A portfolio consists of two securities: a risk-free asset and an equity security.The expected return on the risk-free asset is 4.75%.The expected return of the equity security is 17% with a standard deviation of 23%.What is the portfolio expected return if the standard deviation for the portfolio is 18%?
A)7.41%
B)14.34%
C)18.00%
D)20.40%

Question

Quizplus · Accepted Answer

Let x be the proportion of the portfolio invested in the equity security.
Then, (1-x) is the proportion of the portfolio invested in the risk-free asset.
We know that the standard deviation of the portfolio is 18%, thus:
0.23^2 * x^2 + (1-x)^2 * 0 = 0.18^2
Solving for x, we get x = 0.722.
Thus, the proportion invested in the equity security is 0.722 and the proportion invested in the risk-free asset is 0.278.
Portfolio expected return = (0.722)(0.17) + (0.278)(0.0475) = 0.14 = 14.34%

A Portfolio Consists of Two Securities: a Risk-Free Asset and an Equity