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Erinwu · 2019年12月05日

问一道题:NO.PZ2018031301000003

问题如下:

John Tomb is an investment advisor at an asset management firm. He is developing an asset allocation for James Youngmall, a client of the firm. Tomb considers two possible allocations for Youngmall. Allocation A consists of four asset classes: cash, US bonds, US equities, and global equities. Allocation B includes these same four asset classes, as well as global bonds. Youngmall has a relatively low risk tolerance with a risk aversion coefficient (λ) of 7. Tomb runs mean–variance optimization (MVO) to maximize the following utility function to determine the preferred allocation for Youngmall:

Um= E(R)- 0.005λσm2

The resulting MVO statistics for the two asset allocations are presented in Exhibit 1.



Determine which allocation in Exhibit 1 Tomb should recommend to Youngmall. Justify your response.

选项:

解释:

Tomb should recommend Allocation B.
The expected utility of Allocation B is 1.89%, which is higher than Allocation A’s expected utility of 1.74%.
MVO provides a framework to determine how much to allocate to each asset class or to create the optimal asset mix. The given objective function is:
Um= E(R)- 0.005λσ
m2
Using the given objective function and the expected returns and expected standard deviations for Allocations A and B, the expected utilities (certainty equivalent returns) for the two allocations are calculated as:
Allocation A: 6.7% – 0.005 (7) (11.9%)2 = 1.74%
Allocation B: 5.9% – 0.005 (7) (10.7%)2 = 1.89%
Therefore, Tomb should recommend Allocation B because it results in higher expected utility than Allocation A.

计算公式是否有误。因为如果代入公式的是带着百分号的数据,则系数是不是应该是0.5?

2 个答案

Shimin_CPA税法主讲、CFA教研 · 2019年12月05日

嗨,爱思考的PZer你好:


silviaws 同学的回答是正确的。

Um= E(R)- 0.005λσm2,用0.005的时候,%相当于符号,不是0.01的意思,相当于 Allocation A: 6.7 – 0.005 (7) (11.9) (11.9) = 1.74,算出结果后直接加%,最终结果为1.74%。

Um= E(R)- 0.5λσm2,用0.5的时候,代入6.7%就是0.067了,这是中国人的习惯,相当于 Allocation A: 0.067 – 0.5 (7) (0.119) (0.119) = 0.0174,所以最终结果为1.74%。

 


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silviaws · 2019年12月05日

没反哦。输入变量是百分数就是0.005,输入变量是小数的话0.5。 For example, if E(Rm) = 0.10, λ = 2, and σ = 0.20 (variance is 0.04), then Um is 0.06, or 6% [= 0.10 –0.5(2)(0.04)] .

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