Interest rate futures 3 / 13

Interest rate futures

Are standardised exchange-traded contract agreement for settlement at a future date, normally in March, June, September and December.

Pricing futures contracts

The pricing of an interest rate futures contract is determined by the three months interest rate (r %) contracted for and is calculated as (100 – r). 

For example if three months Eurodollar time deposit interest rate is 9%, a three months Eurodollar futures contract will be priced at (100-9) = 91; and if interest rate is 10%, the future price = 90= (100-10).

The decrease in price or value of the contract reflects the reduced attractiveness of a fixed rate deposit in times of rising interest rates.

Ticks and tick values

Examples of ticks and tick values are:

  • For 3 months Eurodollar futures, the amount of the underlying instrument is a deposit of $1,000,000. 

    With a tick of 0.01%, the value of the tick is:

    0.01% x $1m x 3/12 = $25

  • For 3 months sterling, the underlying instrument is a 3 months deposit of £500,000. 

    With a tick of 0.01%, the value of tick is:
    500,000 x 0.01% x 3/12 = £12.5

Basis and basis risk

Example

If three months LIBOR is 7% and the September price of three months sterling future is 92.70 now, at the end of March (let’s say), the basis is:

LIBOR (100 - 7) 93.00 
Futures 92.70
0.30% = 30 basis points

Maturity mismatch

Maturity mismatch occurs if the actual period of lending or borrowing does not match the notional period of the futures contract (three months). 

The number of futures contract used has to be adjusted accordingly. 

Since fixed interest is involved, the number of contracts is adjusted in proportion to the time period of the actual loan or deposit compared with three months.

Diagram

Example

The company will need £18m in two months time for a period of four months. 

The finance director fears that short term interest rates could rise by as much as 150 ticks (ie 1.5%). 

LIBOR is currently 6.5% and AA plc can borrow at LIBOR plus 0.75%.

LIFFE £500,000 3 months futures prices are as follows:

December 93.40
March       93.10

Required:

Assume that it is now 1st December and that exchange traded futures contract expires at the end of the month, estimate the result of undertaking an interest rate futures hedge on LIFFE if LIBOR increases by 150 ticks (1.5%).

Solution

  • What contract = 3 months contract = March futures contract.

  • What type = sell as interest rates are expected to rise.

  • Number of contracts
    = (18m × 4) / (0.5m × 3) = 48 contracts.

  • Tick size = 0.01% x 500,000 x 3/12 = 12.5

  • Calculate the closing future price using basis and basis risk.

    Calculate opening basis as
    Current LIBOR    6.5% = (100 –6.5) = 93.50
    Future price                                    = 93.10
    Basis                                               = 0.40

    This will fall to zero when the contract expires, and it is assumed that it will fall at an even or linear manner.

    There are four months until expiry and the funds are needed in two month time, therefore the expected basis at the time of borrowing is:

    0.4 x 2/4 = 0.2

    Closing future price:

    LIBOR = 6.5% + 1.5% = 8% = (100 –8) = 92.0
    Basis                                                         0.2
    Future price                        92.0 - 0.2 = 91.8

  • Calculate profit or loss

    Selling price                                         93.10
    Buying price                                         91.80
    Gain per contract         93.10 - 91.80 = 1.3 = 130 ticks

    Total profit 130 x 0.01% x 500,000 x 3/12 x 48 = £78,000
    OR
    130 x 12.5 x 48 = £78,000

  • Overall outcome (total cost)

    Interest cost (8 +0.75) = 8.75% x 4/12 x 18m = 525,000
    Profit on future position                                      (78,000)
    Net cost                                                             447,000

    Effective rate of interest

    = (447,000/18m) x 12/4 x 100% 
    = 7.45%

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