Consider the Treynor-Black Model

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 these