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C_M_ · 2025年03月27日

计算过程

NO.PZ2023101902000020

问题如下:

A wealth management firm has a portfolio consisting of USD 37 million invested in US equities and USD 48 million invested in emerging markets equities. The US equities and emerging markets equities both have a 1-day 95% VaR of USD 1.3 million. The correlation between the returns of the US equities and emerging markets equities is 0.25. While rebalancing the portfolio, the manager in charge decides to sell USD 7 million of the US equities to buy USD 7 million of the emerging markets equities. At the same time, the CRO of the firm advises the portfolio manager to change the risk measure from 1-day 95% VaR to 10-day 99% VaR. Assuming that returns are normally distributed and that the rebalancing does not affect the volatility of the individual equity positions, by how much will the portfolio VaR increase due to the combined effect of portfolio rebalancing and change in risk measure?

选项:

A.USD 4.373 million

B.USD 6.428 million

C.USD 7.034 million

D.USD 9.089 million

这道题能给个计算过程吗

1 个答案

李坏_品职助教 · 2025年03月27日

嗨,爱思考的PZer你好:


首先,计算原始组合的1天95% VaR。原始组合包括3700万美元的美国股票和4800万美元的新兴市场股票,两者的1天95% VaR均为130万美元,相关性为0.25。


​1.原始组合的计算:


2. 调整后的组合波动率计算​(头寸调整为3000万美元美国股票和5500万美元新兴市场股票):

3.​转换为10天99% VaR

​4.VaR增加量

  • 调整后的组合10天99% VaR:9.07 百万美元
  • 原始组合1天95% VaR:2.055 百万美元
  • 增加量:9.07−2.055=7.015 百万美元

最接近的选项是C选项。



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