You would like to combine a risky stock with a beta of 1.8 with U.S. 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) 44%
C) 50%
D) 62%
E) 78%

Question

Quizplus · Accepted Answer

The risk level of the overall market is represented by the beta of the market, which is typically 1. Therefore, we need to combine the stock with Treasury bills in such a way that the portfolio beta is equal to 1. To find the percentage of the portfolio that should be invested in Treasury bills, we can use the following formula:

Portfolio beta = (% invested in stock * stock beta) + (% invested in T-bills * T-bills beta)

Plugging in the given values, we get:

1 = (% * 1.8) + ((100% - %) * 0)

Solving for %, we get:

% = 44%

Therefore, 44% of the portfolio should be invested in Treasury bills.

You Would Like to Combine a Risky Stock with a Beta