Duration of an IRS

[Angshuman]

Hi David,
can you please tell how to compute duration of an Interest Rate Swap? The problem is that the cash flow of the floating leg, if we consider up to first reset date, is too small compared to the fixed leg. Does the 'Duration' of an IRS has got any practical application/significance or it is a mere theoretical exercise?

 

[David Harper CFA FRM]

Hi Angshuman,
Please this modified sample question (question 9b) from the 2009 Sample L1 exam:
http://forum.bionicturtle.com/viewthread/1180/

....the duration of an interest rate swap is the sort of question that may be asked. You are quite right about the cash flows: since we can view a fixed-for-floating swap as two bonds (per Hull's valuation), the duration is the net duration of the two bonds. The floater will have duration of approximately "time to next coupon payment" (e.g., semi-annual settment implies duration of less than 6 months).

So the swap will have (net) duration = (duration on long bond leg) - (time to next coupon on floater).

Practical application: yes, b/c altering duration is solution to a problem of "how can i change the (rough) sensitivity of portfolio to interest rate change (market risk)?" There may be various motives to engaging in the swap, but if changing the interest rate sensitivity (or hedging the same) of portfolio is the goal, then duration may be useful to measure that.

David