How to Calculate Fair Value

Equity Futures Arbitrage Trading

What is Fair Value

Understanding how to calculate fair value is essential to anyone that undertakes to trade equity futures.

The fair value measurement of an assets value is a relatively simple calculation but it is surprising how even experienced traders can fail to understand the whole concept of 'fair-value' itself.

Why is there a difference between the futures price of an asset  and the markets cash price? Some traders believe that this price differential simply reflects the markets sentiment and that all they have to do is buy one and sell the other as a hedge, then sit back until the futures contract expires and reap the rewards. Wouldn't that be fantastic?

Unfortunately there is no such thing as a free lunch in trading the stock market, trading equity futures is no different. If it were as simple as that the Stock Exchanges would be very quiet places, all the traders would all be on the beach.

It is true to say that the Futures and Cash prices will always return to parity but there is slightly  more to it than simply trading one against the other. To find out if the futures really are trading at a premium or a discount to the cash price you need to fully understand  Fair Value.

A futures contract is an agreement to buy or sell an asset at a predefined point in the future at a price that is agreed today.

Fair Value is the theoretical price at which the futures contract should be trading at to reflect todays cash price and the cost of carry

Fair Value = Cash price + Cost of Carry

How to Calculate Fair Value for Commodities

The cost of carry is a suppliers associated costs with fulfilling that contract so these need to be taken in to account to calculate fair value for commodities.

      • Storage costs
      • Insurance costs
      • Loss of interest on funds that could have been reinvested if the asset had been sold immediately

These costs vary between assets and also between contracts.

The cost of storing and insuring Crude Oil for example, might be substantially higher than storing and insuring Lumber or Cotton and the cost of storing Live Cattle can be substantially lower in the summer months when they are put out to graze than it is in winter when they may need to be kept indoors and fed.

How to Calculate Fair Value for Financial Products

There are no storage costs to pay If you were to purchase a futures contract of a Financial Product such as the Dow Jones Industrial Average stock index (DJIA) but there are interest payment costs and dividend payments to take in to account when you calculate fair value for financial products.

Fair Value = Cash price + Interest  Costs - Dividend Payments

It is August and Wall Street cash is at 10221.....Decembers Futures Contract is quoted at 10152....69 points lower!

The interest costs are based on the Libor interest rate over the time to run until expiry. To calculate the daily rate this done by using a divisor of 360, in the UK it is 365.

The calculation  for fair value measurement using the formula above is

Fair Value = Cash + [Cash x Days till Expiry / ( Libor / 360 ) ] - Dividends

If the Libor rate is 2.4% and there are 105 days to expiry the interest payable over the 105 day period is 2.4 / 360 x 105 = 0.7%

Example of how to calculate Fair Value

DJIA Futures Price             10152            
DJIA Cash Price 10221
Interest Rate (Libor) 2.4%
Days until Expiry 105
Dividends Payable before Expiry
(Value of dividend payments in index points)
Interest Payable over the 105 day period = 0.024 / 360 x 105 0.007
Fair Value = Cash + [Cash x Days till Expiry / ( Libor / 360 ) ] - Dividends
Fair Value = 10221 + [ 10221 x 105 / ( 0.024 / 360 ) ] - 142 10150.55
DJIA Futures vs Fair Value 10152 - 10150.55 + 1.45

As we can see in this example using the Dow Jones Industrial Average, even though futures may be trading at a lower level than the cash price, it is possible that they may be priced at a premium and if a trader were to short cash and buy the futures in the search of that guaranteed 69 point profit, they in fact be locking in a guaranteed loss instead, in this case 1.45 points.

It is possible to make a profit form that type of trade, it is called Arbitrage Trading, but most traders and investors do not have access to the extremely tight spreads or the spread of dealing that is required to do it successfully. Most of this type of trade is done by computerized trading systems.

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