Derivatives
Forwards, futures, and hedging
A derivative transfers risk: the forward price follows the cost of carry, and a hedge fixes a price at the cost of giving up the upside.
Definition
A derivative is a contract whose value depends on an underlying asset, rate, or index. Used deliberately, it moves an exposure from the party who does not want it to the party willing to hold it.
The forward price is not a forecast. It is the spot price grown at the cost of carrying the asset until delivery, so any other price would create a riskless arbitrage.
Intuition
Hedging is buying certainty. You pay for it with the upside you would have enjoyed, and with the margin you must post while the contract runs.
When to use it
- Fixing the price or rate on a known future cash flow.
- Reducing the volatility of a budget or a portfolio.
- Replacing a physical exposure you hold with a contract you can trade.
When not to use it
- To take a view on a market you have no exposure to; that is speculation, not hedging.
- When the margin calls cannot be funded from available liquidity.
- When the hedge is in a different asset and basis risk is large.
Formula
Forward price from cost of carry
F = S × (1 + r)ᵀ
The no-arbitrage price for delivery in T periods.
- S
- Spot price today
- r
- Cost of carry per period
- T
- Time to delivery
Formula
Hedged proceeds
Proceeds = (Spot at delivery × Quantity) + Futures gain
Spot value plus the profit or loss on the offsetting futures position.
Worked example
A farmer locks in a price
A farmer expects 1,000 tonnes and sells futures at ৳32,000 a tonne. At harvest the spot price is ৳29,000.
- 1
Sell the crop
1,000 × ৳29,000 = ৳29,000,000 in the cash market.
- 2
Close the hedge
Futures gain = (32,000 − 29,000) × 1,000 = ৳3,000,000.
- 3
Total
29,000,000 + 3,000,000 = ৳32,000,000, exactly the locked-in price.
The hedge delivered ৳32,000,000 whatever the spot price did, at the cost of the margin posted and the upside forgone.
Common mistakes
- Treating the forward price as a prediction of the future spot price.
- Forgetting that a hedge removes gains as well as losses.
- Over-hedging a quantity that is not yet certain.
How it connects
is used in
The source appears as an input to the target.
- Risk and return: A hedge changes the shape of the risk-return trade-off.
relates to
Useful to study together, in either order.
is an advanced form of
The source extends the target once the basics are secure.