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Endymion · 2024年01月21日

想请问一下这题考的是哪个知识点呢？讲义上我没找到

  1. CFA I
  2. Portfolio

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.

想请问一下这题考的是哪个知识点呢？讲义上我没找到

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1 个答案

Kiko_品职助教 · 2024年01月22日

嗨，爱思考的PZer你好：


这是一道考察组合原理的题目。书上没有具体的公式，本题考查比较灵活，可以参考我们求组合的预期收益率，其实就等于组合中各个资产的收益率乘以权重， 然后求和是一个原理。

本题中Rf的权重是-0.5，市场组合的权重是1.5，那么乘以各自的beta，Rf的beta是0（没有系统性风险），市场组合的β是1（beta的定义），所以两个组合的beta=0(–0.5) + 1(1.5) = 1.5.

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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