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中二 · 2020年02月11日

问一道题:NO.PZ2016070201000032 [ FRM II ]

问题如下:

Suppose a financial institution has a two-asset portfolio with $7 million in asset A and $5 million in asset B. The portfolio correlation is 0.4, and the daily standard deviation of returns for asset A and B are 2% and 1%, respectively. -what is the 10-day value at risk (VaR) of this portfolio at a 99% confidence level ( α = 2.33)? Supposed the mean of portfolio returns is zero.

选项:

A.

$1.226 million.

B.

$1.670 million.

C.

$2.810 million.

D.

$3.243 million.

解释:

A

The first step in solving for the 10-day VaR requires calculating the covariance matrix.

lcov11=σ12=0.022=0.0004cov22=σ22=0.012=0.0001cov12=ρ1,2×σ1×σ2=0.4×0.02×0.01=0.00008{l}{\mathrm{cov}}_{11}=\sigma_1^2=0.02^2=0.0004\\{\mathrm{cov}}_{22}=\sigma_2^2=0.01^2=0.0001\\{\mathrm{cov}}_{12}=\rho_{1,2\times}\sigma_1^{}\times\sigma_2=0.4\times0.02^{}\times0.01=0.00008

Thus, the covariance matrix C, can be represented as:

(0.0004amp;0.000080.00008amp;0.0001)(\begin{array}{cc}0.0004&0.00008\\0.00008&0.0001\end{array})

Next, the standard deviation of the portfolio, σp\sigma_p, is determined as foJlows:

Step 1: Compute βh\beta_h × C:

l[7,5](0.0004amp;0.000080.00008amp;0.0001)=[(7×0.0004)+(5×0.00008)amp;(7×0.00008)+(5×0.0001)]=[0.0032amp;0.00106]{l}{\lbrack7,5\rbrack}{(\begin{array}{cc}0.0004&0.00008\\0.00008&0.0001\end{array})}\\={\lbrack{(7\times0.0004)}+{(5\times0.00008)}\begin{array}{cc}&\end{array}{{(7\times0.00008)}+{(5\times0.0001)}\rbrack}}\\={\lbrack0.0032\begin{array}{cc}&\end{array}}{0.00106\rbrack}

Step 2: Compute ( βh\beta_h × C)* βv\beta_v:

l[0.0032amp;0.00106][75]=(0.0032×7)+(0.00106×5)=0.0277{l}{\lbrack0.0032\begin{array}{cc}&\end{array}}{0.00106\rbrack}{\lbrack\begin{array}{c}7\\5\end{array}\rbrack}\\={(0.0032\times7)}+{(0.00106\times5)}=0.0277

Step 3:Compute σp\sigma_p:

σp=βh×C×βV=0.0277=0.1664\sigma_p=\sqrt{\beta_h\times C\times\beta_V}=\sqrt{0.0277}=0.1664

The 10-day portfolio VaR(in millions) at the 99% confidence level is then computed as:

VaRP=σPαX=0.1664×2.33×10=VaR_P=\sigma_P\alpha\sqrt X=0.1664\times2.33\times\sqrt{10}=$1.226 million

老师,请问这个解析讲义上有类似例题么?我听完了市场风险部分,但是对解析过程没有印象啊…

2 个答案

品职答疑小助手雍 · 2020年05月01日

使用具体金额而不是百分比算var的时候不用考虑权重的问题了,直接把具体金额带进去就可以了。

这里已经带入了7和5 million。

品职答疑小助手雍 · 2020年02月12日

这个解析写的太多了,其实主要就是求组合的标准差,然后*2.33*根号10就行了。标准差过程如下:

中二 · 2020年02月13日

不考虑mean吗?

品职答疑小助手雍 · 2020年02月13日

题面最后一句说了,假设收益期望为零。

卡布达 · 2020年05月01日

为什么不用乘以权重7/12和5/12