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亚利 · 2024年03月23日

请解释一下各个选项

NO.PZ2019042401000058

问题如下:

A portfolio manager is revising an equity portfolio with the goal of attaining the optimal portfolio on the portfolio’s efficient frontier. The manager believes this goal can be achieved by replacing a stock in the portfolio with a new stock that is not part of the existing portfolio and keeping the portfolio value constant. The manager considers the following alternative actions:

• Action 1: Sell the stock with the highest marginal VaR and purchase an equivalent value of a new stock that would have the lowest marginal VaR in the portfolio.

• Action 2: Sell a particular stock and purchase an equivalent value of a new stock, which would cause the ratio of expected excess returns to portfolio beta for all stocks in the portfolio to be equal.

• Action 3: Sell a particular stock and purchase an equivalent value of a new stock, which would cause the portfolio betas of all stocks in the portfolio to be equal.

• Action 4: Sell a particular stock and purchase an equivalent value of a new stock, which would significantly decrease the portfolio standard deviation without changing the average excess portfolio return.

Which of the actions above would create an optimal portfolio?

选项:

A.

Action 1

B.

Action 3

C.

Action 2

D.

Action 4

解释:

C is correct. The optimal portfolio is on the efficient frontier. It is the one that maximizes the slope of the tangent from the origin. At this point, the ratio of expected excess returns to portfolio beta (or marginal VaR) for all stocks in the portfolio is equal.

A is incorrect. This action would only minimize the risk of the portfolio. B is incorrect. This action would only minimize the risk of the portfolio.

D is incorrect. This action doesn’t necessarily create an optimal portfolio.

Risk Management and Investment Management

Explain the risk-minimizing position and the risk and return-optimizing position of a portfolio.

Philippe Jorion, Value-at-Risk: The New Benchmark for Managing Financial Risk, 3rd Edition (New York, NY: McGraw-Hill, 2007). Chapter 7. Portfolio Risk: Analytical Methods

c为什么对,哪里隐含了组合标准差不变的选项吗

2 个答案

李坏_品职助教 · 2024年03月24日

嗨,努力学习的PZer你好:


当股票的收益率服从正态分布时(这也是用公式求VaR的基本假设):

△VaR = β * α * σP,而不同股票的α都是相同的(α是置信度决定的),σP是投资组合的标准差,这也是一样的,所以△VaR也就主要取决于股票β的大小。

所以去掉不起作用的常数,不同股票的△VaR可以替换为β来表示。


这个过程推导没有放进讲义里,但是结论是在讲义的Managing Portfolios Using VAR

下面这个公式,分子就是excess return,Ei,分母就是△VaR。它的意思是所有股票的Ei / △VaR都应当相等,也就是Ei / βi都相等。


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李坏_品职助教 · 2024年03月23日

嗨,努力学习的PZer你好:


题目问的是哪一个action可以得到optimal portfolio(最优组合)?


optimal portfolio是在 efficient frontier(有效边界)上的,按照FRM2级Risk management and investment management原版书的说法:

最优组合对应的特征是:夏普比率最大。而夏普比率最大化的时候,对应的是投资组合中的每一个股票的excess return除以β是相等的,也就是恰好达到最优点,无法继续优化了。所以Action 2是对的。


其他的说法都不符合最优组合的特征。



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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!

亚利 · 2024年03月23日

没懂,为什么△VAR=β,请问这个老师上课在哪有讲到吗

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