FRAs - calculation 6 / 13

Compensation payment

Compensation period is calculated as the difference between the FRA rate fixed and the LIBOR rate at the fixing date (actual LIBOR) multiplied by the amount of the notional loan/deposit and the period of the loan/deposit.

The FRA therefore protects against the LIBOR but not the risk premium attached to the customer.

The settlement of FRA is made at the start of the loan period and not at the end and therefore compensation payment occurs at start of the loan period.

As a result the compensation payment should be discount to it present value using the LIBOR rate at the fixing date over the period of the loan.

Example

A company will have to borrow an amount of £100 million in four month time for a period of six months. 

The company borrow at LIBOR plus 50 basis points. 
LIBOR is currently 3.4%. 

FRA prices (%)
4v10    3.63   3.68

Required:

Show the expected outcome of FRA:

(a) If LIBOR increases by 0.6%.

(b) If LIBOR decreases by 0.6%.

Solution

The FRA will be 4 v 10 as the money will be needed in four months time and will last for six months. 

The applicable interest rate will be 3.68%.

  • (a) If LIBOR increases by 0.6%

    LIBOR (Actual) at fixing date = 3.4 + 0.6 = 4.0%

    Actual interest paid on the loan = 4.5% x 100m x 6/12 = £2.25m
    (4 + 50/100)

    Compensation received from the bank (4 – 3.68) = 0.32% x100m x 6/12 = (£0.16m)

    Net interest payment = £2.09m

    Effective rate = (2.09/100) x (12/6) x 100% = 4.18%

    Same as FRA rate + spread= 3.68 + 50/100 = 4.18%

  • (b) If LIBOR decreases by 0.6%

    LIBOR (Actual) at fixing date = 3.4 - 0.6 = 2.8%

    Actual interest paid on the loan = 3.3% x 100m x 6/12 = £1.65m
    (2.8 + 50/100)

    Compensation received from the bank (2.8 – 3.68) = -0.88% x100m x 6/12 = £0.44m

    Net interest payment = £2.09m

    Effective rate = (2.09/100) x (12/6) x 100% = 4.18%

    Same as FRA rate + spread= 3.68 + 50/100 = 4.18%