You would like to combine a risky share with a beta of 1.5 with Treasury bills in such a way that the risk level of the portfolio is equivalent to the risk level of the overall market.What percentage of the
Portfolio should be invested in Treasury bills?
A)25%
B)33%
C)50%
D)67%
E)75%

Question

Quizplus · Accepted Answer

To achieve a risk level equivalent to the market, the portfolio needs a beta of 1. The risky share has a beta of 1.5, so to lower the overall beta to 1, we need to combine it with an asset that has a beta of 0 (Treasury bills). Let x be the proportion of the portfolio in Treasury bills and (1-x) the proportion in the risky share. The equation to solve is: 1.5(1-x) + 0(x) = 1. Solving for x gives x = 0.33 or 33%, meaning 33% of the portfolio should be in Treasury bills.

You Would Like to Combine a Risky Share with a Beta