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Confused in the GARP response to this question

SamuelMartin

New Member
Consider the following 6-9 FRA. Assume the buyer of the FRA agrees to a contract rate of 6.35% on a notional amount of $10 million USD. Calculate the settlement amount of the seller if the settlement rate is 6.85%. Assume a 30/360 day count basis ?
a) -12500,
b) -12290,
C) 12500
d) 12290

In the solution the correct answer is b. However, in the solution the amount given is positive, which answer would be D no B.

My question is: It is positive or negative and why? Thank you so much


Solution:
The difference in the interest rates is 0.5% for one year, or 0.125% for 3 months; 0.125% of $10 million is $12,500. However, FRAs are settled at inception, not at maturity, so that $12,500 has to be discounted for three months at 6.85% (the market rate), to get a present value (at inception of the loans, 6 months after the initiation of the FRA) of $12,290
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi @SamuelMartin

I do not like this question; what's the source (I don't see it sorry) so I can feedback to GARP?

The FRA buyer promises to pay the fixed rate (the "buyer" is the one who hedges future borrowing, such that the buyer is seeking to effectively lock-in a future borrowing rate). So, in the case, when the prevailing market rate (settlement rate) is higher (which will be the borrower's actual cost), they will receive the difference to achieve a net rate equal to the fixed rate. That is, the FRA seller will pay 12,290 to the FRM buyer. If the settlement (aka, market or floater) rate were lower than contract (fixed) rtae of 6.35%, then the FRA buyer would pay the difference to the FRA seller (i.e., the buyer would enjoy a better market rate so owes the difference to the seller). To keep this straight, just remember the FRA buyer will pay the fixed rate because the FRA buyer plans to hedge a future borrowing.

But I am opposed to buyer/seller semantics for FRAs and swaps: Hull does not employ these terms. Fixed/floating and fixed/market are more intuitive and used by Hull.

If the question really reads "Calculate the settlement amount of the seller if the settlement rate is 6.85%" then I think's poorly worded ... I hope that helps.
 

Arnaudc

Member
Hi Samuel,

Maybe this is clear from vgodawat but here is how to see it:
A FRA buyer buys a contract with a strike rate set an contract inception (the FRA rate). Then at settlement, you compare the actual rate with the strike rate (which was set at initiation).
If the actual rate is > FRA, then the buyer of the contract earns money : the difference between Actual rate - FRA, discounted at this same rate because you would settle immediately (you do not wait 3 months to receive the money). As a result, the seller loses money.
The amount is negative here (and the question is a bit misleading I find) because they start by saying " Assume the buyer of the FRA agrees to a contract rate of 6.35%" but actually the question is: "Calculate the settlement amount of the seller" which might be the reason for your confusion?

Hope this helped clarifying...

Kind regards,
 
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