Interest Rate Swaps

[roumancesoiree]

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

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

 

[Ishi93]

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

 

[QNA2012]

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

 

[ganeshrpl]

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.

 

[janakisri]

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