Measuring Investors' Historical Returns: Hindsight Bias in Dollar-Weighted Returns

Abstract

A growing number of studies use dollar-weighted returns as evidence that consistently bad timing substantially reduces investor returns, and that consequently the equity risk premium must be considerably lower than previously thought. These studies measure the impact of bad timing as the difference between the geometric mean return (corresponding to a buy-and-hold strategy) and the dollar-weighted return. However, the present paper demonstrates that this differential combines two distinct effects: The correlation of investor cashflows with (i) future asset returns, and (ii) past asset returns. Both correlations tend to alter the dollar-weighted return, but only the first affects investors’ expected wealth. The second generates a hindsight bias. This paper also derives a method which separates these two effects. The results show that the great majority of the return differential for mainstream US equities has been due to hindsight bias, and very little due to bad investor timing. Dollar-weighted returns have been low because aggregate investment flows reflect past returns rather than future returns, and these low returns should not lead us to adopt correspondingly low estimates of the risk premium. The decomposition method which is derived here also has many applications in other fields where dollar-weighted returns are used, such as project finance and investment management.