Question

You would like to combine a risky stock with a beta of 1.87 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 the risky stock?

Group of answer choices

1- 54.15%

2- 55.09%

3- 52.91%

4- 53.48%

5- 54.67%

Answer 1

In order to have risk equivalent to overall market, the resultant portfolio should have a beta of 1.

Beta of a portfolio is weighted average of the beta of individual portfolio constituents.

Assume percentage of portfolio in risky stock to be w. So, percentage in risk free asset would be 1 - w

1 = w * 1.87 + (1 - w) * 0

1 = w * 1.87

w = 0.5348

w = 53.48%