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The fair market value of a futures contract is the price at which an arbitrageur who buys (sells) the futures market and sells (buys) the spot market and holds both positions until the expiry of the futures contract just breaks even before transaction costs.
If the futures contract trades at fair market value, this is called spot-futures parity.
The fair market value can be calculated by continuously compounding the spot price at the cost of carry rate over the period until the delivery of the futures contract.
Definitions:
S = spot price of the commodity
F = futures price at parity
r = continous risk free rate used to calculate the borrowing cost
y = storage cost for the commodity
q = dividends or revenues accruing to the holder of the spot position until delivery
u = convenience yield refering to cost due to not having the asset
T = time from today until expiry of the futures contract
Formula:
F = S * exp( (r + y - q - u) * T)
r, y, q and u are all expressed in terms of percentage of the spot price. It is easy to find the correct sign, if you just take the perspective of an arbitrageur, who has the choice
(1) either to invest into a cash position (pays borrowing cost at risk free rate r, pays storage cost at rate y, receives dividends at rate q, receives rental revenues at rate u)
(2) to invest into a futures position (does not have borrowing cost nor storage cost, but does neither receive dividends nor rental revenues)
For calculating the fair value, the risk free rate is used, although the arbitrageur will effectively pay a higher rate for borrowing. Storage costs are known, if you have a cash position, dividends can only be estimated. The convenience yield can be explained by other advantages. For example, as an owner of stocks you can rent them to other market participants who have entered a short position. Physical gold can be used for generating a rental revenue as well.
If you ask for a resource, I recommend the book by John C. Hull, Options, Futures and Other Derivatives. Please also find a link below. You can download the ppt slides for the 8th edition and then open the 5th file, which is on pricing forward contracts.
If you want to calculate the fair value for ES, you would need to take into account 500 stock prices (to calculate the index value) and the current dividend expectations for all those stocks from now until the last trading day.
You cannot put that into an indicator, because
- you won't probably get the dividend expectations for 500 different stocks.
- and the calculation would be too complex.
The fair value calculation is much easier for a futures contract based on a total return index such as the FDAX, because you do not need to take into account the dividends.
Some brokers offer such a fair value calculation and compare it to the price of the front month futures contracts. For example Interactive Brokers has such an arbitrage meter.
As far as the fair value for stocks, one of the best estimation I have seen is the one by Bart Diloddo, PhD, the founder of VectorVest, "Stocks, Strategies & Common Sense."
His approach to value any stock is purely based on inflation rate, earning yield and growth, and bond rates. This is independent of the size of the company, industry or sector, or any of the other fundamentals, technicals, etc.
The basic formula is:
V=100*(E/I)*SQR(R+G)/(I+F)
Where:
V = Stock Value in $/Share
E = Earning Per Share in $/Share
I = AAA Corp. Bond Rate in Percent
SQR = Square Root
ROTC = Return in Total Capital in Percent
R = I*SQR(ROTC/I)
G = Annual Earning Growth Rate in %/yr
F = CPI inflation Rate in %/yr
Here are some examples on the close of Friday 11-22-2013:
I am afraid that this has nothing to do with the fair value. The fair value is the value at which a futures price should trade in order to allow no arbitrage between the futures and the cash market.
Basically you can calculate the fair value by comparing the discounted cash flow (net present value) associated with the forward or futures contract to the spot market price.
