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梦梦 · 2025年04月06日

横轴既是b又是VaR?

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

“根据右边5.38这个公式,此时每一个asset的excess return / β”

老师好,应该是得塔E/得塔b吧?E/b是斜率吗?横轴既代表了E又代表了b?

1 个答案

李坏_品职助教 · 2025年04月06日

嗨,从没放弃的小努力你好:


你看这个5.38最上面那一行字,他说的是at the optimum,就是在最优组合那个点的时候(左图有optimal portfolio这一点),满足下面的等式,E / △Var = E/β = constant.


既然是最优点,那么超额收益(E,就是股票收益率 - 无风险收益率)除以每单位的风险,这个比率无法继续扩大了,达到了稳定值。这里用β近似代表了VaR的变化值,β ≈ △VaR。 β本来就是衡量组合风险的指标,这样做也合理。


坐标图里面纵轴是收益率,Expected excess return,也就是E。 横轴是风险,β。

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