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罗豆花Lori · 2022年06月16日

请问RL和Rf的区别是什么 在我看来似乎都是保证不亏损的临界值

  1. CFA I
  2. Quantitative

NO.PZ2015120601000010

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-ratio?
highest Sharpe ratio?
A.
No
Yes
B.
Yes
No
C.
Yes
Yes

解释：

C is correct.

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.

这道题仍然是要从公式入手，SFR公式为 SFR=[E(Rp) – RL ] / σp 。所以可以看出，当threshold / minimum return 也就是RL被设定为 risk free return Rf时，这个公式恰好就等于Sharpe Ratio（SR）。所以SFR等于SR是有前提的。

Shortfall risk是SFR里Rp低于RL的风险(就是投资的收益率低于了最低要求的门槛收益率的风险)。所以要让shortfall risk最小，相当于让SFR最大，也就是让E(Rp)尽量的大于RL。由于这道题RL=Rf，所以也相当于让SR最大。

请问RL和Rf的区别是什么 在我看来似乎都是保证不亏损的临界值

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星星_品职助教 · 2022年06月16日

同学你好，

Rf是投资者购买无风险投资工具时可以获得的收益率。

RL是投资者要求基金经理需要为其达到的最低收益率，这个收益率可以设定为Rf，但通常都要比Rf高，否则投资者自行购买无风险投资工具就可以了。


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