Yield Curve

Question 1(20%).
Consider a financial institution with a bond portfolio comprised of sovereign country debt that has both interest rate and exchange rate risk exposure. The duration of assets is 3.4 years and the duration of liabilities is 5.2 years. The portfolio has assets of US$18 billion (including 2.5 billion euro) and liabilities of US$16 billion (including 4.15 billion euro) with no other currencies bought or sold forward.
a. What is the interest rate risk of the bond portfolio?
b. What is the foreign exchange rate risk of the bond portfolio?
c. If there is only a 1% chance that interest rates will decline 10 basis points or more tomorrow, what is the dollar daily value at risk at the 1% level?
d. If there is only a 1% chance that US dollar/euro exchange rates will increase by at least US$0.25 per euro tomorrow, what is the daily dollar value at risk at the 1% level?
e. What is the 1% dollar VaR for both interest rate and currency risks if the correlation between the risk exposures is –0.05?

Question 2 (20%).
You have been hired by a local Polish bank to help them design a bond portfolio to fund a $10 million pension obligation that will come due in 4 years. The managers of the bank would like to use a 2-year zero coupon bond along with an 8-year zero coupon bond to fund this obligation. Suppose that the yield curve is flat so that the yields to maturity on all zero coupon bonds are 5%.
(a) Design a portfolio of the two bonds that will protect the pension from fluctuations in interest rates. Provide both the current percentage and monetary positions in this portfolio.
(b) Suppose, that right after you create this portfolio, the yield curve shifts to 6% at all maturities. Calculate what you expect the future value of the investment in the two bonds to be in year 4. Do you meet the obligation of the bank? Explain any difference.