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魏丽aa · 2019年11月30日

问一道题: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.

老师 我咋感觉我计算器坏了 我是这样算的 0.1-0.005*8*0.12*0.12 =0.099424 跟答案哪不一样呢 有点迷

2 个答案
已采纳答案

Shimin_CPA税法主讲、CFA教研 · 2019年11月30日

嗨,爱思考的PZer你好:


代小数点形式的话,用U=E(r)-0.5Aσ^2= 0.1-0.5*8*0.12*0.12=0.0424

代百分号前面的数字,用U=E(r)-0.005Aσ^2= 10 – 0.005(8)(12)^2= 4.24


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JR · 2021年09月27日

答案里 Asset Allocation A:UA = 10.0% – 0.005(8)(12%)2= 4.24% 老师解析里 代小数点形式的话,用U= 0.1-0.5*8*0.12*0.12=0.0424 这看起来就很矛盾啊,这俩式子明显不一样,一个0.005还是0.5,怎么可能结果相同

pzqa015 · 2021年09月28日

嗨,努力学习的PZer你好:


看下面的解释吧:

计算Utility有两个公式,一是E(R)与σ取百分号前面的数字,用U=E(R)-0.005*λ*σ^2,计算结果再人工加上百分号;二是E(R)与σ取带百分号的数字,此时用U=E(R)-0.5*λ*σ^2,,计算得到小数,不用调整。

比如以asset allocation A为例:

按照第一种方法:U=10-0.005*8*12^2=4.24,人工加上百分号是4.24%。

按照第二种方法:U=0.1-0.5*8*0.12^2=0.0424=4.24%。

两种方法的结果是一样的。

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