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Richard Tobiassen had posted some information on the fair value of an index
futures contract. Larrence McMillan gave a fairly complete description in
"Options As a Strategic Investment" (2nd edition, page 492). The fair value
is defined as follows:
FairValue= index X (1+ time[years] X rate) - divididends
index = cash value of the index
time = time remaining in years of the expiration date of the futures
contract (e.g. 90days = .25)
rate = cost of funds (e.g. broker loan rate or treasuries for some
investors)
dividends = present worth of all dividends paid by stocks held in the index
prior to the expiration date of the futures contract. The calculation of
present worth for dividends will vary depending upon whether the index is
price weighted or capitalization weighted.
The value of the "synthetic future" is determined by the following formula:
SyntheticFairValue = index + call price[at the money] - put price[at the
money]
Some strategies will track divergence/convergence between the actual
futures fair value and the synthetic to spot pricing inefficiencies.
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