Robust parameter estimation is only one part of ensuring that the quantitative portfolio management process as a whole is reliable. It has been observed that portfolio allocation schemes are very sensitive to small changes in the inputs that go into the optimizer. In particular, a well-known study by Black and Litterman40 demonstrated that in the case of mean-variance optimization, small changes in the inputs for expected returns had a substantial impact on the portfolio composition. “Optimal” portfolios constructed under conditions of uncertainty can have extreme or nonintuitive weights for some stocks.
With advances in computational capabilities and new research in the area of optimization under uncertainty, practitioners in recent years have been able to incorporate considerations for uncertainty not only at the estimation, but also at the portfolio optimization stage. Methods for taking into consideration inaccuracies in the inputs to the portfolio optimization problem include simulation (resampling) and robust optimization. We explain portfolio resampling in this section, and robust portfolio optimization in the following section.
A logical approach to making portfolio allocation more robust with respect to changes in the input parameters is to generate different scenarios for the values these parameters can take, and find weights that remain stable for small changes in the input parameters. This method is referred to as portfolio resampling.41 To illustrate ...