Consider the Treynor-Black model. The alpha of an active portfolio is 1%. The expected return on the market index is 11%. The variance of return on the market portfolio is 0.06. The nonsystematic variance of the active portfolio is 0.02. The risk-free rate of return is 4%. The beta of the active portfolio is 1.1. The optimal proportion to invest in the active portfolio is
A) 45%.
B) 25%.
C) 50%.
D) 100%.

Question

Quizplus · Accepted Answer

The optimal proportion to invest in the active portfolio is calculated using the formula: (alpha / nonsystematic variance) / (market variance + (alpha / nonsystematic variance)). Substituting the given values: (0.01 / 0.02) / (0.06 + (0.01 / 0.02)) = 0.5 / 1.1 = 0.4545 or approximately 45%.

Consider the Treynor-Black Model