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比夏 · 2024年10月28日

information ratio和VaR之间的关系是怎么联系到一起的?有什么前提条件吗?

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

如题

1 个答案

李坏_品职助教 · 2024年10月28日

嗨,爱思考的PZer你好:


这个题目本身和information ratio与VaR都没关系,他是问你如何通过卖掉一部分股票,买入一部分新股票,来以此创造一个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。



information ratio = alpha / alpha的σ,这个指标和VaR结合起来用于Risk Budgeting。比如一个投资者,给自己的投资组合设定了最大的VaR限制是3billion, 首先第一步要根据VaR限制选择拟投资的基金经理(所有经理组合起来的VaR不得超过3billion),第二步是根据各个基金经理的Information ratio确定每个基金的投资权重:

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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