I am reading a book of J.C Hull on Future and option where he explained the basis risk which is S2 + F1 - F2 or F1 + b2 I got this concept but reading further he expand above expression as F1 + (S*2 - F2) + (S2 - S*2) where S*2 is price of the asset underlying the futures contract at time t2 (maturity time). Here I don't get the meaning of price of the asset underlying the futures contract.

S1 : Spot price at time t1
S2 : Spot price at time t2
F1 : Futures price at time t1
F2 : Futures price at time t2
b1 : Basis at time t1
b2 : Basis at time t2.

Screenshot of paragraph I'm reading from that Book:

1 Answer 1


Often you can't buy a futures contract on what you are actually trying to hedge, so you have to buy a future on a different (but very similar) asset. This is common in commodities, where producers buy a commodity that's similar to the specific commodity that's traded on futures markets (WTI Oil futures, for example, are for a very specific quality of oil to be delivered in a specific location).

So I may produce one type of oil that has one price (call is S) and have to trade futures on another type of oil that trades at another price (call it S*). If those two prices diverge, then I have a source of risk even though I've locked in a price via my futures F.

Take an extreme example. Let's say I produce S that is currently selling for $100, and I want to sell mine in 1 month. I don't want to risk that price going down, down, so ideally I would use a futures contract. There are no futures contracts on S, but there are futures on a very similar product, S*, that is also currently trading for $100. I enter into a 1-month futures contract F on S* at $101 (the expected price of S* in 1 month).

The price of S stays stable and gains $1 in one month, which matched my expectations. However, for some reason, the price of S* collapses to $50. I now can sell my S for $101, but I must pay $50 on the futures contract.

So "basis risk" is the risk that the price of the underlying asset of the futures contract (S*) diverges from the price of the asset that we're actually hedging (S).

Clear as mud?

  • I understand all symbols S1,S2,F1,F2,b1 and b2 but I didn't get the meaning of S*2?@D Stanley
    – zircon
    Jun 12, 2020 at 15:50
  • OK I see the difference now. That completely changes my answer...
    – D Stanley
    Jun 12, 2020 at 15:58

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