Is the correct answer is B or C ? please add comments
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&P500 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
Your answer: B was incorrect. The correct answer was C) Below average Short
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® = RF + _β_m) – 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.