Efficient Frontiers using Estimated Parameters

The mean-variance model for portfolio selection requires estimates of many parameters. This paper investigates the effect of errors in parameter estimates on the results of mean-variance analysis. Using a small amount of historical data to estimate parameters exposes the model to estimation errors. However, using a long time horizon to estimate parameters increases the possibility of nonstationarity in the parameters. This paper investigates the tradeoff between estimation error and stationarity. A simulation study shows that the effects of estimation error can be surprisingly large. The magnitude of the errors increases with the number of securities in the analysis. Due to the error maximization property of mean-variance analysis, estimates of portfolio performance are optimistically biased predictors of actual portfolio performance. It is important for users of meanvariance analysis to recognize and correct for this phenomenon in order to develop more realistic expectations of the future performance of a portfolio. This paper suggests a method for adjusting for this bias. A statistical test is proposed to check for nonstationarity in historical data.