Question goes… Which of the following is equivalent to a receive-fixed swap with a tenor of one and a half years with semi annual payments and a fixed rate of 5% (exchanged for LIBOR)? Assume notional of $10m. A) A forward rate which obligates parties to receive a fixed rate of 5% and pay six month libor on a notional $10m. B) A strip of two FRAs which obligates the party to receive a fixed rate of 5% and pay six month LIBOR on $10m C) A strip of three FRAs which obligates party to receive a fixed of 5% and pay six-month LIBOR on a notional principle of $10m — Now, I’d see a semi annual swap as having three pay offs over 1.5 years. Month 6,12,18. So naturally, thought option C, the strip of 3 FRAs would be equivalent. Not so! Can somebody explain in non CFA English why we’re talking 2 payoffs from the FRA and not three? David

Interest rate Swaps are in arrears. So at the time of starting you already know the current LIBOR - and you would be paying it in say 6 months time. Then you need the LIBOR rates for the 6 months (paid in 1 year’s time) and then the 1 Year rate (paid in 18 months time). So you really need to know only 2 more rates.

So a Swap=FRA(N-1) since pmt 1 is known? Am I right in saying that the FRA will pay off in advance. So if at t=12 months, 180 day libor is 5%, I’ll be paid the PV = 5%/1+05*.05. This payment goes against my 12 month swap payment to net to zero. Again at t=18 months, I get the PV of the 180 day libor. The swap pays off in arrears so is essentially good for 18 months + 6 month libor. I think I’m getting rather confused with the payment timings.

I also think you get the payoff in advance in an FRA. This means on the settlement day. If I have a 6/12 FRA the settlement day is in 6 months and there the payment will occur in my opinion.

At t=0 you know LIBORt0 At t=1 Floating pays LIBORt0, Fixed pays fixed. Now you know LIBORt1 At t=2 Floating pays LIBORt1, Fixed pays fixed. Now you know LIBORt2 At t=3 (18 months) Floating pays LIBORt2, Fixed pays fixed. does that make it clearer.

CP, many thanks. I don’t mean to sound stupid here but… Each FRA has one payoff. The answer states we use a strip of two FRAs. So how do we get 3 payoffs with two FRAs? David

you already know one payoff, so you need only a strip with 2 payoffs.

what question number is this in qbank?

CPK, quick question regarding this. What if instead of FRA they had said what is equivalent to a SWAP in terms of interest rate caps and floors. Would we need two or three floorlets to be equal to teh SWAP? I always gets caps/floor and FRA, SWAP mixed up in figuring out which pays in arrears and which doesn’t.

not sure either.

floors and caps are not paid in arrears, as far as I know they are calculated on the expiration date like a stock option. Back to the question, you still know the payment at initiation, and the other two payments are unknown, so I would think you would have a set of two caplets and two floorlets - the caplets to simulate the payoff if interest rates increase and conversely, two floorlets to simulate payments if interest rates decrease.

TheAliMan Wrote: ------------------------------------------------------- > floors and caps are not paid in arrears, as far as > I know they are calculated on the expiration date > like a stock option. Back to the question, you > still know the payment at initiation, and the > other two payments are unknown, so I would think > you would have a set of two caplets and two > floorlets - the caplets to simulate the payoff if > interest rates increase and conversely, two > floorlets to simulate payments if interest rates > decrease. got it…thanks