这道题怎么求解的，解释一下

问题如下：

A risk manager is evaluating the risks of a portfolio of stocks. Currently, the portfolio is valued at CAD 248 million and contains CAD 15 million in stock T. The annualized standard deviations of returns of the overall portfolio and of stock T are 16% and 13%, respectively. The correlation of returns between the portfolio and stock T is 0.45. Assuming the risk analyst uses a 1-year 95% VaR and the returns are normally distributed, what is the component VaR of stock T?

选项：

A.

CAD 0.096 million

B.

CAD 2.041 million

C.

CAD 1.444 million

D.

CAD 3.948 million

解释：

C is correct.

The component VaR for stock T (CVaRT) can be presented as:

CVaRT = VaRT*ρT,p,

where

VaRT = VaR of stock T

ρT,p = correlation coefficient between stock T and the portfolio.

Let;

wT represent the value of stock T,

σT represent the standard deviation of stock T returns, and α(95%) represent the 95% confidence factor for the VaR estimate, which is 1.645.

Hence,

VaRT = wT*σT*α(95%) = CAD 15 million x 0.13 x 1.645 = CAD 3.208 million.

Therefore,

CVaRT = ρT,p*VaRT = 0.45 x 3.208 = CAD 1.444 million.

A is incorrect. 0.096 is the marginal VaR of stock T, calculated as follows: (0.45*0.13/0.16)*1.645*0.16. Marginal VaR measure is unitless.

B is incorrect. CAD 2.041 million is the component VaR of stock T if the manager incorrectly uses the 99% VaR, i.e., 15*0.13*2.326*0.45.

D is incorrect. CAD 3.948 million is the incremental VaR of stock T (assuming that the volatility of the portfolio without stock T remains 16% and the correlation of returns between stock T and the portfolio without stock T is 0.45). It is simply the weight of stock T in the portfolio multiplied by the portfolio VaR, i.e. (15/248)*(248*0.16*1.645).