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okbella · 2024年08月01日

解释

NO.PZ2023091901000026

问题如下:

The market portfolio (M) contains the optimal allocation of only risky asset 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 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

B.

No, but S2 = S1.

C.

Yes (still efficient), but S2

D.

Yes and S2 = S1.

解释:

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.


借用或借出的能力将凹/凸有效边界变为线性CML;
也就是说,杠杆投资组合具有较高的风险和较高的收益。
CML上的所有投资组合都有相同的夏普比率:CML的斜率。

老师您好,我看了解析也不是太懂,您能给我解释一下吗

1 个答案

pzqa27 · 2024年08月02日

嗨,爱思考的PZer你好:


这道题目问的是CAL上能获得比切点组合还高的return是因为什么?

因为可以得到一个borrowing portfolio,也就是说可以跟银行借钱来投资切点组合。

投资者通过利用杠杆构建借款投资组合,可以在资本配置线上实现比切点组合本身更高的投资回报。他们以无风险利率借款,并将所借资金投入切点组合,从而加大对高风险调整后收益资产的暴露,有可能在承受相应更高风险的同时获得更高的总回报。


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