ABSTRACT
Chapter 8 explores “overfitting” in the portfolio setting. The techniques of the two previous chapters support inference on the signal-noise ratio of the population Markowitz portfolio. However, due to sample error, the sample Markowitz portfolio will have lower signal-noise ratio. The distribution of this “haircut” off of the maximal signal-noise ratio is approximated. It is shown how to attribute portfolio error separately to the estimates of the mean and covariance. A fundamental upper bound on the expected signal-noise ratio of sample portfolios is given. This bound is expanded to the conditional expectation model. Inference on the achieved signal-noise ratio of the sample Markowitz portfolio is then considered, via the “Sharpe ratio information criterion”, as well as an confidence interval, which is also applied to constrained problems. An empirical study compares different measures for strategy selection.
