LOS b: Calculate and interpret the duration of an interest rate swap.

Q1. The duration of a pay-floating swap is obtained by:

A)   adding the duration of the floating-rate payments to the duration of the fixed-rate payments.

B)   dividing the duration of the floating-rate payments by the duration of the fixed-rate payments.

C)   subtracting the duration of the floating-rate payments from the duration of the fixed-rate payments.

Q2. For a plain-vanilla interest-rate swap with annual reset and one year to maturity, which of the following is the swap’s duration?

A)   0.

B)   1.

C)   0.5.

Q3. For a pay-fixed counterparty, the duration of the swap will generally be (in absolute value terms):

A)   greater than the duration of the fixed-rate payments.

B)   equal to the duration of the fixed-rate payments.

C)   less than the duration of the fixed-rate payments.

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Q1. The duration of a pay-floating swap is obtained by:

A)   adding the duration of the floating-rate payments to the duration of the fixed-rate payments.

B)   dividing the duration of the floating-rate payments by the duration of the fixed-rate payments.

C)   subtracting the duration of the floating-rate payments from the duration of the fixed-rate payments.

Correct answer is C)

The duration of a pay-floating swap is the difference between the duration of the payments. Expressed as the formula: D_Pay-floating = D_{Fixed-rate payments} – D_{Floating-rate payments}.

Q2. For a plain-vanilla interest-rate swap with annual reset and one year to maturity, which of the following is the swap’s duration?

A)   0.

B)   1.

C)   0.5.

Correct answer is A)

Since this is an annual pay swap with 1 year left the durations of both the fixed and floating side are both 1 thus they cancel each other out so the overall duration of the swap to either side would be zero.

Q3. For a pay-fixed counterparty, the duration of the swap will generally be (in absolute value terms):

A)   greater than the duration of the fixed-rate payments.

B)   equal to the duration of the fixed-rate payments.

C)   less than the duration of the fixed-rate payments.

Correct answer is C)

Since the problem asks only about the absolute value, we can ignore the fact that the duration for this position will be opposite in sign to that we usually calculate. Although most of the duration is associated with the fixed payments, the next “floating” payment is predetermined. Therefore, for example, the duration of a quarterly-reset swap might be duration of fixed payments minus 0.25. Because she receives floating-rate cash flows, taking the pay–fixed/receive–floating position in a swap decreases the dollar duration of a fixed income portfolio.

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