24 a 25 a each of these benchmarks has several

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24. a. 25. a. Each of these benchmarks has several deficiencies, as described below. Market index: A market index may exhibit survivorship bias. Firms that have gone out of business are removed from the index, resulting in a performance measure that overstates actual performance had the failed firms been included. A market index may exhibit double counting that arises because of companies owning other companies and both being represented in the index. It is often difficult to exactly and continually replicate the holdings in the market index without incurring substantial trading costs. The chosen index may not be an appropriate proxy for the management style of the managers. The chosen index may not represent the entire universe of securities. For example, the S&P 500 Index represents 65% to 70% of U.S. equity market capitalization. The chosen index (e.g., the S&P 500) may have a large capitalization bias. The chosen index may not be investable. There may be securities in the index that cannot be held in the portfolio. 24-9
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Benchmark normal portfolio: This is the most difficult performance measurement method to develop and calculate. The normal portfolio must be continually updated, requiring substantial resources. 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
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24 a 25 a Each of these benchmarks has several deficiencies...

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