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LOS c: Describe how an analyst’s accuracy in forecasting alphas can be measured and how estimates of forecasting can be incorporated into the Treynor-Black approach. ffice ffice" />
Q1. Collette Gallant, CFA, employs the capital asset pricing model (CAPM) to determine the required returns for stocks. Gallant works for Trey-Black Inc. (TBI) which uses the Treynor-Black model for portfolio optimization. Gallant is deciding whether to include stock ABZ in the TBI’s actively managed portfolio. She forecasts that the ABZ stock return will be 15% next year. TBI provides Gallant with the following information.
- Expected return on the S&
 500 stock market index = 15%.
- 1-year Treasury bill rate = 5%.
- ABZ stock beta = 1.25.
TBI determines that Gallant’s forecast ability has been very poor. TBI also finds that the average alpha across stocks in their actively managed portfolio equals 1%. Determine if Trey-Black’s allocation to ABZ in its actively managed portfolio should be an above or below average, long or short position.
Magnitude Position
A) Below average Long
B) Above average Short
C) Below average Short
Correct answer is C)
According to the Treynor-Black model, the actively-managed portfolio takes long positions in positive alpha stocks and short positions in negative alpha stocks. The alpha is defined as the difference between the analyst’s forecast return for the stock and its required return. As stated in the question, the required return for stock ABZ is calculated using the CAPM:
E(R) = RF + β[E(Rm) – RF] = 0.05 + 1.25[0.15 – 0.05] = 0.175 = 17.5%.
Gallant’s forecast return (15%) is less than the required return (17.5%):
alpha = 0.15 – 0.175 = ?0.025 = ?2.5%.
Therefore, Gallant’s predicted alpha is much higher in absolute magnitude than the average alpha (1%), which would suggest an above-average short position if Gallant’s forecasting ability is reliable. However, TBI has determined that Gallant’s forecast ability is poor. Therefore, her forecast alpha will be adjusted severely toward zero to account for her poor forecast ability. The end result is that only a small short position will be taken in ABZ.
Q2. According to the Treynor-Black portfolio optimization model, assets are allocated to both a passively managed portfolio and to an actively managed portfolio. Which of the following is most likely to lead to a larger allocation to the actively managed portfolio?
A) Unsystematic risk.
B) Short sales prohibition.
C) Market inefficiencies.
Correct answer is C)
The Treynor-Black model combines modern portfolio theory and market inefficiency. Money is allocated to a passively managed portfolio and to an actively managed portfolio. Allocation to the actively managed portfolio increases as assets become more mispriced (market inefficiencies). The remaining choices lead to smaller allocation to the actively managed portfolio. Short sale prohibitions cause the active portfolio alpha to fall. The Treynor-Black model allocates smaller percentages to assets with high unsystematic risk.
Q3. Frederick Kurzonkowski, CFA, employs the Treynor-Black portfolio optimization model at his firm, TBP, where he serves as portfolio manager. TBP recently decided against holding short positions in their portfolios. Kurzonkowski is asked to determine the most likely result of the short-sale prohibition on the weights allocated to the long positions in the active portfolio, and to the alpha on the active portfolio. Kurzonkowski should make the following predictions about the effects of the prohibition on short sales on the actively managed portfolio:
Allocation to long positions Alpha
A) Decreases Decreases
B) Increases Decreases
C) Decreases Increases
Correct answer is A)
The prohibition on short sales removes the negative weights within the actively managed portfolio, along with the leverage that the short positions offer to the long positions. When short sales are allowed, more than 100% can be allocated to the long positions. When short sales are not allowed, only 100% can be allocated to the long positions. Therefore, the prohibition on short sales causes the weights to the long positions within the actively managed portfolio to fall. The alpha also is expected to fall: smaller weight is now assigned to positive alpha stocks, and there are no negative weights to assign to negative alpha stocks.
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发表于 2009-4-2 14:13
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