Historical stock market returns are predictable using the average level of “idiosyncratic volatility,” which is the volatility of the return of a stock that is not correlated with the overall market return. Numerous studies have shown that at times in the past when idiosyncratic volatility was high, the market return over the subsequent months was higher than average.
This pattern might suggest abnormal profits can be made trading stocks, weighting stocks more heavily in an investment portfolio as idiosyncratic volatility rises. None of the existing studies adequately explained why this might be possible, at least in the eyes of my colleague Miguel A. Ferreira of the Nova School of Business and Economics and myself, and we wanted to better understand the phenomenon.
We first studied whether the relationship between volatility and return was evident in big and small stocks, which are stocks of firms with big and small values of total market equity. We found that SMALL is special, where SMALL is the average idiosyncratic volatility of small stocks as a group. The idiosyncratic volatility of big stocks does not forecast future market returns, while SMALL does have predictive power for stocks of all size groups, big and small. In other words, an investor can expect to earn higher returns in the stock market generally at times when SMALL is high. Thus, a proper explanation of the general phenomenon must also explain why the predictability is located in the idiosyncratic volatilities of small companies.
Entrepreneurs and other small business owners as a group hold a significant proportion of the value of U.S. stocks. These individuals, if they own successful businesses, often choose to diversify their wealth, investing a part of their profits into financial assets, including stocks. We show that stocks of small public firms are more highly correlated with the values of private firms than those of big firms. In addition, the average level of risk of small public firms, which is represented by SMALL in our study, tends to rise and fall with the level of risk in private firms. Those who face entrepreneurial risk, i.e., those whose livelihoods are tied to ownership of private firms, should avoid holding equity in public firms that tend to exhibit the same type of risk. Therefore, entrepreneurs would do well to tilt their investment portfolios toward big stocks and away from small stocks.
Other investors, who do not face this same risk in their human capital, can earn higher returns than they might otherwise by tilting their portfolios in the opposite direction, taking positions in the stock market that private business owners tend to avoid. Portfolios constructed in this fashion take on idiosyncratic risk, because they do not hold the market portfolio of stocks. As a consequence, investors in these portfolios will bear a large share of the entrepreneurial risk that is inherently a part of the stock market as a whole, and which private business owners are wise to avoid. These investors should expect their stock portfolio value to fall as SMALL goes up, and rise as SMALL goes down.
For more on this topic, see our paper “Idiosyncratic Volatility of Small Public Firms and Entrepreneurial Risk” in the Quarterly Journal of Finance.
David Brown is Harold G. and Margaret W. Laun Professorship Fund in Finance, and professor of finance at the Wisconsin School of Business.