sm26 - CHAPTER 26 EVALUATION OF PORTFOLIO PERFORMANCE...

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CHAPTER 26 EVALUATION OF PORTFOLIO PERFORMANCE Answers to Questions 1. The two major factors would be: (1) attempt to derive risk-adjusted returns that exceed a naive buy-and-hold policy and (2) completely diversify - i.e., eliminated all unsystematic risk from the portfolio. A portfolio manager can do one or both of two things to derive superior risk-adjusted returns. The first is to have superior timing regarding market cycles and adjust your portfolio accordingly. Alternatively, one can consistently select undervalued stocks. As long as you do not make major mistakes with the rest of the portfolio, these actions should result in superior risk-adjusted returns. 2. Treynor (1965) divided a fund’s excess return (return less risk-free rate) by its beta. For a fund not completely diversified, Treynor’s “T” value will understate risk and overstate performance. Sharpe (1966) divided a fund’s excess return by its standard deviation. Sharpe’s “S” value will produce evaluations very similar to Treynor’s for funds that are well diversified. Jensen (1968) measures performance as the difference between a fund’s actual and required returns. Since the latter return is based on the CAPM and a fund’s beta, Jensen makes the same implicit assumptions as Treynor - namely, that funds are completely diversified. The information ratio (IR) measures a portfolio’s average return in excess of that of a benchmark, divided by the standard deviation of this excess return. 3. For portfolios with R 2 values noticeably less than 1.0, it would make sense to compute both measures. Differences in the rankings generated by the two measures would suggest less-than-complete diversification by some funds - specifically, those that were ranked higher by Treynor than by Sharpe. 4. Jensen’s alpha ( α ) is found from the equation R jt – RFR t == α j + β j [R mt – RFR t ] +e jt . The a j indicates whether a manager has superior ( α j > 0) or inferior ( α j < 0) ability in market timing or stock selection, or both. As suggested above, Jensen defines superior (inferior) performance as a positive (negative) difference between a manager’s actual return and his CAPM-based required return. For poorly diversified funds, Jensen’s rankings would more closely resemble Treynor’s. For well-diversified funds, Jensen’s rankings would follow those of both Treynor and Sharpe. By replacing the CAPM with the APT, differences between funds’ actual and required returns (or “alphas”) could provide fresh evaluations of funds. 5. The Information Ratio (IR) is calculated by dividing the average return on the portfolio less a benchmark return by the standard deviation of the excess return. The IR can be viewed as a benefit-cost ratio in that the standard deviation of return can be viewed as a cost associated in the sense that it measures the unsystematic risk taken on by active 26 - 1
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management. Thus IR is a cost-benefit ratio that assesses the quality of the investor’s
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sm26 - CHAPTER 26 EVALUATION OF PORTFOLIO PERFORMANCE...

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