 # swaps similar to a series of forwards?

I still don’t get how an interest rate swap can be described as a series of forward contracts. Can someone explain please? with numbers if possible

I don’t get the following paragraph from the notes:

Taliking about a one-year swap that pays at the end of each quarter

“a forward on 90-day Libor that settles 90 days from now, based on 90 day Libor at that time, actually pays the present value of the difference between the fixed rate F and 90-day Libor 90 days from now( times the notional principal amount). Thus, the forwards in our above example actually pay on days 90.180, and 270. However, the amounts paid are equivalent to the differences between the fixed rate payment and floating rate payment that are due when interest is actually paid on days 180,270 and 360,”

Consider a 4-year swap which settles every year. The notional principal is 100 million. The swap fixed rate is 10%. Say you are the fixed rate payer so you need to pay 10 million at the end of every year. If interest rates go up you benefit because you are paying 10 million even through the market rates are higher. If interest rates to down that is bad for you because you are paying a 10% rate even though the market rate is lower.

The swap I described above is similar to following series of agreements:

Paying 10% on a 100 million 1-year loan.

Forward rate agreement to pay10% on a 100 million 1-year loan which will starts one year from today.

Forward rate agreement to pay10% on a 100 million 1-year loan which will starts two years from today.

Forward rate agreement to pay10% on a 100 million 1-year loan which will starts three years from today.

As with the swap described earlier you benefit when rates go up because you’ve locked in a 10% rate even though the market rate is higher. When the market rates go down you are not happy because you still need to pay 10%.

Hopefully that clarfies how a swap is similar to a series of forward rate agreements.

Note that the simplified discussion above is based on a flat yield curve. When the yield curve is not flat we should say: a swap is similar to a series of off-market FRAs.

Regards,

Arif Irfanullah, CFA

Hi Arif,

Thanks so much for the explanation. I had a followup question, we know that in swaps variable payment at t=1 is based on LIBOR t=0.
Is this also the case in FRA, that the variable payment at t=n, is calculated as per the floating rate at t=n-1?

In an m×n FRA the FRA expires m months from inception, and the loan period extends from that time to n months from inception (i.e., it’s an (nm)-month loan). The floating rate on the loan is determined at time m; it’s the (then) current (nm)-month spot rate.

For example, in a 3×7 FRA the floating rate will be the 4-month spot rate at the expiration of the FRA (which is 3 months from inception).

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Thanks so much this makes it super clear.
Just to confirm in that in case of swaps interest payment at t=n is based on rate at t=n-1
Correct?

Absitively and posolutely.