题目
The market portfolio (M) contains the optimal allocation of only risky assets and no risky assets. Let the S1be 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 risk-free rate to invest + 30% in M, is the investor still on the efficient frontier and how do the Sharpe ratios?
选项
A.No (no longer efficient), and S2 < S1.
B.No, but S2 = S1.
C.Yes(still efficient), but S2 < S1.
D.Yes, and S2 = S1.
答案
D
解析
The ability to borrowing or lend morphs the concave/convex efficient frontier into the linear CML; i.e., the leveraged portfolio is efficient with higher risk and higher return.All portfolios on the CML have the same Sharpe ratio: the slope of the CML.借入或借出的能力使凹/凸有效边界变形成线性CML。 即，杠杆投资组合是高效的，具有更高的风险和更高的回报。CML上的所有投资组合都具有相同的Sharpe比率：CML的斜率。