Surveys And Crossover – Unrealistic Expectations: The Futility of Precisely Estimating a Stock’s Expected Return
Vol. 22, No. 1, 2024
Sanjiv R. Das and Daniel Ostrov
…dedicated to the memory of Mark S. Joshi, who worked to make results like these better known
We reprise the result that even underthe best circumstances, it is impossible to use observed return data for a stock to determine its expected return with any useful precision in a reasonable time frame. This is because the sample mean of returns, which is the best estimator for the expected return, has a large standard error. More specifically, the formula for this standard error is σ/√T, where σ is the stock’s annual volatility and T is the number of years over which the returns are sampled. We note in particular that this standard error formula is not reduced by increasing the frequency of sampling the returns within the given time frame T.