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Unformatted text preview: Chapter 18  Portfolio Performance Evaluation CHAPTER 18 PORTFOLIO PERFORMANCE EVALUATION 1. a. Possibly. Alpha alone does not determine which portfolio has a larger Sharpe ratio. Sharpe measure is the primary factor, since it tells us the real return per unit of risk. We only invest if the Sharpe measure is higher. The standard deviation of an investment and its correlation with the benchmark are also important. Thus positive alpha is not a sufficient condition for a managed portfolio to offer a higher Sharpe measure than the passive benchmark. b. Yes. It is possible for a positive alpha to exist, but the Sharpe measure decline. Thus, we would experience inferior performance. 2. Maybe. Provided the addition of funds creates an efficient frontier with the existing investments, and assuming the Sharpe measure increases, the answer is yes. Otherwise, no. 3. The Msquared is an equivalent representation of the Sharpe measure, with the added difference of providing a riskadjusted measure of performance that can be easily interpreted as a differential return relative to a benchmark. Thus, it provides the same information as the Sharpe measure. But in a different format. 4. Definitely, the FF model. Research shows that passive investments (e.g., a market index portfolio) will appear to have a zero alpha when evaluated using the multiindex model but not using the singleindex one. The nonzero alpha appears even in the absence of superior performance. Thus, the singleindex alpha can be misleading. 5. a. E(r) σ β Portfolio A 11% 10% 0.8 Portfolio B 14% 31% 1.5 Market index 12% 20% 1.0 Riskfree asset 6% 0% 0.0 The alphas for the two portfolios are: α A = 11% – [6% + 0.8(12% – 6%)] = 0.2% α B = 14% – [6% + 1.5(12% – 6%)] = –1.0% Ideally, you would want to take a long position in Portfolio A and a short position in Portfolio B. 181 Chapter 18  Portfolio Performance Evaluation b. If you hold only one of the two portfolios, then the Sharpe measure is the appropriate criterion: S A = 5 . 10 6 11 = S B = 26 . 31 6 14 = Therefore, using the Sharpe criterion, Portfolio A is preferred. 6. We first distinguish between timing ability and selection ability. The intercept of the scatter diagram is a measure of stock selection ability. If the manager tends to have a positive excess return even when the market’s performance is merely “neutral” (i.e., the market has zero excess return) then we conclude that the manager has, on average, made good stock picks. In other words, stock selection must be the source of the positive excess returns. Timing ability is indicated by the curvature of the plotted line. Lines that become steeper as you move to the right of the graph show good timing ability. The steeper slope shows that the manager maintained higher portfolio sensitivity to market swings (i.e., a higher beta) in periods when the market performed well. This ability to choose more marketsensitive securities in anticipation of market upturns is the essence of...
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 Spring '11
 UNKNOWN
 Modern portfolio theory, sharpe ratio, Jensen's alpha, Portfolio Performance Evaluation

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