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Abstract:
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The actual performance of mean-variance tracking-error-optimized portfolios is inferior to the anticipated performance when the optimization is performed in the presence of estimation error, due to systematic bias that occurs when the optimization procedure exploits the noise in the data. Given a universe of n assets, a benchmark portfolio weight, and a target mean, we wish to find the portfolio with this target mean that minimizes the variance of its deviations from the benchmark. When the asset mean vector and covariance matrix are known, the optimal portfolio can be determined. When estimated means and covariances are used instead, the resulting portfolio will achieve neither the target mean nor the anticipated error variance. We use matrix Taylor series expansions with respect to the estimation error in order to derive second-order approximations to these systematic biases.
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