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)- 0.005λσm2
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.
关于代入百分号的问题：
如果考到主观题，写公式以解析中的公式为准，将百分号%当作一个单位来理解。
计算时不要带入百分号%，即按照这个公式来计算：6.7 - 0.005 × 7 × 11.92 计算的结果后面直接加上%。
关于计算题，列出计算过程，有几个疑惑：
1.计算公式是要列出公式、例如预期收益率E(r)，还是只要列出数字、例如6.7%即可？
2.计算过程中涉及到公式，比如填写分数，需要填写分子/分母、有上下分隔符；比如平方、需要右上角的上标；比如乘法，是否可以用*星号代替？文本框里怎么编辑公式？
3.本题如果按照下述作答是否可以？感觉平方就写个^2，好像不是很规范啊
Utility A = 6.7%-0.5 *7 *0.119^2=1.743%
Utility B = 5.9%-0.5 *7 * 0.107^2=1.8929%
since utility of B is larger than utility A,to maximize utility we should choose allocation B
