ANSWERS TO QUESTIONS AND PROBLEMS
215
B.
Construct a time line showing the net payments resulting from the two bonds.
Bond Portfolio Time Line:
C.
Construct a time line showing the payments for the swap.
Pay-Fixed Swap Time Line:
D.
Based on the two time lines from parts B and C, what conclusion can you draw regarding the relationship
between swaps and bond portfolios?
A plain vanilla swap can be constructed or synthesized by a bond portfolio. This is the case, because the
bond portfolio and the swap have identical cash flows. This suggests that the prices of bonds can be used to
value swaps, and that swaps can be used to transform cash flow patterns on bond portfolios.
2.
Assume that today is December 17, 2003. A firm enters a plain vanilla interest rate swap as the receive-fixed
party on a swap with a tenor of one year, quarterly payments at the end of the next four quarters, and a notional
principal of $25 million. At the same time, this firm buys a strip of Eurodollar futures for the next four con-
tracts, with 25 contracts per expiration. (Ignore daily settlement; in other words, assume that all futures-related
cash flows occur at the expiration of the futures contract, which occurs at the end of each quarter.) At present,
t
0, the LIBOR yield curve is flat at 8 percent, and the fixed rate on the swap is also 8 percent.
A.
Complete the following table using our familiar
LIBOR
t
notation. Assume that the Eurodollar futures rate
converges to LIBOR at expiration.
0
1
2
3
4
5
Year
0
LIBOR
× $10,000,000
1
LIBOR
× $10,000,000
2
LIBOR
× $10,000,000
3
LIBOR
× $10,000,000
4
LIBOR
× $10,000,000
$700,000
$700,000
$700,000
$700,000
$700,000
0
1
2
3
4
5
Year
0
LIBOR
× $10,000,000
1
LIBOR
× $10,000,000
2
LIBOR
× $10,000,000
3
LIBOR
× $10,000,000
4
LIBOR
× $10,000,000
$700,000
$700,000
$700,000
$700,000
$700,000
QuarterNet Receive-Fixed Swap Cash Flow
Net Long Futures Cash Flow
0
0
0
1
(0.08
LIBOR
0
)/4
$25,000,000
(0.08
LIBOR
1
)/4
$25,000,000
2
(0.08
LIBOR
1
)/4
$25,000,000
(0.08
LIBOR
2
)/4
$25,000,000
3
(0.08
LIBOR
2
)/4
$25,000,000
(0.08
LIBOR
3
)/4
$25,000,000
4
(0.08
LIBOR
3
)/4
$25,000,000
(0.08
LIBOR
4
)/4
$25,000,000