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Jingwen · 2023年07月02日

老师,这计算器到底该怎么按呀?

NO.PZ2022122801000023

问题如下:

Sandeep Sarzi is an investment advisor who has institutional and high net worth clients. Sarzi meets with a potential new client, Jerry Robson, to assess his capacity for risk. Sarzi estimates the risk aversion coefficient for Robson to be 5 on a scale of 1 to 10, where 10 represents the highest risk aversion. Sarzi provides expected returns and standard deviations of returns for two possible portfolios for Robson in Exhibit 1.

Exhibit 1 Portfolio Expected Returns and Standard Deviations

A. Determine which portfolio Sarzi should recommend to Robson based solely on expected utility. Justify your response.

选项:

解释:

Based solely on expected utility, Sarzi should recommend Portfolio B since it results in higher expected utility. The expected utility for each portfolio is calculated as follows:

Um =E (Rm ) - 0.005λσm2

Where Um = the investor’s expected utility for asset mix (allocation) m

Rm = return for asset mix (allocation) m

λ = the investor’s risk aversion coefficient

𝜎𝑚2 = the expected variance of return for asset mix (allocation m)

The expected utility of Portfolio A is: UA = 8% – 0.005 (5) (14%)2 = 3.1%

The expected utility of Portfolio B is: UB = 6% – 0.005 (5) (10%)2 = 3.5%

我按照这个公式输入:8%-0.005x5x(14%)^2,算出来是0.07951。0.005*5*0.0196=0.00049。

只有按照8-0.005*5*14^2=3.1

就有点懵,有的时候好像算出来就是对的,但这道题就是不对的了。

1 个答案
已采纳答案

lynn_品职助教 · 2023年07月03日

嗨,努力学习的PZer你好:


我按照这个公式输入:8%-0.005x5x(14%)^2,算出来是0.07951。0.005*5*0.0196=0.00049。


只有按照8-0.005*5*14^2=3.1


就有点懵,有的时候好像算出来就是对的,但这道题就是不对的了。


恭喜同学,你在考试前夕发现了这个问题,有时候算对有时候不对,在考场上一紧张可就一定是不对的了。


同学应该知道这个计算有两个公式,


如果用Um= E(R)- 0.005λσm2这个公式,应当代入E(R)=8,σ=14。相当于把百分号当成了一个符号


8%-0.005x5x(14%)^2,这个公式解答写得误人子弟,应该是(14)^2%,等于只有一个百分号,而且还是以符号的形式,


还要注意一点


为什么不是14%*14%=1.96%呢?(一个百分号作为符合,另一个是小数点)


因为这个%已经在前面的0.005中体现了。



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