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veronica_gxy · 2021年04月22日

老师可以详细解释下为什么算出来的3个数越大越好吗

  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  

如标题、为什么选最大的那个、不太懂
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星星_品职助教 · 2021年04月23日

同学你好，

根据题干“According to Roy’s safety-first criterion....”，可以判断这道题是根据SFR来判断哪个portfolio最优。

而SFR的判断准则是越大越好。可以根据讲义上的公式看出，SFR越大，单位风险所对应的excess return就越高。

所以本题的解题思路即为算出三个SFR，然后挑最大的那个，就是最好的portfolio。

由于公式中的E(Rp)，σp都给出了，所以需要求一下Rl，根据题干可知，Rl=90,000/2,000,000=4.5%。

此后逐个portfolio的数据分别代入公式计算SFR即可。



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