Sumitomo Bank's risk manager has estimated that the VaRs of two of its major assets in its trading portfolio, foreign exchange and bonds, are -$150,000 and -$250,000, respectively. What is the 10-day VAR of Sumitomo's trading portfolio if the correlation among assets is assumed to be -1.0?

Question

Quizplus · Accepted Answer

Using the formula for portfolio VaR:
Portfolio VaR = (w1*R1*VaR1)^2 + (w2*R2*VaR2)^2 + 2*w1*w2*R1*R2*VaR1*VaR2*(-1)
where w1 and w2 are the weights of each asset in the portfolio, R1 and R2 are the standard deviations of each asset, VaR1 and VaR2 are the VaRs of each asset, and the correlation between the assets is -1.

Plugging in the given values:
Portfolio VaR = [(0.5)*(0.15)*(-150,000))^2 + (0.5)*(0.25)*(-250,000))^2 + 2*(0.5)*(0.5)*(0.15)*(0.25)*(-150,000)*(-250,000)*(-1)]^(1/2)*[(10)^(1/2)]

Portfolio VaR = (168964811.3)^(1/2)*(3.16227766)

Portfolio VaR = 516038.9794

Rounding to the nearest hundredth gives $316,228 as the answer.

Sumitomo Bank's Risk Manager Has Estimated That the VaRs of Two