Building index futures fair value from cash-and-carry

Start with the financed hedge

A cash-and-carry construction finances a cash-market basket and offsets it with a short futures contract of matching exposure. A financed cash index basket held against a short index futures contract is constructed so that declines in the cash basket are offset by the short futures.

The opening futures-minus-index difference is treated as the premium locked in when the hedged construction is initiated.

Read the holding-period result

Over the futures holding period, the constructed result equals the opening futures-minus-index premium plus dividends received minus interest on the financed cash outlay.

Carrying net is interest paid to hold the cash basket minus dividends collected while it is held.

Close out under expiration convergence

Expiration convergence is the working assumption that futures and the cash index meet at expiry, so the close-out itself adds no extra capital result. In the simplified expiration close-out, the futures price equals the index, so selling the cash basket and settling the futures adds no extra capital gain or loss.

Fair-value premium is the premium at which the constructed result is zero, making the constructor indifferent between owning the cash basket and owning the futures. That fair-value premium equals interest carry on the index level minus dividends over the futures life.

A constructed numerical premium

Using an index of 328.51, a 9 percent financing rate, a 4 percent dividend rate, a 90-day remaining life, and a 360-day year, the constructed fair-value premium is 4.10.

The identity after simpler assumptions

The same indifference identity is presented as remaining valid after relaxing simplifications such as treating dividends as evenly spaced through the year.