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wenwen_422 · 2021年02月17日

由daily转换为annual的转化是√250*VaRdaily,为什么monthly不是√21*VaRdaily?

NO.PZ2018091701000086

问题如下:

A portfolio has daily expected return of 0.03% and standard deviation of 0.25%. Assume the portfolio’s market value is $20million, its 1% monthly VaR should be (suppose there are 21 business days in a month):

选项:

A.

$638,420

B.

$409,900

C.

$110,500

解释:

B is correct.

考点: VaR计算

解析将天化的收益和标准差转化月化E(Rp)=0.03%*21=0.63%, σp =0.25%*(21)0.5=1.15%,

VaR=$(2.33*1.15%-0.63%)*20million=$409900

由daily转换为annual的转化是√250*VaRdaily,为什么monthly不是√21*VaRdaily?

1 个答案

星星_品职助教 · 2021年02月17日

同学你好,

直接适用平方根法则的是σ,而不是VaR。即原始的关系是Annual σ=√252×daily σ

VaR适用平方根法则的前提是假设了均值μ=0。这个假设下才有Annual VaR=√252×daily VaR。

-------------------推导过程--------------

这是因为此时VaR=|μ-z*σ|=|z*σ|=|z|*σ。所以Annual VaR=|z|*Annual σ;Daily VaR=|z|*Daily σ;

由于Annual σ=√252×daily σ,所以Annual VaR=|z|*Annual σ=|z|*√252×daily σ=√252×daily VaR

可以看出此时VaR适用平方根法则的原因是:1)假设了μ=0;2)实质是公式里的σ适用了平方根法则。

-------------------推导结束--------------

而这道题里的μ≠0(A portfolio has daily expected return of 0.03%)。所以VaR的平方根法则不能直接套用。

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