# Unit 7 Notes: Futures

Corporate Finance lecture notes for the EMBA at UNSW.

## Futures

Actively traded on exchanges.

Standardised contracts: you don’t know who the other party is. So you are expose to counterparty risk. Daily price changes posted to trading account. Post price in the exchange via **Mark to market**.

No money exchanged when you buy or sell a future contract at time 0. Except for initial margin plus fees. You earn money or loss money via the margin account.

Zero sum game (two sides of the same coin) – If buyer gains then seller loses the same amount

### Purpose of futures

Future contracts allow producers and consumers of commodities to **hedge price; **Future is good if sales volume is known or fixed because we can hedge against price. Revenue = Sales price x volume.

- Producers and consumers are protecting themselves from adverse price increase or decrease depending which side of contract they are on;
- Long position – the buyer of the futures contract. Protected from futures price increases;
- Short position – the seller of the futures contract. Protected from future price decreases;

### Final day of futures contract (T)

Future price will the same as the current asset market price.

You can either settle or close out the position

Settlement (rarely)

- Cash settlement for future based on indices;
- Physical delivery of other assets;

Close out position (common)

- Do opposite of original transaction;
- If bought 10 Apples futures then sell 10 Apples futures;
- Net position is zero so no obligations;

### Future price (F)

Commodity Futures | Share and index futures |

F_{0} = S_{0}(1+ r_{f} + q)^{T}F = Futures price agreed priceS = Price of current commodityr_{f} = risk free rate p.a.T = years to expiry of futureq = cost of storage p.a. | F_{0} = S_{0}(1+ r_{f} – d)^{T}F = Futures price agreed priceS = Price of current commodityr_{f} = risk free rate p.a.T = years to expiry of futured = dividend yield p.a. |

Arbitrage keeps futures price to the formula

Note: Futures price (F) formula is use to calculate the **changes in the value **of Futures contract day to day to find out how much money is deposited or withdrawn from margin account, **it is not how much it costs to buy a future**. There is no cash flow when buying or selling a futures contract.

Use to calculate value of 1 futures contract

Value of 1 futures contract = Futures price x Z

Use to calculate daily change in margin account

Daily change = futures price x Z x number contracts

### Payoff for a futures position

When buying futures then

When buying futures then | D_{T} = Z x (S_{T} – F_{0}) x N |

When selling futures then | D_{T} = Z x (F_{0} – S_{T}) x N |

where

D_{T} = Total gain or loss on future from now to maturity T

Z = Number of underlying asset in 1 futures contract

S_{T} = Value of underlying asset at maturity T

F_{0} = Futures price when contract is established at t = 0

N = Number of futures contracts bought or sold

## Hedging

Can hedge cash profits

market value of equity

Hedging eliminates uncertainty

Combine Uncertainty from price changes + Derivative linked to price changes = Certainty with prices.

Hedging: taking a future position opposite to an existing position in the underlying commodity or financial instrument;

Offset price uncertainty with derivative e.g. Forward, futures and options

Perfect negative correlation ρ = -1

** Constructing and proving hedges**

- Calculate value of position to lock in;
- Calculate number of future contracts;
- Identify whether buy or sell futures contracts;
- Show net position if price decreases;
- Show net position if price increases;
- Identify that net position is identical

Hedging foreign exchange rate using forward contracts

Australia manufactures export to United States. You will receive a payment of US$1M for the exported goods in January next year. Suppose current exchange rate is US$0.80 / A$1.00 and the forward rate for next January is US$0.82 / A$.100.

Suppose the spot exchange rate in January next is actually US$0.85 / A$1.00.

The value of export revenue if it is hedged at US0.82 / A$1.00 would be US$1M ÷ 0.82 = A$1,219,512

The value of export revenue if is unhedged at US$0.85 / A$.1.00 = A$1,176,471

The gain (or loss) from the hedge here is A$1,219,512 – AUD$1,176,471 = A$43,041

Suppose the spot exchange rate in January next is actually US$0.78 / A$1.00.

The value of export revenue if it is hedged at US0.82 / A$1.00 would be US$1M ÷ 0.82 = A$1,219,512

The value of export revenue if is unhedged at US$0.78 / A$.1.00 = A$1,282,051

The gain (or loss) from the hedge here is A$1,219,512 – A$1,282,051 = A$-62,539

Australian Dollar Appreciates to US$0.85 / A$1.00 | Australian Dollar depreciates to US$0.78 / A$1.00 | |

Unhedged revenue | A$1,176,471 | A$1,282,051 |

Gain (loss) on hedge | A$43,041 | A$-62,539 |

Hedged position | A$1,219,512 | A$1,219,512 |