Brief about Futures and Forwards

Before reading about the Futures , have a look at Introduction to financial markets and Financial Assets or Securities.

Buying & selling of Future & Forward contracts takes place in what we term as Futures markets. Forward & future contracts are essentially agreements to buy or sell an asset at a future date at a certain price. This underlying asset could be for eample gold, silver, stocks, stock indices, currency, commodities like pulses, wheat, rice  or metals like copper, nickel etc.

Let S = Spot/Cash price

      S  = price for delivery today for an asset

Futures prices F are continuously quoted and change from second to second (and moves almost one-for-one with movements in S). When you buy or sell in futures market, it is the contract you are buying and selling not the underlying asset itself

Difference between Forward & Future contract

Although conceptually forward & future contracts are same, there are some significant differences.

  

Forward Contract	Future Contract
Private (non-marketable) contract between two parties	Traded on an organised exchange
Delivery or cash settlement at expiry	Contract is usually closed out prior to maturity
Usually one delivery date	Range of delivery dates
No cash paid until expiry	Cash payments into (out of) margin account, daily
Negotiable choice of delivery dates, size of contract	Standardised Contract
Credit Risk is borne by the counter parties	Credit risk taken care of by the exchange

  

Price determination

While considering forward & future contract, it is important to distinguish between investment & consumption asset.

Investment Asset: This is an asset held for investment purposes by significant number of investors. Stocks & Bonds are clearly examples of this. Gold & Silver are other examples, however Silver has many industrial uses.

Consumption Asset: This is an asset primarily held for consumption & not usually held for investment. Commodities like Oil & metals can be best examples for these. 

We will use arbitrage arguments to determine the forward & futures prices of an investment asset. 

Some of the assumptions that would be assumed to be true for all participants:

1. There are no transaction costs
2. Tax rate is same on all net trading profits
3. All can borrow & lend at the same risk free rate of interest
4. Arbitrage opportunities are quickly availed by all.  

Forward price for an Investment asset that provides no income

Non dividend paying stocks & zero coupon bond could be examples of such assets. The general formula used to price a forward contract is: 

The above formula would be used where the risk-free rate is expressed on an annual basis. The formula below, by contrast, is used where the risk-free rate is expressed on a continuous compounding basis.

We would generally use formula that uses the continuous compounding basis. Lets see how arbitrage argument guides the forward price.

Assume that the current stock price is $ 40, three month risk free rate is 5% p.a. Let us also assume that forward price is $43. An arbitrageur can

1. Borrow $40 at 5%  & buy one share
2. He can short a forward contract to sell one share of the stock at $43.

The sum required to pay off the loan is = 40e^0.05*3/12  = $40.5

i.e the arbiutrager can make $43 -$40.5 = $ 2.5 as risk less profit.

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