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P1.T1.59. MVP and the efficient frontier

David Harper CFA FRM

David Harper CFA FRM
Staff member
AIMs: Define the minimum variance portfolio. Define the efficient frontier and describe the impact on it of various assumptions concerning short sales and borrowing (Elton & Gruber)


59.1. A portfolio contains only two assets. The first asset (a) has volatility of 9.0% and the second asset (b) has volatility of 16.0%. If the assets are uncorrelated, what is nearest to the weight in the first asset (a) in the minimum variance portfolio?

a. 43.75%
b. 56.25%
c. 75.96%
d. 100.0%

59.2. The market portfolio (M) contains the optimal allocation of only risky assets and no risky assets. Let the (S1) be the Sharpe ratio of this market portfolio. There exists a risk-free asset. Initially, an investor is fully (100%) invested in (M) with a portfolio Sharpe ratio of (S1). Subsequently, the investor borrows 30% at the risk-free rate, such that she is 130% invested in the market portfolio (M) where this leverage portfolio has a Sharpe ratio of (S2). After the leverage (i.e., borrowing at the riskfree rate to invest +30% in M), is the investor still on the efficient frontier and how do the Sharpe ratios?

a. No (no longer efficient), and S2 < S1
b. No, but S1 = S2
c. Yes (still efficient), but S2 < S1
d. Yes and S2 = S1

59.3. According to Elton & Gruber, which of the following statements is true?

a. The nominal returns of U.S. Treasury bills are risk-free returns
b. Predicted variance is always greater than historical variance
c. When using historical data to determine expected return inputs into a mean-variance portfolio optimization model, the longest possible time frame is best
d. Treasury bill returns tend to be positively autocorrelated and this implies that T-bills are effectively an decreasingly risky asset as the investment time horizon grows