One often hears of Fair Market Values when listening to CNBC or other business channels. What seems mysterious is actually a time value of money relationship. Here, the underlying basket of stocks is related to a futures contract. One of the more common examples is the S&P 500. Stock futures and options are predicated on this actual equity index.

Generally, the futures are expected to trade a premium relative to the underlying basket of actual stocks. This is due to the effect of the time value of money. By carefully selecting an interest rate which should reflect the cost of financing this procedure, the implied futures price would be higher.

Key determinants of calculating fair value are:

CI = Cash Stock Index
FP = Futures Price
i = interest rate or discounting factor
D_{pv} = expected value of dividends during holding period
t = time between now for cash and then for futures maturity or expiration
These factors are constructed into the following mathematical expression:

FP = CI (1 + i)^{t} - D_{pv}
When dividends are equal to zero (D_{pv} = 0), then the expression simply imputes a higher price for the futures over cash or actual stocks.

When dividends are greater than zero, then the futures price is trimmed. This occurs because the actual stocks pay dividends whereas futures do not pay dividends.

All other things being equal, here, longer time periods and/or higher interest rates imply a higher futures price relative to the cash index. This does not mean that higher interest rates would propel the overall stock market higher. It just suggests that the price differential, spread or premium should be greater due to higher financing and opportunity costs.

Besides real dividends, it should be noted that there is a real advantage owning actual stocks relative to synthetic ownership via a derivative and that is the value of the vote. Most models assume that the value of the vote is zero. The assumption is not necessarily true. Only properly recorded shares have voting power - derivatives do not vote. Management control issues, takeovers and proxy fights depend on voting powers.

Complicating issues are whether to model simple or compounded interest, exact dates and amounts for dividends, one interest rate or multiple interest rates to reflect for different points on the yield curve, and other variables such as slippage and margining.

Often these relationships reflect the cost structure of the most efficient participants. That is if the most efficient participant can borrow at LIBOR and another good credit but less efficient borrower must borrow at LIBOR plus 50bps, then the former has an advantage and will drive the spreads to tighter differences.

Click here, for a few quick intuitive examples.

For help in this important area, Contact Consulting Services.