A margin user has a situation where the riskfree rate is 5% and the risky portfolio has an expected return of 18% with standard deviation of 12%. If the proportion in the riskfree asset is -.5, the resulting expected return, standard deviation is

Question

Quizplus · Accepted Answer

Given, proportion in the risk-free asset = -0.5
Let R be the expected return on the risky portfolio and r be the risk-free return.
Expected return = (1-0.5)R + (-0.5)r = 0.5R - 0.5r
Standard deviation = 18%
Using the Capital Market Line equation:
E(R) = r + (R-r) * sigma(R)/sigma(M)
0.5R - 0.5r = 0.03 + (R-0.03) * 18%/15%
Solving the equation, we get R = 0.245 or 24.5%
Thus, the expected return with a proportion of -0.5 in the risk-free asset is 24.5% and the standard deviation is 18%. Therefore, the best choice is B.

A Margin User Has a Situation Where the Riskfree Rate