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 + βm) – 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.
