李坏_品职助教 · 2024年11月18日
嗨,爱思考的PZer你好:
在引入无风险借贷(就是引入leverage)之后,新的有效边界从原来的曲线变成了CML这条直线。所以此时CML就是新的有效边界。
在引入杠杆之后,新的组合的确不在曲线上,现在是在CML上(从下图的点M变成了点B):
题目最后问的是,投资者的组合是否在有效边界上?是的(在CML上,就是在有效边界上)。
另外,由于是在rf与M组合之间进行线性组合,那么并不会改变斜率,所以sharpe ratio也一样,D选项是正确的。
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NO.PZ2023091901000026 问题如下 The market portfolio (M) contains the optimallocation of only risky asset anno risky assets. Let the S1 the Sharpe ratio of this market portfolio. There exists a risk-free asset. Initially, investor is fully (100%) investein M with a portfolio Sharpe ratio of S1. Subsequently, the investor borrows 30% the risk-free rate, suthshe is 130% investein the market portfolio (M) where this leverage portfolio ha Sharpe ratio of S2。After the leverage (i.e., borrowing the risk-free rate to invest +30% in M, is the investor still on the efficient frontier anhow the Sharpe ratios? A.No (no longer efficient), anS2 S1. B.No, but S2 = S1. C.Yes (still efficient), but S2 S1. Yes anS2 = S1. The ability to borrowing or lenmorphs the concave/convex efficient frontier into the lineCML; i.e., the leverageportfolio is efficient with higher risk anhigher 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。 有效前沿线不是那条曲线吗?借钱的组合不是在CML上,那个线没在EL上了啊?
NO.PZ2023091901000026 问题如下 The market portfolio (M) contains the optimallocation of only risky asset anno risky assets. Let the S1 the Sharpe ratio of this market portfolio. There exists a risk-free asset. Initially, investor is fully (100%) investein M with a portfolio Sharpe ratio of S1. Subsequently, the investor borrows 30% the risk-free rate, suthshe is 130% investein the market portfolio (M) where this leverage portfolio ha Sharpe ratio of S2。After the leverage (i.e., borrowing the risk-free rate to invest +30% in M, is the investor still on the efficient frontier anhow the Sharpe ratios? A.No (no longer efficient), anS2 S1. B.No, but S2 = S1. C.Yes (still efficient), but S2 S1. Yes anS2 = S1. The ability to borrowing or lenmorphs the concave/convex efficient frontier into the lineCML; i.e., the leverageportfolio is efficient with higher risk anhigher 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,您能给我一下吗
NO.PZ2023091901000026问题如下 The market portfolio (M) contains the optimallocation of only risky asset anno risky assets. Let the S1 the Sharpe ratio of this market portfolio. There exists a risk-free asset. Initially, investor is fully (100%) investein M with a portfolio Sharpe ratio of S1. Subsequently, the investor borrows 30% the risk-free rate, suthshe is 130% investein the market portfolio (M) where this leverage portfolio ha Sharpe ratio of S2。After the leverage (i.e., borrowing the risk-free rate to invest +30% in M, is the investor still on the efficient frontier anhow the Sharpe ratios? A.No (no longer efficient), anS2 S1.B.No, but S2 = S1.C.Yes (still efficient), but S2 S1. Yes anS2 = S1. The ability to borrowing or lenmorphs the concave/convex efficient frontier into the lineCML; i.e., the leverageportfolio is efficient with higher risk anhigher return. All portfolios on the CML have the same Sharpe ratio: the slope of the CML. 借钱不是在线外了吗