Quiz: Interest Rate Swaps

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6 questions to check your understanding of the chapter “Interest Rate Swaps”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.

1. Question 1

   As a hypothetical example, in an interest rate swap that exchanges a fixed rate and a floating rate on a notional amount of 10 billion yen, what do the two parties actually pay each other?

   1. A.The 10 billion yen notional amount at the start and the end of the trade, plus the interest each year
   2. B.Only the 10 billion yen notional amount at the end of the trade
   3. C.Only the interest calculated by multiplying the notional amount by each rate
   Answer and explanation

   Answer: C

   In an interest rate swap, the parties exchange only interest. The notional amount is the principal that the pay-fixed side and the receive-fixed side each multiply by their own rate to calculate interest, and it is not exchanged at the start or at the end of the trade. If you think of the swap like a loan of 10 billion yen, it is easy to assume that 10 billion yen moves at the start and the end, or is repaid at the end. Neither happens in an interest rate swap.

   Learn more: Interest Rate Swaps

2. Question 2

   Which fixed rate is the par rate of an interest rate swap?

   1. A.The fixed rate agreed when the trade is made, which stays the same until maturity
   2. B.The fixed rate at which the swap's value, using current market rates, is zero
   3. C.The rate for a future period, derived from today's curve
   Answer and explanation

   Answer: B

   The par rate is the fixed rate at which the value is zero. At this rate, the present value of the floating-rate payments equals the present value of the fixed-rate payments.

   The agreed fixed rate is set so that the present values of both sides are equal when the trade is made, so for a trade made at market rates it equals the par rate right after the trade. Once market rates move after the trade and the value is no longer zero, the par rate differs from the agreed fixed rate. For example, if all market rates rise by 1bp, the par rate rises by 1bp, but the agreed fixed rate stays the same. A rate for a future period derived from today's curve is a forward rate, which is used to project the floating-rate payments.

   Learn more: Valuing an Interest Rate Swap

3. Question 3

   As a hypothetical example, you hold a pay-fixed swap with a notional amount of 10 billion yen, 5 years remaining, and a fixed rate of 1.00%. Today's 5-year par rate is 1.10%, and the sum $A$ of each payment date's discount factor times the period length (1 year) is 4.857148. Which value is closest to the value of the swap for the pay-fixed side?

   1. A.−48.57 million yen
   2. B.10 million yen
   3. C.50 million yen
   4. D.48.57 million yen
   Answer and explanation

   Answer: D

   The value of a pay-fixed swap is the difference between today's par rate $S$ and the agreed fixed rate $K$, multiplied by the notional amount $N$ and by $A$. A new 5-year swap would require you to pay 1.10% each year, while this trade requires only 1.00%, so the value is positive.

   $$V = N (S - K) A = 10 \text{ billion yen} \times 0.10\% \times 4.857148 \approx 48.57 \text{ million yen}$$

   Calculated to the nearest yen, the value is 48,571,481 yen. The choice "10 million yen" is the difference for a single year (10 billion yen × 0.10%). The choice "50 million yen" adds up the five years of differences without applying the discount factors. The choice "−48.57 million yen" is the value of the same trade for the receive-fixed side, which is the pay-fixed side's value with the opposite sign.

   Learn more: Valuing an Interest Rate Swap

4. Question 4

   A yen OIS (overnight index swap) exchanges a fixed rate for a floating rate calculated by compounding TONA (Tokyo Overnight Average Rate) over the period. When is the amount of floating-rate interest determined?

   1. A.On the last day of the interest period
   2. B.On the day the trade is agreed
   3. C.Before the interest period starts
   Answer and explanation

   Answer: A

   The floating rate of an OIS is set at the end of the period by compounding TONA for every business day in the period. This method is called compounding in arrears. As a result, the amount of floating-rate interest is not known until the last day of the period. In one example, the Bank of Japan publishes the final figure for the previous business day's TONA at around 10:00 a.m. on the last day of the period (the maturity date), and the floating amount is calculated using that figure.

   The fixed-rate interest is set on the day the trade is agreed. The floating rate is built up by compounding TONA over the period, so it is not set before the interest period starts.

   Learn more: Overnight Index Swaps (OIS)

5. Question 5

   As a hypothetical example, Bank E enters a 3-year basis swap with a notional amount of 10 billion yen. It pays 3-month TIBOR (Tokyo Interbank Offered Rate) and receives the compounded TONA over the period plus 0.2% a year as the basis spread. What determines Bank E's profit or loss every 3 months?

   1. A.Whether TIBOR and compounded TONA have each risen or fallen from the previous period
   2. B.Only the level of the 3-month TIBOR that Bank E pays
   3. C.Whether the gap between TIBOR and compounded TONA is smaller or larger than 0.2%
   Answer and explanation

   Answer: C

   The profit or loss of a basis swap is determined by the gap between the two floating rates, not by the level of rates. Bank E receives in a period when the gap between TIBOR and compounded TONA is smaller than 0.2%, and pays in a period when it is larger. For example, if 3-month TIBOR is 0.9% a year for a period and compounded TONA is 0.6% a year, the gap is 0.3%. After subtracting the 0.2% spread, the net is 0.1%, and Bank E pays 10 billion yen × 0.1% × 0.25 years (3 months) = 2.5 million yen.

   Even if TIBOR and compounded TONA both rise from the previous period, the payments balance when the gap equals the spread. Looking only at the level of TIBOR does not settle the result unless you know the gap from compounded TONA.

   Learn more: Basis Swaps

6. Question 6

   As a hypothetical example, Company B uses a 4-year amortizing swap, whose notional amount falls from 10 billion yen by 2.5 billion yen each year, to change the floating rate on its loan into a fixed rate. Company B repays the rest of the loan at the end of year 2 and leaves the swap contract unchanged. What happens to the swap from year 3?

   1. A.The swap's value becomes 0 at the moment the loan is repaid
   2. B.It remains as an interest rate swap that pays a fixed rate with no loan behind it
   3. C.The notional amount keeps falling as scheduled, but the fixed-rate payments stop
   Answer and explanation

   Answer: B

   The way the notional amount declines is fixed in the contract when the trade is made, so even if the loan is repaid early, the swap's notional amount keeps falling as scheduled unless the contract is changed. In this example, the swap with a notional amount of 5 billion yen in year 3 and 2.5 billion yen in year 4 remains with no loan behind it, and it is the same as an interest rate swap that pays a fixed rate without a loan.

   Repaying the loan alone does not stop the swap's payments. To end the swap early, one party must pay the other an amount equal to its value, and the value does not become 0 just because the loan is repaid.

   Learn more: Amortizing Swaps