Portfolio Construction by Mitigating Error Amplification: The Bounded-Noise Portfolio

We address the problem of poor portfolio performance when a minimum-variance portfolio is constructed using the sample estimates. Estimation errors are mostly blamed for the poor portfolio performance. However, we argue that even small unbiased estimation errors can lead to significantly bad performance because the optimization step amplifies errors, in a nonsymmetric way. Instead of trying to independently improve the estimation step or fix the optimization step for robustness, we disentangle the well-estimated aspects from the poorly estimated aspects of the covariance matrix. By using a single parameter held constant over all data sets and time periods, our method achieves excellent performance both empirically and in the simulation. We also show how to use information from the sample mean to construct mean-variance portfolios that have higher out-of-sample Sharpe ratios.