最近复习FRM level1, 做到2008年practice exam里的第12题：

Bank Omega’s foreign currency trading desk is composed of 2 dealers; dealer A, who holds a long

position of 10 million CHF against the USD, and dealer B, who holds a long position of 10 million SGD

against the USD. The current spot rates for USD/CHF and USD/SGD are 1.2350 and 1.5905 respectively.

Using the variance/covariance approach, you worked out the 1 day, 95% VAR of dealer A to be

USD77,632 and that of dealer B to be USD27,911. If the correlation coefficient between the SGD and

CHF is +0.602 and assuming that these are the only trading exposures for dealer A and dealer B, what

would you report as the 1 day, 95% VAR of Bank Omega’s foreign currency trading desk using the

variance/covariance approach?

a. USD 97,027

b. USD 105,543

c. USD 113,932

d. Cannot be determined due to insufficient data

答案为a，解释是：

Note that the question asks for the VAR number to be expressed in USD. Therefore, the first step is toconvert the foreign currency positions in terms of USD.Dealer A’s position in USD: 10,000,000/1.2350 = USD8,097,166Dealer B’s position in USD: 10,000,000/1.5905 = USD6,287,331Given that the VAR of dealer A is USD77,632, we first work the daily volatility for the USD/CHF,denoted here by sCHF By definition we get 8,097,166 x 1.645 x sCHF = 77,632Therefore, sCHF = 77,632/(8,097,166 x 1.645) = 0.005828 or 0.5828%Similarly, the daily volatility for the USD/SGD, denoted here by sSGD is worked out as follows:sSGD = 27,911/(6,287,331 x 1.645) = 0.002699 or 0.2699%. By definition, the standard deviation ofthe change in the portfolio which comprises of both the currency pairs over a 1-day period is given by:[(0.005828 x 8,097,166)2 + (0.002699 x 6,287,331)2 + 2 x 0.602 x (0.005828 x 8,097,166) x(0.002699 x 6,287,331)]0.5 = [(46,963.56)2 + (16,975)2 + 959,881,479.22]0.5 =[3,453,608,072.09]0.5 = 58,983. Therefore, The 1-day, 95% VAR is 1.645 x 58,983 = USD97,027
我不能理解的是题中写的current spot rates for USD/CHF and USD/SGD are 1.2350 and 1.5905，dealer A有10million的CHF，为什么答案中dealer A的position换成USD是10,000,000/1.2350 = USD8,097,166？不应该是10,000,000＊1.2350吗？谢谢高手指导