ANSWERS TO QUESTIONS AND PROBLEMS
233
B. Assuming a notional principal of $100 million, state the transactions that you would enter to secure the arbi-
trage profit.
t
5
0
Sell 1 call for 150 basis points
5
0.0150
3
$100,000,000
51
$1,500,000.
Buy 1 put for 143 basis points
5
0.0143
3
$100,000,000
52
$1,430,000.
Enter a pay-fixed position in the FRA on one-year LIBOR with a one-year maturity at a contract rate of 5.70 percent.
Net Cash Flow:
1
$70,000
t
5
1
There will be a net zero obligation no matter what the one-year spot rate for LIBOR is. Consider two examples, with one-year
LIBOR at 5.60 and 5.80 percent:
LIBOR
5
5.60 percent
Call expires worthless.
Long put is worth (0.0570
2
0.0560)
3
$100,000,000
51
$100,000.
FRA obligation is (
2
0.057
1
0.056)
3
$100,000,000
52
$100,000.
Net Obligation: 0
LIBOR
5
5.80 percent
Short call is exercised against arbitrageur: (0.0580
2
0.0570)
3
$100,000,000
52
$100,000.
Put expires worthless.
Pay-fixed FRA pays (0.0580
2
0.0570)
3
$100,000,000
51
$100,000.
Net Obligation: 0
C. Compute the present value of the arbitrage profit.
The present value of the arbitrage profit is $70,000, because it is received immediately at the time of
contracting and no other cash flows are incurred.
2. An inverse floating rate note, or inverse floater, is a debt instrument with a floating rate that moves inversely
with market rates. Generally, an inverse floater pays a fixed rate minus LIBOR. Consider an FRN with a
principal amount of $50 million paying LIBOR with a five-year maturity. Consider also a plain vanilla interest
rate swap with a fixed rate of 7 percent, a floating rate equal to LIBOR, a notional principal of $100 million,