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For example what if the manager were optimistic over

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average weights need not correspond to a client’s “neutral” weights. For example, what if the manager were optimistic over the entire year regarding long-term bonds? Her average weighting could reflect her optimism, and not a neutral position. c. Method III uses net purchases of bonds as a signal of bond manager optimism. But such net purchases can be motivated by withdrawals from or contributions to the fund rather than the manager’s decisions. (Note that this is an open- ended mutual fund.) Therefore, it is inappropriate to evaluate the manager based on whether net purchases turn out to be reliable bullish or bearish signals. 15. Treynor measure = (17 – 8)/1.1 = 8.182 16. Sharpe measure = (24 – 8)/18 = 0.888 17. a. Treynor measures Portfolio X: (10 – 6)/0.6 = 6.67 S&P 500: (12 – 6)/1.0 = 6.00 Sharpe measures Portfolio X: (10 – 6)/18 = 0.222 S&P 500: (12 – 6)/13 = 0.462 Portfolio X outperforms the market based on the Treynor measure, but underperforms based on the Sharpe measure. b. The two measures of performance are in conflict because they use different measures of risk. Portfolio X has less systematic risk than the market, as measured by its lower beta, but more total risk (volatility), as measured by its higher standard deviation. Therefore, the portfolio outperforms the market based on the Treynor measure but underperforms based on the Sharpe measure. 24-8
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18. Geometric average = (1.15 × 0.90) 1/2 – 1 = 0.0173 = 1.73% 19. Geometric average = (0.91 × 1.23 × 1.17) 1/3 – 1 = 0.0941 = 9.41% 20. Internal rate of return = 7.5% 21. d. 22. Time-weighted average return = (15% + 10%)/2 = 12.5% To compute dollar-weighted rate of return, cash flows are: CF 0 = $500,000 CF 1 = $500,000 CF 2 = ($500,000 × 1.15 × 1.10) + ($500,000 × 1.10) = $1,182,500 Dollar-weighted rate of return = 11.71% 23. b. 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.
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