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Susie · 2023年04月25日

这一题考查的知识点不太理解

  1. Quantitative

NO.PZ2022123001000072

问题如下：

At the end of the current year, an investor wants to make a donation of $20,000 to charity but does not want the year-end market value of her portfolio to fall below $600,000. If the shortfall level is equal to the risk-free rate of return and returns from all portfolios considered are normally distributed, will the portfolio that minimizes the probability of failing 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 ratio minimizes the probability that the portfolio return will be less than the shortfall level (given normality). In this problem, the shortfall level is equal to the risk-free rate of return and thus the highest safety-first ratio portfolio will be the same as the highest Sharpe ratio portfolio.



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1 个答案

星星_品职助教 · 2023年04月27日

同学你好，

根据题干条件：

1）shortfall level （Rl）等于Rf。根据Safety first Ratio（SFR）的公式，可知如将公式中分子的Rl替换为Rf，SFR的公式就等同于了Sharpe Ratio（SR）的公式，即本题中SFR=SR；

2）要最小化portfolio return低于shortfall level（minimizes the probability of failing to achieve the investor's objective），就相当于要最大化SFR。因为SFR越大，达不到投资者要求的shortfall level的可能性越低。再根据上一条得出的SFR=SR，可知最大化SFR的同时也就是要最大化SR。


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提问时需要标注级别，如CFA I，否则问题是无法分配给对应助教的。

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