A new critique of the traditional method for empirically estimating the returns associated with strategies of stock investment: impact of fixing the investment horizon
AbstractMuch of the empirical literature on behavioral finance involves analyzing historical databases of stock prices. The null hypothesis in these analyses is that risk-adjusted returns are unpredictable, and the alternative hypothesis is that risk-adjusted returns are predictable in a way that is consistent with an insight from behavioral finance. The value investment hypothesis is such an insight, and it predicts that regression toward the mean will cause the returns of poorly performing stocks to be better than average. Empirical tests using historical databases typically involve selecting a portfolio of stocks that satisfy a certain criterion (e.g., low price-earnings ratio) at a given time, holding the stocks for a fixed period such as a year, selling the stocks, calculating the return, and then repeating the process.We performed a simulation of the returns of a mean-reverting stock that might be purchased by a value investor. Mean-reverting stocks tend to have less business risk than average and also exhibit lower volatility in their prices and thus satisfy two operational definitions of having relatively low investment risk. For simplicity, the return on the mean-reverting stock was assumed to be 0, and performing the simulation in the usual way (i.e., with pre-specified dates of purchase and sale) yielded an annual return of 0. However, when the holding time was allowed to vary stochastically -- that is, by holding the stock for a random period of time until a certain absolute level of return is achieved rather than in the usual way – the return was positive, and perhaps would even exceed the returns of stocks with higher risk. Thus, the usual procedure underestimates the returns of stocks whose prices regress toward their means. Moreover this simulation, in the limited technical sense described above, provides a counter-example to the usual relationship between risk and return.The presentation is of particular interest to economists and investors who study stock market returns, and is accessible to readers with an intermediate level of statistical knowledge.