Consultants and clients are concerned that managers

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Consultants and clients are concerned that managers who are involved in developing and calculating their benchmark portfolio may produce an easily-beaten normal portfolio, making their performance appear better than it actually is. Median of the manager universe: It can be difficult to identify a universe of managers appropriate for the investment style of the plan’s managers. Selection of a manager universe for comparison involves some, perhaps much, subjective judgement. Comparison with a manager universe does not take into account the risk taken in the portfolio. The median of a manager universe does not represent an “investable” portfolio; that is, a portfolio manager may not be able to invest in the median manager portfolio. Such a benchmark may be ambiguous. The names and weights of the securities constituting the benchmark are not clearly delineated. The benchmark is not constructed prior to the start of an evaluation period; it is not specified in advance. A manager universe may exhibit survivorship bias; managers who have gone out of business are removed from the universe, resulting in a performance measure that overstates the actual performance had those managers been included. b. i. The Sharpe ratio is calculated by dividing the portfolio risk premium (i.e., actual portfolio return minus the risk-free return) by the portfolio standard deviation: Sharpe ratio = (r P – r f )/ σ P The Treynor measure is calculated by dividing the portfolio risk premium (i.e., actual portfolio return minus the risk-free return) by the portfolio beta: Treynor measure = (r P – r f )/ β P Jensen’s alpha is calculated by subtracting the market risk premium, adjusted for risk by the portfolio’s beta, from the actual portfolio excess return (risk premium). It can be described as the difference in return earned by the portfolio compared to the return implied by the Capital Asset Pricing Model or Security Market Line: α P = r P –[r f + β P (r M r f )] 24-10
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ii. The Sharpe ratio assumes that the relevant risk is total risk, and it measures excess return per unit of total risk. The Treynor measure assumes that the relevant risk is systematic risk, and it measures excess return per unit of systematic risk. Jensen’s alpha assumes that the relevant risk is systematic risk, and it measures excess return at a given level of systematic risk. 26. i. The statement is incorrect. Valid benchmarks are unbiased. Median manager benchmarks, however, are subject to significant survivorship bias, which results in several drawbacks, including the following: The performance of median manager benchmarks is biased upwards. The upward bias increases with time. Survivor bias introduces uncertainty with regard to manager rankings.
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