#### sorry, they do equal.. please ignore this post ####
Hello David,
I'm sorry but this question is from 2008 practice exam and the answer is quite long, but I'm just wondering why can't we simply just use sqrt(VaR1^2+VaR2^2+2(VaR1)(VaR2)(p)) to get the portfolio variance (ie. sqrt(77632^2+27911^2+2(.602)(77632)(27911))? The VaRs were already in USD units - I tried that but got a different answer.
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. Note that the question asks for the VAR number to be expressed in USD. Therefore, the first step is to convert the foreign currency positions in terms of USD.
Dealer A’s position in USD: 10,000,000/1.2350 = USD8,097,166
Dealer B’s position in USD: 10,000,000/1.5905 = USD6,287,331
Given 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 = 77,632
Therefore, 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 of the 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
Thank you!
Hello David,
I'm sorry but this question is from 2008 practice exam and the answer is quite long, but I'm just wondering why can't we simply just use sqrt(VaR1^2+VaR2^2+2(VaR1)(VaR2)(p)) to get the portfolio variance (ie. sqrt(77632^2+27911^2+2(.602)(77632)(27911))? The VaRs were already in USD units - I tried that but got a different answer.
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. Note that the question asks for the VAR number to be expressed in USD. Therefore, the first step is to convert the foreign currency positions in terms of USD.
Dealer A’s position in USD: 10,000,000/1.2350 = USD8,097,166
Dealer B’s position in USD: 10,000,000/1.5905 = USD6,287,331
Given 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 = 77,632
Therefore, 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 of the 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
Thank you!
