You would like to combine a highly risky stock with a beta of 2.6 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)57.91 percent
B)61.54 percent
C)50.00 percent
D)38.46 percent
E)42.09 percent

Question

Quizplus · Accepted Answer

To calculate the percentage of the portfolio that should be invested in Treasury bills, we need to use the formula:
beta of the portfolio = (percentage of the portfolio invested in risky stock) x beta of risky stock + (percentage of the portfolio invested in Treasury bills) x beta of Treasury bills
Since we want the beta of the portfolio to be equal to the beta of the overall market, which is typically around 1, we can set beta of the portfolio = 1 and substitute the given values:
1 = (1 - percentage in Treasury bills) x 2.6 + percentage in Treasury bills x 0
Solving for percentage in Treasury bills, we get:
percentage in Treasury bills = 61.54%
Therefore, the best choice is B.

You Would Like to Combine a Highly Risky Stock with a Beta