Forward rates in commodity markets

We use the following notations for calculations of forward price. These notations are also commonly used for stocks.

S₀  = This is the current spot price of a commodity.

e^rT  = Continuously compounded rate for a period 'T'. 'r' refers to risk free rate.

The forward price of the commodity is expected to be  = S₀ e^rT

This means, the present price of a commodity is expected to grow at the risk free rate of 7.79% (Practically, it is not the case). Let us see, why practically we cannot use the above formula.

Presently the 364 days, the risk free rate (RBI T-Bills rate) is 7.79% 

^{(Source: http://www.bloomberg.com/quote/GINYA364:IND )}

For example: Go to http://www.mcxindia.com/ (MCX - Multi Commodity Exchange, India)

The Spot price of Aluminium for 1 kg = Rs103.50 (As on 22.03.2013)

The futures price of Aluminum for 1kg = Rs105.30 (30April, 2013 contract) 

There is a difference of  Rs105.30- Rs103.50 = Rs 1.74 against an investment of Rs103.50

Step 1: Borrow 1kg of Aluminum and sell it forward at Rs105.30 to return it on 28.04.2013

Step 2: Assume that the commodity prices grow at risk free rate.

Step 3: Enter into a forward contract to sell Aluminum on 28.04.2013 (Sell forward)

This comes to 0.65% per month. Therefore, for the borrowed 1kg aluminum, we need to pay Rs1.00 as the interest for 45 days or 1.5 months. Because 7.78% is the risk free rate for one year or 364 days T-Bill.

Step 4: Sell the forward contract on 28.04.2013 and receive Rs105.30 

Step 5: Buy 1kg of Aluminum from the spot market, that is expected to be as:

Spot price (22.03.2013) + Commodity price growth @ risk free rate

        Rs103.50 + Rs1.00 (the value of commodity growth in 45 days at risk free rate)

ð        Rs104.50 (We need to have to buy from the spot market)

       Buy the asset from the spot market and return it to the lender of commodity.

ð        Speculative profit expected to be: Rs105.30-104.50 = Rs0.80 per kg

This implies that there are many factors that affect the forward prices and using only

 S₀ e^rT to calculate the forward prices of a commodity is not correct.