Portfolio Optimization With Noisy Covariance Matrices
Vol. 17 No.1, 2019
Jose Menchero and Lei Ji
In this paper, we explore the effect of sampling error in the asset covariance matrix when constructing portfolios using mean–variance optimization.We show that as the covariance matrix becomes increasingly ill-conditioned (i.e., “noisy”), optimized portfolios exhibit certain undesirable characteristics such as under-prediction of risk, increased out-of sample volatility, inefficient risk allocation, and increased leverage and turnover. We explain these results by utilizing the concept of alpha portfolios (which explain expected returns) and hedge portfolios (which serve to reduce risk). We show that noise in the covariance matrix leads to systematic biases in the volatility and correlation forecasts of these portfolios, which in turn explains the adverse effects cited above.