to allocate more of their wealth. This positive size-return relation is masked because small firms have higher idiosyncratic volatilities and therefore earn higher returns as a result of investor under-diversification.