Consider the Treynor-Black model.The alpha of an active portfolio is 1%.The expected return on the market index is 16%.The variance of the return on the market portfolio is 4%.The nonsystematic variance of the active portfolio is 1%.The risk-free rate of return is 8%.The beta of the active portfolio is 1.05.The optimal proportion to invest in the active portfolio is __________.
A)48.7%
B)50.0%
C)51.3%
D)100.0%
E)none of the above

Question

Quizplus · Accepted Answer

The optimal proportion to invest in the active portfolio is calculated using the formula: (alpha / nonsystematic variance) / [(expected market return - risk-free rate) / market variance]. Substituting the given values: (0.01 / 0.01) / [(0.16 - 0.08) / 0.04] = 1 / 2 = 0.5 or 50%. However, since the beta of the active portfolio is 1.05, the proportion is adjusted to 51.3%.

Consider the Treynor-Black Model