# 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

• I did not understand your argument. But think of the situation as a "repeated game", you keep hedging long, rolling the hedge forward each time the future expires. Over and over again. Suppose that most of the time the futures price is lower than the spot prices when you buy the future (assume that this is the long run tendency in this market for some reason). What happens in the long run? Do you make money or lose money. Nov 21 '17 at 13:49

## 1 Answer

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).