NO.PZ2018011501000009
问题如下：
Investment adviser Carl Monteo determines client asset allocations using quantitative techniques such as mean–variance optimization (MVO) and risk budgets. Monteo is reviewing the allocations of three clients. Exhibit 1 shows the expected return and standard deviation of returns for three strategic asset allocations that apply to several of Monteo’s clients.
Exhibit1 Strategic Asset Allocation Alternatives
Monteo interviews client Mary Perkins and develops a detailed assessment of her risk preference and capacity for risk, which is needed to apply MVO to asset allocation. Monteo estimates the risk aversion coefficient (λ) for Perkins to be 8 and uses the following utility function to determine a preferred asset allocation for Perkins:
Um =E (Rm) - 0.005λσm2
Based on Exhibit 1 and the risk aversion coefficient, the preferred asset allocation for Perkins is:
选项：
A. Asset Allocation A.
B. Asset Allocation B.
C. Asset Allocation C.
解释：
C is correct.
The risk aversion coefficient (λ) for Mary Perkins is 8. The utility of each asset allocation is calculated as follows:
Asset Allocation A:UA = 10.0% – 0.005(8)(12%)2= 4.24%
Asset Allocation B:UB = 8.0% – 0.005(8)(8%)2= 5.44%
Asset Allocation C:UC = 6.0% – 0.005(8)(2%)2= 5.84%
Therefore, the preferred strategic allocation is Asset Allocation C, which generates the highest utility given Perkins’s level of risk aversion.
考点：MVO
解析：MVO方法下objective function的应用。将每个组合的Expected Return和Standard Deviation of Returns代入公式，计算后比大小，选结果最大的一个。公式题干已给：
Um =E (Rm) - 0.005λσm2
λ=8, 由于公式中λ前面是0.005，因此代入数字时不带百分号。举例：UA = 10 - 0.005*8*(12)2=4.24。
分别计算三个组合的utility，结果为4.24，5.44，5.84，因此C选项结果最大。
E（r）和标准差都带入%，lamda前系数就带1/2算出来结果一样，这样对吗？
