How a Long Futures Hedge Locks In a Purchase Price
Summary
A baker who will need wheat later can hedge the uncertain purchase price by going long futures contracts that mature when the wheat is needed. The document explains the cash flows at maturity: the futures gain is the spot price at maturity minus the initial futures price, while buying wheat in the spot market costs the spot price. Adding the two leaves an effective outflow equal to the initial futures price, assuming the futures price converges to spot at maturity.
The explanation addresses both cash settlement and physical delivery. With cash settlement, the baker separately buys wheat and the futures gain offsets the higher spot cost. With physical delivery, the wheat is received through the futures contract, so the separate spot purchase and its matching cash flows are not needed. The example assumes a matched quantity and maturity; it does not discuss basis risk, contract mismatch, transaction costs, or margin cash flows.
Key ideas
- A long futures position can hedge the cost of a future commodity purchase.
- At maturity, futures convergence makes the futures payoff equal to spot price minus the initial futures price.
- Under cash settlement, the futures gain offsets the cost of buying the commodity in the spot market.
- Under physical delivery, the hedge can supply the commodity directly.
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Full text
# Constructing a long futures hedge
# Constructing a long futures hedge
I'm taking a financial engineering course through coursera and on a slide one of the lecturers talks about how a long hedge is used in the futures market. Here is the text:
> Today is Sept 1st. A baker needs 500,000 bushels of wheat on December 1st. So, the baker faces the risk of an uncertain price on Dec. 1st. Hedging strategy: buy 100 futures contracts maturing on Dec 1st - each for 5000 bushels
It goes on to talk about the cash flows on Dec 1st. (numbering mine):
- Futures position at maturity: $F_T - F_0 = S_T - F_0$
- Buy in the spot market: $S_T$
However, the lecturer glosses over how (3) is arrived at.
So my questions are as follows:
for (2) - why are we buying in the spot market? Shouldn't the baker be taking delivery of the underlying and therefore already own the underlying?
How is (3) arrived at algebraically? I can see how (1) is mutated into it, but I'm wondering the reasoning behind how the $-F_0$ got there, as well as the second $S_T$ (which I'm assuming comes from (2).
Thank you! It's been a while since I've messed with this stuff and it sure shows.
## Answer by Archetupon (score 1, accepted)
https://quant.stackexchange.com/a/38350
As LocalVolatility has pretty much summed up, it seems that the example assumes that the futures are cash settled. However, it all works out the same way. Consider the algebra, with a little added explanation
1) Futures position at maturity $$F_T-F_0=\underbrace{S_T-F_0}_{\text{Futures converge to spot at maturity}}$$
2) Buy in the spot market $$\underbrace{-S_T}_{\text{negative number denotes a cash outflow to purchase spot}}$$
3) Adding 1 and 2 together yields $$\require{cancel}\underbrace{\cancel{S_T}-F_0\cancel{-S_T}}_{\text{simultaneous inflow and outflow of $S_T$ cancel}}=\underbrace{-F_0}_{\text{effective outflow/price paid by baker}}$$
Which shows your ending outflow is simply equal to the futures price at time 0, that is, the baker was hedged at this price. The same holds under physical delivery, or I guess that instead of thinking of the $S_T$ terms as cancelling, they are simply not there.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.