What is the portfolio expected return with 125% invested in A and the remainder in the risk-free asset via borrowing at the risk-free rate?
A) 9.8%
B) 11.3%
C) 16.8%
D) 17.5%
E) 20.1%

Question

Quizplus · Accepted Answer

First, we need to find the expected return of stock A.
Expected Return of A = (0.5 x 0.2) + (0.3 x 0.15) + (0.2 x 0.1) = 0.16 or 16%
Next, we need to find the borrowing cost at the risk-free rate.
Borrowing cost = Risk-free rate x (1 + amount borrowed) = 0.04 x (1 + 0.25) = 0.05 or 5%
Now, we can calculate the portfolio expected return using the formula:
Portfolio Expected Return = (Weight of A x Expected Return of A) + (Weight of Risk-Free Asset x Risk-Free Rate - Borrowing Cost)
Weight of A = 1.25
Weight of Risk-Free Asset = -0.25

Portfolio Expected Return = (1.25 x 0.16) + (-0.25 x 0.04 - 0.05) = 0.175 or 17.5%

Therefore, the best choice is D, with a portfolio expected return of 17.5%, the highest among the given options.

What Is the Portfolio Expected Return with 125% Invested in a and the Remainder