•Survivor bias skews the shape of the distribution curve. ii. The statement is incorrect. Valid benchmarks are unambiguous and able to be replicated. The median manager benchmark, however, is ambiguous because the weights of the individual securities in the benchmark are not known. The portfolio’s composition cannot be known before the conclusion of a measurement period because identification as a median manager can occur only after performance is measured. Valid benchmarks are also investable. The median manager benchmark is not investable. That is, a manager using a median manager benchmark cannot forego active management and, taking a passive/indexed approach, simply hold the benchmark. This is a result of the fact that the weights of individual securities in the benchmark are not known. iii. The statement is correct. The median manager benchmark may be inappropriate because the median manager universe encompasses many investment styles and, therefore, may not be consistent with a given manager’s style. 27. a. Sharpe ratio = (rP– rf)/σPWilliamson Capital: Sharpe ratio = (22.1% −5.0%)/16.8% = 1.02 Joyner Asset Management: Sharpe ratio = (24.2% −5.0%)/20.2% = 0.95 Treynor measure = (rP– rf )/βPWilliamson Capital: Treynor measure = (22.1% −5.0%)/1.2 = 14.25 Joyner Asset Management: Treynor measure = (24.2% −5.0%)/0.8 = 24.00 b.The difference in the rankings of Williamson and Joyner results directly from the difference in diversification of the portfolios. Joyner has a higher Treynor measure (24.00) and a lower Sharpe ratio (0.95) than does Williamson (14.25 and 1.202, respectively), so Joyner must be less diversified than Williamson. The Treynor measure indicates that Joyner has a higher return per unit of systematic risk than does Williamson, while the Sharpe ratio indicates that Joyner has a lower return per unit of total risk than does Williamson. 24-11
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