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 |
| F0 = S0(1+ rf + q)TF = Futures price agreed priceS = Price of current commodityrf = risk free rate p.a.T = years to expiry of futureq = cost of storage p.a. | F0 = S0(1+ rf – d)TF = Futures price agreed priceS = Price of current commodityrf = 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is use to calculate the changes in the value of Futures contract day to day to find out how much money is deposited or withdrawn from margin account, it is not how much it costs to buy a future.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 | DT = Z x (ST – F0) x N |
| When selling futures then | DT = Z x (F0 – ST) x N |
where
DT = Total gain or loss on future from now to maturity T
Z = Number of underlying asset in 1 futures contract
ST = Value of underlying asset at maturity T
F0 = 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 |
