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shining · 2024年10月27日

lognormal VaR 计算时收益率和方便用年化的就可以嘛

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000017

问题如下：

The annual mean and volatility of a portfolio are 10% and 40%, respectively. The current value of the portfolio is GBP 1,000,000. How does the 1-year 95% VaR that is calculated using a normal distribution assumption (normal VaR) compare with the 1-year 95% VaR that is calculated using the lognormal distribution assumption (lognormal VaR)?

选项：

A.

Lognormal VaR is greater than normal VaR by GBP 130,400

B.

Lognormal VaR is greater than normal VaR by GBP 175,900

C.

Lognormal VaR is less than normal VaR by GBP 130,400

D.

Lognormal VaR is less than normal VaR by GBP 175,900

解释：

C is correct.

考点 ： Parametric Estimation Approaches

解析：Normal VAR=0.1-(1.645×0.4）=0.558，

Lognormal VAR=1-exp[0.1-(1.645×0.4)]=0.4276

Hence, lognormal VaR is smaller than Normal VaR by 13.04% per year. With a portfolio of GBP 1,000,000, this translates to GBP 130,400 .

本题中计算 daily lognormal VaR 没有进行收益率和方差的转换，直接使用年化数据进行计算，原因呢。 那如果是 daily lognormal VaR 如何计算 呢

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李坏_品职助教 · 2024年10月27日

嗨，爱思考的PZer你好：


因为本题问的就是 1-year的VaR，所以不需要进行时间转换。


如果是daily的VaR，那要进行转换，daily return = 0.1 / 252, daily σ = 0.4 / 根号252。

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