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NO.PZ2015121801000051

问题如下：

With respect to risk-averse investors, a risk-free asset will generate a numerical utility that is:

选项：

the same for all individuals.

positive for risk-averse investors.

equal to zero for risk seeking investors.

解释：

A is correct.

A risk-free asset has a variance of zero and is not dependent on whether the investor is risk neutral, risk seeking or risk averse. That is, given that the utility function of an investment is expressed as $U = E (r) - \frac{1}{2} A σ^{2}$ , where A is the measure of risk aversion, then the sign of A is irrelevant if the variance is zero (like that of a risk-free asset).

b为什么不对？无风险那爽度不是positive的吗？

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Kiko_品职助教 · 2023年08月17日

嗨，努力学习的PZer你好：

是的，其实严格来说，utility最后得到的是无风险利率，那么其实是positive的。确实题目出得不好，同学了解他出题的本意就好了，其实他是想考察，对于所有投资者，无风险资产的方差是0，所以不管A的值是多少，得到的效用都是相同的，也就是A选项，对所有投资者都是相同的。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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