For LOS 40a where you hedge the principal (naive hedge) the gain/loss on the futures contract depends on the change in the futures price. Maybe I’ve been starring at the books too long, but I thought if you sell a futures contract the payoff depends on what the spot price does, not what the new futures price is at expiration. Why is it the change in the futures price is in this case?

No, has not relationship to the spot. So let’s say the you sell the S&P futures to hedge a long equity position. Now let’s say that something happens and the basis dramatically widens because the futures stopped tracking the underlying - your are SOL and your profit or loss is based on those futures no matter what happens to the spot. The only way that you are affected by the spot is that the futures and the spot trade on a relative basis but if that relationship snaps then you are no longer hedged. Make sense?

Here is the payoff formula in today’s terms: Ft - So*(1+i)^(t) Look at it this way: You own gold that is worth $100 today. In a year, this amount of gold will be worth $120 according to the futures price curve. You don’t know for sure what the price will be in a year, so you hedge your position and short futures. This means that in one year, you will sell your gold for $120, regardless of what the market is doing… Now you can be either better off (if the actual price has ended up being less than $120) or worse off (if greater than $120). Your payoff at that point is simply (St-So) + (F-St) = F - So = $20 because you owned the underlying… and this is a risk-free payoff… however, if the Futures price has changed, you will have a payoff on futures position as well… At this point… I am getting lost in my own thoughts… so I am losing confidence in my answer… I would appreciate if I am confirmed or proved otherwise… thanks!

Guys - you are both over complicating things. When you trade futures, you are trading futures. Your profit or loss has nothing to do with the spot rate but whether the futures went up or down. Your pay-off formula is theoretical and for forwards which are not actively quoted. In real life futures are quoted on a second by second basis. The forward formula is only used by arbitrageurs to try to make a return above the risk free rate. Again, if you hedge with futures, the only thing that matters is the price of the futures.