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努努奔 · 2024年03月16日

本题权重问题

NO.PZ2022081802000059

问题如下:

Question An investor with $10,000 decides to borrow an additional $5,000 at the risk-free rate and invest all the available funds in the market portfolio. This investor’s portfolio beta is closest to:

选项:

A.0.5.

B.1.0.

C.1.5.

解释:

Solution

C is correct. The weight in the market portfolio is 15,000/10,000 = 1.5 and the weight in the risk-free asset is –5,000/10,000 = –0.5. Because the beta of the risk-free asset is 0 and the market portfolio’s beta is 1, the portfolio’s beta is βp = 0(–0.5) + 1(1.5) = 1.5.

A is incorrect because it is computed using weights of 0.5 for the risk-free asset and the market portfolio, that is: 0(0.5) + 1(0.5) = 0.5.

B is incorrect because it is the market portfolio’s beta.

答案中”weight in the market portfolio is 15,000/10,000 = 1.5 and the weight in the risk-free asset is –5,000/10,000 = –0.5”

为什么不是10000/15000和5000/15000?

1 个答案
已采纳答案

Kiko_品职助教 · 2024年03月18日

嗨,爱思考的PZer你好:


因为题目中说了是borrow5000,本来有10000,相当于跟银行借钱,举杠杆了,所以相当于给了Rf一个负的权重。你的做法相当于一共有15000,其中10000投资market portfolio,5000投资Rf,但事实不是这样。

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