Why Is It So Hard to Estimate Expected Returns?

Abstract: A key part of experiment design is determining how much data to collect. When the data comes in the form of a time series, the sample size can be expressed by the count N of the observations and the duration T of the historical period. For forecasting the drift of an asset price process with continuous sample paths it turns out the duration is key. I generalize a result by Merton and demonstrate that the standard error of any unbiased estimator of the price of risk is bounded below by 1/\sqrt T, which I believe this is higher than many practitioners realize.

Event Topic

Professional Mathematical Finance