Futures: Principles of pricing.
by J Victor on April 11th, 2012At any point of time, Futures price of a share differs from the spot price. As we have already learned, the spot price of a share is determined by lot of factors like demand and supply, performance of the company, broad economic conditions, media news, general market psychology etc.
Do the same factors decide futures prices? Or is there anything else we need to know?
The answer is – yes. We need to learn a concept called continuous compounding.
THE PRICE OF FUTURE.
Of course, economic conditions, demand and supply of the underlying asset and countless other factors like hedging and short selling influence futures pricing. But theoretically, the futures price of stocks at any point of time is determined by two factors
 Short term risk free interest rates and
 Dividends.
HOW TO FIND THE VALUE OF FUTURES
Theoretical futures price when no dividend is expected.
 Value of futures = Spot price x E ^{(R x T)}
 Where E is the exponential value
 R= risk free interest rate
 T= time to maturity
For example – The share of X ltd is Rs 200 in spot market. The risk free interest rate is 8%. What would be the theoretical price of X Ltd’s 3 months futures?
 Value of futures = Spot price x E ^{(R x T)}
 Spot price = Rs 200
 Risk free rate = 8% or 0.08
 Time to maturity = 3 months or 3/12 or 0.25
 So, R x T = .08 x .25 = .02
 E ^{(.02) }= 1.0202 ( from natural logs table)
 Value of futures = 200 x E ^{(.02) }= Rs^{ }204.04
Note: To get the value of E^{(.02) }refer to the E ^{+X }table of natural logarithms. Log tables are nothing new. We all have used log tables in our school days. It’s also available online in many math sites.
What’s mentioned above is the price of futures, theoretically. The method we used is called ‘continuous compounding’. This is one of the vital principles in futures pricing. In some cases, the security in which a futures position is taken may generate income. For example dividend on shares. In such cases the above formula has to be modified to include the expected dividend.
Theoretical futures price when specific dividend is expected.
In this case, we have to consider the dividend expected from the stock. The logic is that if dividend is paid by the company, then the amount required for investment would be lower.
 Value of futures = (Spot price expected dividend) x E ^{(R x T)}
If the dividend expected is expressed as a percentage, then the above formula may be modified a little bit as follows –
 Value of futures = spot price x E ^{(RY) T}
 Where Y is the expected rate of dividend or dividend yield.
To sum it up, if the expected dividend is expressed in terms of money, we deduct the same from the spot price. Whereas, if a specific dividend yield is expected, then adjustment is made on the rate of return.
There are two crucial aspects here –
1. The accuracy of dividend forecasts.Depending on the accuracy , the value computed may vary.
2. Future dividends, expressed in rates or absolute values, have to discounted to the present value. The discounting process of dividends is the exact reverse of continuous compounding discussed earlier. Examples are given in the next post.
RISK FREE INTEREST RATE.
The topic was discussed elsewhere in our earlier posts. Risk free rate is the rate of return that any individual can achieve by investing in risk free assets. Generally, government bonds are considered to be risk free and the rate of return on such bonds are considered as the risk free rate of return.
COST OF CARRY
It’s a jargon used in futures. Cost of carry is theoretically the riskfree interest rate that could be earned by investing your money in a safe investment such as government bonds. So, it represents the cost of ‘carrying’ or ‘holding’ an investment.In the above example the cost of carry would be Rs 4.04
ARBITRAGE OPPURTUNITIES
Mispricings in the theoretical vale of Single stock futures unearths arbitrage opportunities. Such mispricings can be used effectively to earn risk free profits.
More on that in our next post.
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2 Responses to “Futures: Principles of pricing.”
Aniruddha
October 9, 2012 at 6:15 pm
Nice read..can you please post a link to the next post in sequence?
J Victor
October 14, 2012 at 6:18 pm
Sure:)