Consider the following portfolio under continuosly compounded yield curve given below:

- Long $20 million of a 5-year inverse floater with the following quarterly coupon: Coupon at t = 10%-r4(t-0.25) where r4(t) denotes the quarterly compounded, 3-month rate.   

- Long $20 million of a 6-year floating rate bond with a 10 basis point spread paying semiannually.   

- Short $30 million of a 5-year zero coupon bond.   

a. What is the total value of the portfolio?   

b. Compute the dollar duration of the portfolio.   

c. How much should you go short or long on 3-year coupon bond paying 3.50% on a semiannual basis to make it immune to interest rate changes?   

d. What is the total value of the portfolio now?   

 

Maturity 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 Yield (c.c) 2.76% 3.37% 3.70% 3.82% 4.12% 4.27% 4.52% 4.67% 4.76% 4.86% 4.94% 5.02% 5.05% 5.15% 5.24% 5.29% 5.34% 5.36% 5.40% 5.46% 5.49% 5.52% 5.56% 5.51%