Consider the Treynor-Black model.The alpha of an active portfolio is 2%.The expected return on the market index is 12%.The variance of the return on the market portfolio is 4%.The nonsystematic variance of the active portfolio is 2%.The risk-free rate of return is 3%.The beta of the active portfolio is 1.15.The optimal proportion to invest in the active portfolio is __________.
A)48.7%
B)98.3%
C)47.6%
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 Treynor-Black model formula: (alpha / nonsystematic variance) / [(expected market return - risk-free rate) / market variance]. Substituting the given values: (0.02 / 0.02) / [(0.12 - 0.03) / 0.04] = 1 / 2.25 = 0.476 or 47.6%.

Consider the Treynor-Black Model