# 2018 CMP Q&A Bank Question 3.8(iii)

Discussion in 'SP5' started by wyatt.krs, Jul 11, 2019.

1. For ease of reference, I have included a screenshot of the question below. In the solution, it states that

caplet = floorlet + (pay fixed & receive floating)
(1)

and then it goes on to say that

caplet = floorlet + (FRA borrowing at the fixed rate) (2)

and

floorlet= caplet + (FRA lending at the fixed rate) (3)

I don't understand why FRA is borrowing at the fixed rate in the equation (2) while it says that 'pay fixed and receive floating' in equation (1). From whose point of view are we looking at the cashflow?

2. ### Colin McKeeActEd TutorStaff Member

Hi, This is quite a technical question from the old Q&A and is actually in the end of chapter questions from SP5 as well. Your question is why "pay fixed and receive floating" over a future period is the same as "FRA borrowing at a fixed rate" over the period. Essentially an FRA is a derivative that allows an investor to lock in a fixed rate of borrowing over a future period. If the rate turns out to be higher, the investor is compensated to bring the borrowing cost back down to the agreed rate, and if the borrowing rate turns out to be lower then the investor must compensate the counterparty and bring their cost of borrowing back up to the agreed rate.
The payoff is the same as if the investor pays a fixed (agreed) rate over the period and agrees to receive a floating rate. If the actual rate "floats" up above the fixed agreed rate, then the investor gets a net payment. If it floats below the agreed rate, then the net payment is negative. So the two concepts lead to the same payoff profile.

3. Hi Colin, thank you for your explanation.

I think what I don't understand is why we can't view 'pay fixed & receive floating' as the seller of FRA, which means the investor is lending at the fixed rate and receiving floating rate. The payoff profile will still be the same as the buyer of FRA, but just in opposite direction, no?

Last edited: Jul 12, 2019
4. ### Colin McKeeActEd TutorStaff Member

I dont follow this. If you "lend" at the fixed rate you would "receive" fixed. But you have described "pay fixed" as "lending at fixed" which I dont follow.

5. Sorry Colin, I was doing that late at night and couldn't focus too well. Now I understand it! Thank you 