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 percent and a standard deviation of returns of 20 percent. The risk-free asset has an interest rate of 4 percent. Calculate the expected return on the resulting portfolio.
A)20 percent
B)32 percent
C)28 percent
D)12 percent

Question

Quizplus · Accepted Answer

To calculate the expected return on the resulting portfolio, we need to use the formula:

E(Rp) = Rf + [E(Rm) - Rf] * (σp/σm)

where:
- E(Rp) is the expected return on the portfolio
- Rf is the risk-free rate
- E(Rm) is the expected return on the market portfolio
- σp is the portfolio's standard deviation of returns
- σm is the market portfolio's standard deviation of returns

In this case, we can assume that the market portfolio is the one with the expected return of 16 percent and the standard deviation of returns of 20 percent. Therefore:

E(Rp) = 0.04 + [0.16 - 0.04] * (σp/0.2)

Since we borrowed an amount equal to our initial wealth, we can assume that the portfolio will be equally divided between the risk-free asset and the market portfolio. Therefore:

σp = [(0.5)^2*(0.2)^2 + (0.5)^2*(0.2)^2 + 2*(0.5)*(0.5)*0.2*0]^(1/2) = 0.1414

Substituting this into the previous formula, we get:

E(Rp) = 0.04 + [0.16 - 0.04] * (0.1414/0.2) = 0.28

Therefore, the expected return on the resulting portfolio is 28 percent, which corresponds to choice C.

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