Finance 473 Debt and Money Market

Finance 473 Debt and Money Market

Exercise set 8

Andrei Simonov

Swaps

1. Given the following interest-rate swap:

• Fixed-rate payer pays half of the YTM on a T-note of 6.5%.
• Floating-rate payer pays the LIBOR
• Notional principal is $10M
• Effective dates are 3/23 and 9/23 for the next three years

Questions:

        a. Determine the net receipts of the fixed-rate payer given the following LIBORs:

• 3/23/y1           .055
• 9/23/y1                .060
• 3/23/y2         .065
• 9/23/y2                .070
• 3/23/y3                .075
• 9/23/y3                .080

         b. Show in a table how a company with a three-year, $10M variable rate loan, with the rate set by the LIBOR on the dates coinciding with the swap, could make the loan a fixed-rate one by taking a position in the swap. What would be the fixed rate?

        c. Show in a table how a company with a two-year, $10M fixed rate loan at 6.0%, could make the loan a floating-rate one by taking a position in the swap.

a. [pic 1]

b. Fixed Rate = 6.5%:

[pic 2]

c.[pic 3]

1. Explain how the fixed-payer and floating-payer positions in Question 1 could be replicated with positions in fixed-rate and floating-rate bonds.

The fixed position’s cash flows can be replicated by the fixed payer buying a $10M, three-year, flexible-rate note (FRN) with the rate reset every six months at the LIBOR and shorting (issuing) a $10M, 6.5% fixed-rate bond at par. These positions would yield the same cash flow as the fixed-rate payer’s swap in Question 1.

The floatingrate payer's position can be replicated by purchasing a three-year, $10M FRN paying the LIBOR and shorting (issuing) a three-year, $10M, 6.5% fixed-rate bond at par. These positions would yield the same cash flow as the floating-rate payer’s swap in Question 1.

1. Define a Eurodollar futures strip and the positions on the strip that would be similar to the fixed-payer and floating-payer positions in Question 1. Show in the table below the cash flows for each strip position given the LIBOR scenario in Question 1. Note: The interest payments on the swap are determined by the LIBOR at the beginning of the period, while the futures position's cash flows are based on the LIBOR at the end of its period.

The fixedrate payer's position is similar to a short position in a Eurodollar strip in which the short holder agrees to sell 10 Eurodollar deposits each with face values of $1M and maturities of six months at the IMMindex price of 93.5 (discount yield of RD = 6.5% and futures price of $967,500), with the expirations on the strip being March 23 and September 23 for a period of two and half years. Note: For the cash flow from the strip to match those on the swap, the strip payments or receipts need to be made six months after the effective date.