What Exactly is "Fair Value" of an Index Future?

How many of you look at CNBC in the morning to "see what futures are doing"? Key to understanding the futures numbers you see on the screen is the concept of "fair value" of an index future.

Fair Value is a mathematical calculation that takes the cash value of all the stocks in the index (let's use the S&P 500 as an example) and allows for interest rates and dividend payments. Dividend payments must be allowed for because you get the dividend if you own the stocks, but you do not get it if you own futures. Interest rates must be allowed for because you could be using your cash to collect interest instead of trading futures.

The formula is: Fair Value = Cash Index Value * ((1 + r)^t) - dividends. For example:

The S&P 500 Cash Value is 561
The risk free interest rate (r) is 6%
The time remaining to futures expiration (t) is 51 days (0.1397 of a year)
The total of all dividends to be paid over the next 51 days is $3.23
Note: the "^" in the formula means that the interest rate is "raised" to a power equal to the remaining time to expiration.

Putting these values in the formula, you get: 561 * (1.06)^0.1397 - 3.23 = 562.36

How does knowing fair value help you get a feel for what the market will do on the opening? If the fair value is 562.36 and futures are trading at 570.36 then futures are trading 8 points above fair value. To get futures back in line with fair value on the opening, traders will buy stock and sell futures, so stocks should open slightly higher.

But do bear in mind, futures are good for predicting what the market will do in the first few minutes of the day, after that supply, demand, fear and greed rule.