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yan · 2024年06月20日

安全第一比率和夏普公式是一样的呀

NO.PZ2022123001000072

问题如下:

At the end of the current year, an investor wants tomake a donation of $20,000 to charity but does not want the year-end marketvalue of her portfolio to fall below $600,000. If the shortfall level is equalto the risk-free rate of return and returns from all portfolios considered arenormally distributed, will the portfolio that minimizes the probability offailing to achieve the investor's objective most likely have the:

选项:

Highest safety-first ratio?
Highest Sharpe ratio?

A.

no
yes

B.

yes
no

C.

yes
yes

解释:

The portfolio with the highest safety-first ratiominimizes the probability that the portfolio return will be less than theshortfall level (given normality). In this problem, the shortfall level isequal to the risk-free rate of return and thus the highest safety-first ratioportfolio will be the same as the highest Sharpe ratio portfolio.

投资者想要捐赠2万美元,不希望市值低于60万,可不可以理解为投资者的原始本金也是60万,保持本金不亏,预期收益率为2/60=0.0333333; 安全第一比率SF=(E(Rp)-Rl)÷σp Sp=(Rp-Rf)÷σp Rl=Rf 预期收益率都一样,可以理解,两者相等,怎么理解两者最大列?

1 个答案

品职助教_七七 · 2024年06月20日

嗨,从没放弃的小努力你好:


这道题里两者就是相等的。给出“the shortfall level is equalto the risk-free rate”,就相当于在说safety-first ratio=Sharpe ratio。不需要去计算,也不用去考虑题目里的数字。

本题要求最小化该投资者无法达成目标的概率。而当safety-first ratio最大时,无法达成目标的概率是最小的。所以本题需要首先选择最大的safety-first ratio。

由于本题里safety-first ratio还等于Sharpe ratio。故highest safety-first ratio就也是highest SR。

所以两个指标都选Highest。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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