Positive Spot-Futures Basis and the Expected Return of a Long Hedge
Summary
The document explains why a persistent positive basis, defined as spot price minus futures price, can make a long futures hedge profitable on average under a particular assumption. If spot behaves like a martingale and futures begin below spot, convergence at expiration means the futures position gains the initial price gap, while still experiencing the full change in spot prices.
A crude-oil example illustrates the payoff in two equally likely scenarios: a rise in spot produces a futures gain, and a fall produces a loss; the average gain reflects the initial basis. This expected profitability does not remove substantial month-to-month exposure to spot movements. The discussion addresses an intuition about the ending basis but does not establish that a hedge will outperform a spot purchase in every outcome, nor does it cover transaction costs, changing basis, or deviations from the martingale assumption.
Key ideas
- A long futures position can have positive expected return when futures consistently trade below spot and spot is a martingale.
- At expiration, convergence makes the futures payoff depend on the initial basis and the change in spot.
- A favorable average payoff can coexist with large losses when spot prices fall.
- The example relies on a stable basis and equally likely spot increases and decreases.
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Full text
# If spot prices tends to be higher than futures prices, then long hedges are particularly attractive - Why?
# If spot prices tends to be higher than futures prices, then long hedges are particularly attractive - Why?
Explain why
> If spot prices tends to be higher than futures prices, then long hedges are likely to be particularly attractive
Supposed logic behind this is that if spot prices are likely to be higher than futures prices, then one might lock into futures prices, $F_1$, (at the beginning of hedging) and in this case as spot prices $S_1$ are likely to be higher than futures prices $F_1$ the hedging is attractive.
But I have a slight problem with this statement; we know that the basis $b_t=S_t-F_t$ at time $t$ is likely to be positive. If the hedging ends in $t=2$ then the amount paid by (assuming hedging ratio $h=1$) long position is
$$ P=F_1+b_2$$
If it is more likely that $P<S_1$, then the statement makes sense. However, by given condition it is also true that we would expect $b_2>0$ more often, and in particular this probably increases risk of $P>S_1$ e.g. if $F_1=S_1$. Of course we cannot ascertain anything in hedging, but I'm slightly bugged at the fact that there is a chance of this turning worse ($P>S_1$), and in fact I do not know if there is any good reason to believe that $\mathbb{P}(P>S_1)\le \mathbb{P}(P<S_1)$
It seems to me that the first paragraph only says that $\mathbb{P}(P<S_1)$ is higher compared to the case in which spot prices are often lower than futures prices
## Answer by nbbo2 (score 1)
https://quant.stackexchange.com/a/37031
Suppose the future price of crude (for delivery next month) is always 3 USD less than the spot price.
Let's say the spot price of crude is 50, so end of month future is 47. You go long the future. What happens at future expiration?
Case 1. Bad news from the middle east, the spot price has increased to 60. The future expires at 60. You have made 13 USD per barrel.
Case 2. Bad news from China, the economy is tanking and crude imports are tanking. The world is awash in crude and the spot price goes to 40 /bbl. So does the expiring future. You have lost 7 USD.
If Case 1 and Case 2 are equally likely, i.e. the spot price is a martingale, the long future position has made (13-7)/2 = 3 USD per month on average.
That's why if spot prices are a martingale, but spot tends to be consistently higher than futures prices, then long hedges are likely to be profitable on average. (Of course this average profitability is masked by large month to month fluctuations, you are fully exposed to spot price changes).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.