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刘恒君 · 2022年04月21日

罗伊第一安全比率

  1. CFA I
  2. Quantitative

NO.PZ2017092702000101

问题如下：

A client holding a £2,000,000 portfolio wants to withdraw £90,000 in one year without invading the principal. According to Roy’s safety-first criterion, which of the following portfolio allocations is optimal?

选项：

A.

Allocation A

B.

Allocation B

C.

Allocation C

解释：

B is correct.

Allocation B has the highest safety-first ratio. The threshold return level RL for the portfolio is £90,000/£2,000,000 = 4.5%, thus any return less than RL = 4.5% will invade the portfolio principal. To compute the allocation that is safety-first optimal, select the alternative with the highest ratio:

lE[(Rp−RL)]σPAllocation A =6.5−4.58.35=0.240Allocation B =7.5−4.510.21=0.294Allocation C =8.5−4.514.34=0.279{l}\frac{E{\lbrack{(R_p-R_L)}\rbrack}}{\sigma_P}\\Allocation\text{ }A\text{ =}\frac{6.5-4.5}{8.35}=0.240\\Allocation\text{ }B\text{ =}\frac{7.5-4.5}{10.21}=0.294\\Allocation\text{ }C\text{ =}\frac{8.5-4.5}{14.34}=0.279  

我是2022年11月份的考生，想请问在听课时没有听到罗伊第一安全比率这个知识点，强化串讲也没有，是被取消了么


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1 个答案

星星_品职助教 · 2022年04月21日

同学你好，

11月的课程中，SFR的基础班位置如下图。

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NO.PZ2017092702000101 问题如下 A client holng a £2,000,000 portfolio wants to with£90,000 in one yewithout invang the principal. Accorng to Roy’s safety-first criterion, whiof the following portfolio allocations is optimal? A.Allocation B.Allocation C.Allocation B is correct. Allocation B hthe highest safety-first ratio. The thresholreturn level RL for the portfolio is £90,000/£2,000,000 = 4.5%, thus any return less thRL = 4.5% will inva the portfolio principal. To compute the allocation this safety-first optimal, selethe alternative with the highest ratio:lE[(Rp−RL)]σPAllocation A =6.5−4.58.35=0.240Allocation B =7.5−4.510.21=0.294Allocation C =8.5−4.514.34=0.279{l}\frac{E{\lbrack{(R_p-R_L)}\rbrack}}{\sigma_P}\\Allocation\text{ }A\text{ =}\frac{6.5-4.5}{8.35}=0.240\\Allocation\text{ }B\text{ =}\frac{7.5-4.5}{10.21}=0.294\\Allocation\text{ }C\text{ =}\frac{8.5-4.5}{14.34}=0.279lσP​E[(Rp​−RL​)]​Allocation A =8.356.5−4.5​=0.240Allocation B =10.217.5−4.5​=0.294Allocation C =14.348.5−4.5​=0.279 1

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