Exercises 7 to 9 use the two yield curves at two moments in time in Table 3.7, and the following portfolio:

Long $20 million of a 6-year inverse floaters with the following quarterly coupon:

Coupon at t = 20% r4(t 0.25)

where r4(t) denotes the quarterly compounded, 3-month rate.

Short $20 million of 4-year floating rate bonds with a 45 basis point spread paying semiannually

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

7. You are standing on February 15, 1994 and you hold the following portfolio:

(a) What is the total value of the portfolio?

(b) Compute the dollar duration of the portfolio.

8. You are worried about interest rate volatility. You decided to hedge your portfolio a 3-year coupon bond paying 4% on a semiannual basis.

(a) How much should you go short/long on this bond in order to make it immune to interest rate changes?

(b) What is the total value of the portfolio now?

9. Assume that it is now May 15, 1994 and that the yield curve has changed accordingly (see Table 3.7).

(a) What is the value of the unhedged portfolio now?

(b) What is the value of the hedged portfolio?

(c) Is the value the same? Did the immunization strategy work? How do you know that changes in value are not a product of coupon payments made over the period?

Table 3.7 Two Term Structures of Interest Rates 02/15/94 Yield (c.c.) 02/15/94 Z(t,T) 05/13/94 Yield (c.c.) 05/13/94 Zt, T) 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 3.53% 3.56% 3.77% 3.82% 3.97% 4.14% 4.23% 4.43% 4.53% 4.57% 4.71% 4.76% 4.89% 4.98% 5.07% 5.13% 5.18% 5.26% 5.31% 5.38% 5.42% 5.43% 5.49% 5.53% 0.9912 0.9824 0.9721 0.9625 0.9516 0.9398 0.9287 0.9151 0.9031 0.8921 0.8786 0.8670 0.8531 0.8400 0.8268 0.8145 0.8023 0.7893 0.7770 0.7641 0.7525 0.7418 0.7293 0.7176 4.13% 4.74% 5.07% 5.19% 5.49% 5.64% 5.89% 6.04% 6.13% 6.23% 6.31% 6.39% 6.42% 6.52% 6.61% 6.66% 6.71% 6.73% 6.77% 6.83% 6.86% 6.89% 6.93% 6.88% 0.9897 0.9766 0.9627 0.9495 0.9337 0.9189 0.9020 0.8862 0.8712 0.8558 0.8406 0.8255 0.8117 0.7959 0.7805 0.7663 0.7519 0.7387 0.7251 0.7106 0.6977 0.6846 0.6713 0.6619 Notes: Yields are calculated based on data from CRSP (Daily Treasuries). Table 3.7 Two Term Structures of Interest Rates 02/15/94 Yield (c.c.) 02/15/94 Z(t,T) 05/13/94 Yield (c.c.) 05/13/94 Zt, T) 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 3.53% 3.56% 3.77% 3.82% 3.97% 4.14% 4.23% 4.43% 4.53% 4.57% 4.71% 4.76% 4.89% 4.98% 5.07% 5.13% 5.18% 5.26% 5.31% 5.38% 5.42% 5.43% 5.49% 5.53% 0.9912 0.9824 0.9721 0.9625 0.9516 0.9398 0.9287 0.9151 0.9031 0.8921 0.8786 0.8670 0.8531 0.8400 0.8268 0.8145 0.8023 0.7893 0.7770 0.7641 0.7525 0.7418 0.7293 0.7176 4.13% 4.74% 5.07% 5.19% 5.49% 5.64% 5.89% 6.04% 6.13% 6.23% 6.31% 6.39% 6.42% 6.52% 6.61% 6.66% 6.71% 6.73% 6.77% 6.83% 6.86% 6.89% 6.93% 6.88% 0.9897 0.9766 0.9627 0.9495 0.9337 0.9189 0.9020 0.8862 0.8712 0.8558 0.8406 0.8255 0.8117 0.7959 0.7805 0.7663 0.7519 0.7387 0.7251 0.7106 0.6977 0.6846 0.6713 0.6619 Notes: Yields are calculated based on data from CRSP (Daily Treasuries)