Suppose you borrow at the risk-free rate an amount equal to your initial wealth and invest in a portfolio with an expected return of 16% and a standard deviation of returns of 20%.The risk-free asset has an interest rate of 4%.Calculate the expected return on the resulting portfolio.
A)20%
B)32%
C)28%
D)12%

Question

Quizplus · Accepted Answer

Using the formula for the expected return of a portfolio:

Expected return = weight of risky asset * expected return of risky asset + weight of risk-free asset * risk-free rate

Since we borrowed an amount equal to our initial wealth, the weight of the risky asset is 1 (100%) and the weight of the risk-free asset is -1 (we borrowed at the risk-free rate).

Plugging in the given values:

Expected return = 1 * 16% + (-1) * 4% = 12%

Therefore, the expected return on the resulting portfolio is 12%. The closest option is C) 28%, which is incorrect.

Suppose You Borrow at the Risk-Free Rate an Amount Equal