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Investment managers are often hired to produce positive return performance over a benchmark index while keeping tracking error volatility to a minimum. This article provides the exact composition of the particular portfolio for the manager who faithfully adheres to this strategy. Usually the selected portfolio will not be total return mean/variance efficient. It will have a beta greater than 1.0 and cannot dominate the benchmark by having a lower total volatility and a higher expected return. Constraining the beta can improve the managed portfolio.
Richard Roll (Fri,) studied this question.