Interest Rate Swaps

CFA Level III
#1

Hey guys,

Having problems understanding the following:

  • Enter a fixed position to increase P’s duration and enter a floating position to reduce duration;
  • Dfixed - Dfloating > 0
  • Dfloating - Dfixed < 0

Are the above statements true without any qualifications to the direction of interest movement?

Thanks in advance

#2

When interest rates go down, you want to increase your portfolio duration. So you can enter into an IR swap by paying floating and recieving fixed. Therefore, Dswap = Dfixed - Dfloating > 0 and this will increase duration.

If IR goes up, you want to lower duration so you want to recieve floating and pay fixed since IR will be higher than fixed rate. Dswap = Dfloating - Dfixed < 0 thus reducing duration.

#3

key to understanding it is what is the duration of fixed vs. floating

fixed = pro-rated fractional equivalent of time to maturity (assumed in the book for convenience though there is a theoretical support to it discussed in L2) so for example duration of one-year fixed is 0.75

floating= similarly fractional equivalent to time to maturity (which is just the next coupon) so a quarterly payment will be 0.125 (representing average of 0.0 and 0.25 yr).

so now clearly you will see fixed > floating, then take the appropriate position to raise or cut duration

#4

Fixed position in a swap:

Assume the notional principal is 1000$, 2yr swap and fixed rate of 5%, which implies a fixed pay of 50$. The present value of these amount are dependent on the interest rates/discounting rates ( say, LIBOR).

But for the float side of the swap, its dependent on the LIBOR(say). So, if you want to calculate the PV, its already fluctuating with the Interest rate/discounting rates.

Hence, As you can see, the fixed rate payments are more sensitive to the Int. rates. This sensitivity is nothing but Duration. => Fixed Position has higher sensitivity => higher duration.

Like wise Dfixed > Dfloat ======= > Dfixed - Dfloating > 0

Hope this helps.

#5

LIBOR term is usually quite short ( 3 month to 6 month ). So floating rates are offsets from Libor.

Fixed rate loans usually have a term of at least 1 year and usually longer.

So usually ( and traditionally ) fixed always has longer duration than floating

#6

Floating rate bonds have very short (modified) durations, because the price resets to (nearly) par at each coupon date. CFA Institute occasionally tells the candidates to use zero years as the duration of a floating-rate bond, and occasionally tells candidates to use ½ of the time between payment dates.

If you think of a plain vanilla, fixed-for-floating interest rate swap as an exchange of bonds, then the fixed-rate payer will be long a floating-rate bond with a duration close to zero, and short a fixed-rate bond with a longer duration; the net position will be negative duration. The opposite is true for the fixed-rate receiver.

So, if you want to increase the duration of a fixed-income portfolio, add a receive-fixed, pay-floating swap. If you want to decrease the duration of a fixed-income portfolio, add a pay-fixed, receive-floating swap.

By the way, the size of the swap you’ll need is determined by the dollar duration change you want: calculate the (net) duration of the swap (receive duration - pay duration), then divide the dollar duration change by that number to get the notional amount of the swap.