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Work out the cash flows of a plain vanilla interest rate swap, explaining how it operates.

FRM® Part I · Financial Markets and Products · Swaps · FRM1.FM.20.a

The idea

A plain vanilla interest rate swap is an agreement to exchange interest on a notional principal over a stated life. One party pays a fixed rate and receives a floating rate, and the other does the opposite. The notional is never exchanged. It only sizes the payments, and on each date only the net amount moves. For a semi-annual swap, Net payment = N × (K − R) × 0.5. Here N is the notional, K the fixed rate and R the floating rate, and the fixed payer receives the amount if it is negative. The floating rate is set at the start of each period and paid at its end, so the first net payment is known at inception. Day counts matter, because fixed legs often use 30/360 and floating legs actual/360. Common mistakes are dropping the accrual fraction, reversing who pays, and using the rate observed on the payment date.

Formulas

Fixed payer's net swap payment for a period

net payment = N × (K − R) × τ

N
the notional principal
K
the fixed rate
R
the floating rate set at the start of the period
τ
the accrual fraction, 0.5 for semi-annual

A negative result means the fixed payer receives. Apply each leg's own day count when they differ, and never use the rate observed on the payment date.

A practice question

From the question bank, with the reason each wrong option is wrong.

In a plain vanilla interest rate swap, which description of the periodic exchange is correct?

  1. One party pays a fixed rate and the other a floating rate on the same notional, which is not exchanged. - correct
  2. One party pays the fixed rate, and the floating-rate payer's rate is fixed for the whole life too.Why not: The floating rate resets each period; it is not agreed once at initiation.
  3. Both parties pay floating rates, each tied to a different reference rate, on a common notional.Why not: Describes a basis swap, which exchanges two floating rates, not a plain vanilla swap.
  4. The notional is exchanged at inception and returned at maturity, with interest paid in between.Why not: Confuses an interest rate swap with a currency swap; one currency means no principal exchange.

A plain vanilla swap exchanges fixed-rate interest for floating-rate interest on a notional that only scales the payments and is never exchanged. The floating rate resets each period, and in practice only the net amount is paid on each date.

A harder one

A swap with notional USD 100 million pays 4.1% fixed on a 30/360 semi-annual basis against a floating rate on actual/360. The floating rate set at the start of the period is 3.9% and the period has 182 days. What is the fixed payer's net payment for the period?

  1. Receives USD 0.078 millionWhy not: Reverses the direction of the net payment; fixed exceeds floating so the fixed payer pays.
  2. Pays USD 0.105 millionWhy not: Uses actual/365 for the floating leg when the stem states actual/360.
  3. Pays USD 0.100 millionWhy not: Applies 0.5 to the floating leg instead of 182/360, ignoring the stated day count.
  4. Pays USD 0.078 million - correct

Fixed = 100 x 4.1% x 0.5 = 2.050; floating = 100 x 3.9% x 182/360 = 1.972. Net = 0.078 paid by the fixed payer. The day count of each leg must be applied as stated.

The hardest tier

A swap with notional USD 40 million has the fixed leg paid annually at 4.0% and the floating leg paid semi-annually. The floating rate is set at the start of each six-month period: 3.5% for the first and 3.9% for the second. For the fixed payer, what are the net cash flows at month 6 and month 12 (USD million)?

  1. Month 6: pay 0.100; month 12: pay 0.020Why not: Pays half the annual fixed amount every six months, but the fixed leg is paid only annually.
  2. Month 6: receive 0.700; month 12: pay 0.820 - correct
  3. Month 6: receive 0.700; month 12: pay 0.900Why not: Uses the 3.5% rate for both floating periods, ignoring the reset to 3.9%.
  4. Month 6: pay 0.700; month 12: receive 0.820Why not: Reverses the direction, treating the party as the floating payer.

Month 6: only the floating leg pays, 40 x 3.5% x 0.5 = 0.70 received. Month 12: fixed 40 x 4.0% = 1.60 paid, floating 40 x 3.9% x 0.5 = 0.78 received, net 0.82 paid. Payment frequencies of the two legs can differ.

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