Duration and Convexity
Your research department reports continuously compounded interest rates as
Maturity (Years) ---Interest Rate (%)
0.5---1.00
1.0---1.50
1.5---2.00
2.0---2.00
(1) Suppose that the monthly changes in the interest rates have a mean of zero and a standard deviation of 0.5%. Obtain the monthly 95% Value at Risk and Expected Shortfall on the coupon bond.
(2) Construct a hedge portfolio of 1 coupon bond and k one-year zero coupon bonds that has zero duration. What is the value of k? What is the convexity of the hedge portfolio?