It is May 15, 2000 and an investor is planning to invest $100 million in one of the two portfolios below. The investor’s main concern is the change in interest rates that might affect the short-term value of the portfolio.
A. Compute the change in price of the security stemming from duration and convexity. Which portfolio is less sensitive to changes in interest rates (assume 1% increase in interest rates)? Assume today is May 15, 2000, which means you may use the yield curve presented in the following table:
Maturity T Yield r2 (0, T)
0.50 6.49%
1.00 6.71%
1.5 6.84%
2 6.88%
• Portfolio A – 40% invested in 1.5-year zero coupon bond – 60% invested in 1.5-year coupon bond paying 9% annually
• Portfolio B – 50% invested in 2-year zero coupon bond – 50% invested in 1.5-year floating rate bond with zero spread and annual payments.
B. Suppose the investor has chosen portfolio A in part A above, but the investor is still worried about the losses that the portfolio may suffer from an upward shift in the term structure of interest rates.
(a) Consider duration hedging using 1-year zero coupon bonds. Find the dollar position.
(b) Consider duration+convexity hedging using both 1-year and 5-year zero coupon bonds. Find the dollar position on each bond.