Question

A bank bought a "three against six" $5,000,000 FRA for a three-month period beginning three months from today and ending six months from today. The reason that the bank bought the FRA was to hedge: the bank accepted a 3-month deposit and made a six-month loan. The agreement rate with the seller is 5 percent. Assume that three months from today the settlement rate is 4.75 percent. Who pays whom? How much? When? The actual number of days in the FRA is 90 (3 months).

A. The bank pays $3,088.326. This payment will be made at end of 3 months.

B. The counter party pays $3,125. This payment will be made at end of 6 months.

C. The bank pays $3,125. This payment will be made at end of 6 months.

D. The counter party pays $3,088.326. This payment will be made at end of 3 months.

Answer 1

OPtion A) the bank will pay to the seller 3088.326 at the end of 3 months

Here I will try it to keep very simple

Here The FRA says 3 against 6 means the loan amount which is notional ($5,000,000) will be executed after 3 months for next 3 months period. in other words in 6 months the 3 months are included.

Now bank has bought the FRA means he is obligated to borrow the loan after 3 months on the aggred rate of 5%.

If the rate goes up he will be in profits but it goes down to 4.75% so he will bear the loss of the differential that is 0.25%

STEP 1: the loss of 0.25% as calculated above. (5-4.75%)

STEP 2: the amount of differential which bank has to pay to the seller at the end of 6 months 0.25%x 5000000 *3/12 = $3125 ( but it is in the end of 6 months we have to find out the present value at the end of 3 months.)

STEP3: The actual payment made by the bank to the seller = 3125/[1+ (4.75%*3/12)] = $3088.326

If you want to do it with formula then:

Settlement =[ (4.75%-5%) * 5000000 * 3/12] / [1+(4.75%*3/12)] = - 3088.326 ( shows payment to the seller)

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