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滴滴姐姐~ · 2020年07月15日

问一道题:NO.PZ2018031301000003 [ CFA III ]

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.

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.

道理我都懂 但是叭我今儿做题的时候盯表格的时候 然后就想到上课时候老师说选Sharpe ratio大的。。。 hmmm是不是因为没给rf才用效用公式的?
1 个答案

纠纠_品职答疑助手 · 2020年07月15日

嗨,爱思考的PZer你好:


这里是题目明确指出了:

Tomb runs mean–variance optimization (MVO) to maximize the following utility function to determine the preferred allocation for Youngmall

中有 utility function。

另外,看sharpe ratio的时候,我们通常是在资产可以和无风险资产做组合的时候去看sharpe ratio。因为这样可以随意调整用户想要的风险,并且确保在固定风险下的收益是最大。


-------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!


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