Consider two perfectly negatively correlated risky securities, K and L.K has an expected rate of return of 13% and a standard deviation of 19%.L has an expected rate of return of 10% and a standard deviation of 16%. The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.

Question

Quizplus · Accepted Answer

We can find the expected rate of return and standard deviation of the risk-free portfolio using the following formula:

Expected return of portfolio = weight of security K * expected return of K + weight of security L * expected return of L

In a risk-free portfolio where the securities are perfectly negatively correlated, the weights will be such that the standard deviation of the portfolio is 0. We can find the weights using the following formula:

Weight of security K = (standard deviation of L)^2 / ((standard deviation of K)^2 + (standard deviation of L)^2) = (16^2) / (19^2 + 16^2) = 0.435

Weight of security L = 1 - weight of K = 0.565

Therefore, the expected return of the risk-free portfolio is:

Expected return = 0.435 * 13% + 0.565 * 10% = 11.4%

So, the answer is B.

Consider Two Perfectly Negatively Correlated Risky Securities, K and L