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

This paper focuses on the problem of poor portfolio performance when a minimum-variance portfolio is constructed using the sample estimates. This issue is well documented in the literature and has remained in the spotlight ever since Markowitz (1952). Estimation errors are mostly blamed for this problem. However, we argue that even small unbiased estimation errors can lead to significantly bad performance because the optimization step amplifies errors, that too in a non-symmetric 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 and handle them differently and appropriately. By using a single parameter held constant over all datasets and time periods, our method achieves excellent performance in both simulation and empirical data. Finally, we show how to use information from the sample mean to construct mean-variance portfolios, which we demonstrate have higher out-of-sample Sharpe ratios.