Bank Management Solution

Correction for Solution to Class Assignment 3

4.b. The following information is available on a three-year swap contract. One-year maturity zero-coupon

discount yields are currently priced at par and pay a coupon rate of 5 percent. Two-year maturity zero-coupon

discount yields are currently 5.51 percent. Three-year maturity zero-coupon discount yields are currently 5.775

percent. The terms of a three-year swap of $100 million notional value are 5.45 percent annual fixed-rate

payments in exchange for floating-rate payments tied to the annual discount yield. (Hint: Assume Unbiased

Expectation Theory holds in this market)

What are the realized cash flows expected over the three-year life of the swap?

If the current spot rates (YTM of zero-coupon bonds or discount yields) are: d1 = 5 percent, d2 = 5.51 percent, and d3

= 5.775 percent, then the expected future one-year short rates (expected YTM of one –year zero-coupon bonds in

year 2 and year 3) can be calculated from the implied forward rates:

(1.0551)2 = (1.05)[1 + E(1r1)]

(1.05775)3 = (1.0551)2 [1 + E(2r1)]

E(1r1)= 6.02 percent

E(2r1) = 6.31 percent

End of year-1 expected cash flows (paying fixed rate receiving floating rate):

Cash outflow -$5.45 million + Cash inflow $5 million = -$0.45 million net cash outflow

End of year-2 expected cash flows:

Cash outflow -$5.45 million + Cash inflow $6.02 million = $0.57 million net cash inflow

End of year-3 expected cash flows:

Cash outflow -$5.45 million + Cash inflow $6.31 million = $0.86 million net cash inflow