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Jo · 2024年08月18日

求这道题的解题思路。。

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

求这道题的解题思路。。

1 个答案
已采纳答案

李坏_品职助教 · 2024年08月18日

嗨,从没放弃的小努力你好:


题目说,这个人想用一个新的股票(不在当前的投资组合中)替代已有的一只股票,问你如何达到optimal portfolio ?


按照FRM教材的叙述,optimal portfolio的属性如下:

  1. 从原点(origin)做一条直线,与曲线上的一点连接,使这条直线的斜率(slope)达到最大的那个点,就是Optimal portfolio,同时也是直线与曲线的切点。
  2. 根据右边5.38这个公式,此时每一个asset的excess return / β,都是相等的,也就是达到了收益与风险的平衡。


Action 2恰好对应上面的性质2,所以Action 2是对的。


其他的几个Action都不是optimal portfolio的属性。


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

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