wenwen_422 · 2021年02月17日
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?
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。
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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。
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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。
NO.PZ2018091701000086 问题如下 A portfolio hily expectereturn of 0.03% anstanrviation of 0.25%. Assume the portfolio’s market value is $20million, its 1% monthly Vshoul(suppose there are 21 business ys in a month): A.$638,420 B.$409,900 C.$110,500 B is correct.考点: VaR计算解析将天化的收益和标准差转化月化E(Rp)=0.03%*21=0.63%, σp =0.25%*(21)0.5=1.15%,VaR=$(2.33*1.15%-0.63%)*20million=$409900 如题
NO.PZ2018091701000086 问题如下 A portfolio hily expectereturn of 0.03% anstanrviation of 0.25%. Assume the portfolio’s market value is $20million, its 1% monthly Vshoul(suppose there are 21 business ys in a month): A.$638,420 B.$409,900 C.$110,500 B is correct.考点: VaR计算解析将天化的收益和标准差转化月化E(Rp)=0.03%*21=0.63%, σp =0.25%*(21)0.5=1.15%,VaR=$(2.33*1.15%-0.63%)*20million=$409900 为什么不能算出1天的VaR，再乘以根号下21
NO.PZ2018091701000086 问题如下 A portfolio hily expectereturn of 0.03% anstanrviation of 0.25%. Assume the portfolio’s market value is $20million, its 1% monthly Vshoul(suppose there are 21 business ys in a month): A.$638,420 B.$409,900 C.$110,500 B is correct.考点: VaR计算解析将天化的收益和标准差转化月化E(Rp)=0.03%*21=0.63%, σp =0.25%*(21)0.5=1.15%,VaR=$(2.33*1.15%-0.63%)*20million=$409900 请问ily retuen 转换为月度renturn为什么不是用compounrate来计算？而是直接乘以21？
NO.PZ2018091701000086 问题如下 A portfolio hily expectereturn of 0.03% anstanrviation of 0.25%. Assume the portfolio’s market value is $20million, its 1% monthly Vshoul(suppose there are 21 business ys in a month): A.$638,420 B.$409,900 C.$110,500 B is correct.考点: VaR计算解析将天化的收益和标准差转化月化E(Rp)=0.03%*21=0.63%, σp =0.25%*(21)0.5=1.15%,VaR=$(2.33*1.15%-0.63%)*20million=$409900 VAR公式不是μ+-k倍标准差吗？为什么答案是k倍标准差-μ
NO.PZ2018091701000086 我算【21*expecteretrun-2.33*根号下21* stanrviation】=40787
