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正好 · 2024年08月12日

为什么4不对?

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

为什么四不对呢?总收益率不变的情况下,总风险越低,不是越优吗?

1 个答案

pzqa27 · 2024年08月12日

嗨,爱思考的PZer你好:


选项D之所以不正确,是因为它虽然降低了组合的标准差(风险),但并没有考虑到组合在有效边界上的位置。要创建一个在有效边界上的最优组合,关键是要最大化单位风险的回报,即最大化夏普比率(Sharpe Ratio),而不是简单地减少风险。

选项D中,尽管风险降低了,但这并不保证夏普比率得到了优化。如果组合的风险减少,但没有考虑组合回报率的变化,那么它并不一定是在有效边界上的最优组合。

而选项C中的操作使得组合中所有股票的预期超额收益与组合贝塔的比率相等,这意味着组合达到了最大夏普比率,从而位于有效边界上。因此,选项C是正确的,而选项D则不是。

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