Question

A bank sells a “three against twelve” FRA for $1 million at a rate of 8%. In three monthsthe FRA settles at 7.5%. There are 273 days in the FRA period. How much cash does the bank pay or receive?

Answer 1

Solution:

In a Forward Rate Agreement ( FRA )

1. If the Contract rate is greater than the Settlement date Rate, the seller of the FRA receives the settlement payment.
2. If the Contract rate is lesser than the Settlement date Rate, the buyer of the FRA receives the settlement payment.
3. If the contract rate is equal to the settlement rate, no settlement payment occurs

In the given case the Contract rate of 8 % is greater than the settlement date rate of 7.5 %. Thus the seller of the FRA will receive the payment of the differential Interest discounted at the settlement rate.

Calculation of the Cash payment to be received by the bank :

The formula for calculating the cash payment to be received by the bank is

= Interest Differential / [1 + Settlement rate × (Days in FRA period ⁄ 360)]

The formula for calculating the Interest differential

= [( Contract rate − Settlement rate) ] × (Days in FRA period/360) × Notional Principal amount ]

As per the information given in the question we have

Contract rate = 8 % ; Settlement rate = 7.5 %    ; Days in FRA period = 273 ;

Notional Principal amount = $ 1,000,000

Thus the Interest differential = [ ( 8 % - 7.5 % ) * ( 273 / 360 ) * $ 1,000,000 ]

= [ ( 0.5 % ) * ( 273/360 ) * $ 1,000,000 ]

= $ 3791.6667

Thus, the Settlement amount to be paid to the seller is calculated as follows

= Interest Differential / [1 + Settlement rate × (Days in FRA period ⁄ 360)]

= $ 3791.6667 / [ 1 +( 0.075 * ( 273 /360 ) ) ]

= $ 3791.6667 / ( 1 + 0.0568750)

= $ 3791.6667 / 1.0568750

= $ 3587.62

Thus the Bank shall receive an amount of $ 3587.62 as cash settlement amount.