An analyst would like to know the VaR for a portfolio consisting of two asset cl
ID: 2806211 • Letter: A
Question
An analyst would like to know the VaR for a portfolio consisting of two asset classes: long term government bonds issued in the United States and long-term government bonds issued in the United Kingdom. The expected weekly return on U.S. bonds is 0.85 percent, and the standard deviation is 3.2 percent. The expected weekly return on U.K. bonds, in U.S. dollars, is 0.95 percent, and the standard deviation is 5.26 percent. The correlation between the U.S. dollar returns of U.K. and U.S. bonds is 0.35. The portfolio market value is $100 million and is equally weighted between the two asset classes. TASK. Using the analytical or variance-covariance method, compute the following: a. b. c. d. 5 percent monthly VaR. 1 percent monthly VaR. 5 percent weekly VaR. 1 percent weekly VaR.Explanation / Answer
5% VaR = 1.65x portfolio
1% VaR = 2.33xportfolio
2portfolio = w12 12 + w22 22 +2(w1 1w2 2 q(1,2))
Where w1 = the portfolio weight of the first asset
w2 = the portfolio weight of the second asset
1 = the standard deviation of the first asset
2 = the standard deviation of the second asset
q(1,2) = the correlation between the two assets
Monthly 1 = 3.2x2 = 6.4
2 = 5.26x2 = 10.52
Monthly 2portfolio = 0.52(0.064)2 + 0.52(0.10522) +2(0.5x0.064x0.5x0.1052x0.35) = 0.005
Monthly portfolio = 0.0707
Weekly 2portfolio = 0.52(0.0322) + 0.52(0.05262) + 2(0.5x0.032x0.5x0.0526x0.35) = 0.0013
Weekly portfolio = 0.036
a. 5 percent monthly VaR = 1.65x0.0707 = 0.1167 = 11.67%
b. 1 percent monthly VaR = 2.33x 0.0707 = 0.1647 = 16.47%
c. 5 percent weekly VaR = 1.65x0.036 = 0.0594 = 5.94%
d. 1 percent weekly VaR = 2.33x0.036= 0.0839 = 8.39%