# Arbing the Basis?

If basis = spot price - futures price, why can’t you short the underlying and go long the futures contract to make a riskless profit when they converge at the maturity of the contract?

^ I mean to say:

If basis > 0, short the underlying and go long the contract, and;

if basis < 0, go long the underlying and short the contract.

I think that you’re misunderstanding what is meant by the spot price and the futures price converging at maturity.

When you cash-and carry or reverse cash-and-carry today, you do so based on today’s spot and futures prices; convergence doesn’t affect your transaction.

So say the spot price today on asset X is 100 and the 6 months futures price is 110. Then go long asset X and short the contract.

Scenerio 1: Spot price on asset X is 120 at expiration of the contract. Same forward contract will now sell for 120 or there is arbitrage opportunity. Gain on asset X is 20. Loss on shorted contract is 10. Total gain is 10.

Scenerio 2: Spot price on asset is X is 90 at expiration of contract. Same forward contract will now also sell for 90 or there is an arbitrage opportunity. Loss on asset X is -10. Gain on shorted contract is 20. Total gain is 10.

Obviously I must be missing something or the spot price would always equal the futures contract price at t=0.

The futures will be priced to prevent such an arbitrage opportunity; it’s called the no-arbitrage condition.

You are missing a few things: the cost of borrowing the underlying for a short sale, the cost of borrowing money for a long position in the underlying, any carrying costs for the underlying, and any convenience yield from holding the underlying; the first two are discussed at Level I, the last two are discussed at Level II.

Yes, if the prices were as you gave (and we ignore the other costs), there would be an arbitrage opportunity. The market knows this and the futures price will adjust quickly to eliminate the opportunity.

Interesting, thanks S2000.

My pleasure.

If you want to learn about real-world basis trading, pick up “The Treasury Bond Basis”. Great book on the subject.

^ Thanks!