FRA Question

[Delo]

An investor has entered into a forward rate agreement (FRA) where she has contracted to pay a fixed rate of 5 percent on $5,000,000 based on the quarterly rate in three months. If interest rates are compounded quarterly, and the floating rate is 2 percent in three months, what is the payoff at the end of the sixth month? The investor will:

1. receive a payment of $37,500.
2. make a payment of $75,000.
3. receive a payment of $75,000.
4. make a payment of $37,500

Explanation
Payoff = $5,000,000 (0.02 - 0.05)(0.25) = -37,500. The negative sign means the investor will make a payment of $37,500.

....
Shouldn't the question mention "three" months instead of "sixth"? ................."what is the payoff at the end of the sixth month?"

 

[ShaktiRathore]

Hi
It should be sixth only,we are given flaoting rate at t=3mnth,this rate at end of 3rd month shall determine next net pay over next quarter which is at end of sixth month. Net pay at end of 6th mnth=fixed pay-floating received based on floating rate at end of previous quarter i.e. At end of 3rd month=5%*5000000*.25-.02*5000000*.25=.03*5000000*.25=150000*.25=37500 is net pay by fixed rate payer while its -37500 for fixed rate receiver means receiver shall receive net pay of 37500. If net amt receive were calculated then net amt received by ficed rate payer=floating pay receive-fixed rate pay=.02*5000000*.25-.05*5000000*.25=-37500 means fixed payer receives -37500 or pays 37500.
Thanks

 

[cyrilgedeon]

An investor has entered into a forward rate agreement (FRA) where she has contracted to pay a fixed rate of 5 percent on $5,000,000 based on the quarterly rate in three months. If interest rates are compounded quarterly, and the floating rate is 2 percent in three months, what is the payoff at the end of the sixth month? The investor will:

A)make a payment of $37,500.

B)receive a payment of $37,500.

C)make a payment of $75,000.

D)receive a payment of $75,000.

Straight forward question:
Payoff = $5,000,000 (0.02 - 0.05)(0.25) = -37,500. The negative sign means the investor will make a payment of $37,500, Since the question is asking for pay-off in 6 months, then we would take -37,500 X 2 = 75,000, the answer would be C - correct?

I am confused since the answer is A, but I think its a mistake.

 

[David Harper CFA FRM]

Hi @cyrilgedeon Can you I ask you the source of the question so we can tag it? Please see @ShaktiRathore 's response, which I agree with, the answer is (A) because FRA loan period is three months; i.e., it is forward rate beginning in three months and paid at the end of six months. So the payment = Notional * (5.0% paid - 2.0% received) * (0.50 years - 0.25 years) = $5.0 mm * (pay 5.0% - 2.0%) * 0.25 years = pay $37,500. Same as Shakti. To compare, if the FRA were instead for a loan period of six months beginning in three months--that it is, if it were F[0.25, 0.75] instead of the asked-for F[0.25, 0.50]--then the payment in arrears occurs in nine months but references a six month loan period and, then, it would be $5.0 mm * (5.0% - 2.0%) * (0.75 - 0.25) = $75,000. I hope that helps!

 

[cyrilgedeon]

Thanks for the explanation David, It makes sense now.

This was taken from Kaplan Schweser Qbank.