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Victutu · 2020年09月02日

问一道题:NO.PZ2016031202000009 [ CFA I ]

问题如下:

Is it true that the expected payoff of the derivative can be discounted at the risk-free rate plus a risk premium?

选项:

A.

No, because a conbination of a derivative and the underlying can produce a risk-free asset.

B.

Yes, because most investors are risk averse, they require a risk premium.

C.

No, because most investors are risk neutrality, they do not need a premium.

解释:

A is correct. The expected payoff of the derivative can be discounted at the risk-free rate, because a derivative can be combined with an asset to produce a risk-free position and the derivative price can be obtained by assuming that the investor is risk neutral.

C is incorrect because most investors are risk averse, however the investor's risk aversion does not affect the derivative price.

能否请老师解答一下整个题目。为什么risk free rate+risk premium 不对?和各个选项有什么关系?
1 个答案

xiaowan_品职助教 · 2020年09月02日

嗨,爱思考的PZer你好:


同学你好,

risk free rate+risk premium是用来给风险资产本身定价的,也就是给现货资产定价的,而衍生品可以用来规避风险,它的定价是基于无套利原则,和投资者的风险厌恶程度没有关系。

这个知识点对应基础班课程截图如下


-------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!


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NO.PZ2016031202000009问题如下Is it true ththe expectepayoff of the rivative cscountethe risk-free rate plus a risk premium?A.No, because a combination of a rivative anthe unrlying cproa risk-free asset.B.Yes, because most investors are risk averse, they require a risk premium.C.No, because most investors are risk neutrality, they not neea premium. A is correct. The expectepayoff of the rivative cscountethe risk-free rate, because a rivative ccombinewith asset to proa risk-free position anthe rivative pricobtaineassuming ththe investor is risk neutral.C is incorrebecause most investors are risk averse, however the investor's risk aversion es not affethe rivative price.中文解析题干实际问的是为什么对于衍生品的定价时可以用无风险利率其中的逻辑是这样的首先我们知道一个等式asset+ivative=risk-free asset,即衍生品可以帮助我们消除风险。然而大多数投资者的是风险厌恶型的,即承担多一点的风险需要一个风险补偿。所以按理来说,在定价折现的时候应该加上一个风险补偿。但这个方法对衍生品来说并不适用,原因就在于上面这个公式 asset+ivative=risk-free asset。因为衍生品可以消除资产的风险,以获得一个certain payoff,所以风险厌恶对于衍生品的定价来说是not relevant,我们就可以假设投资者是风险中性的,以无风险利率折现。 请问C为什么不对呢?谢谢!

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