Case study on storable commodities

Presently the corn prices are trading at 760 cents per bushel in the spot market. The risk free rate of interest is 2.35% (USD). The trader expects to receive a price of 785 cents per bushel after one year. Using the risk-free rate, forward price quotes are available in the market for 777.85 cents per bushel. At what discount rate the expected spot price after one year E₀(S_T) can be discounted? Can there be a situation of quoting 785 cents per bushel by the trader? Under what circumstances the trader can quote more than 777.85 cents per bushel.

Please understand the concepts for commodities that can be stored.

In this case E₀(S_T) is given. That is the expected price of the commodity, according to the trader. That is given to be 785 cents per bushel. According to McDonald, the present value of the forward price should be equal to the present value of the Future expected prices.

Mathematically: F_{(0, T)} x e^-rT =  (should be equal to) E₀(S_T) x e^-αT

The present value of forward price = 777.85 x e^{-0.0235 x 1 year} = 760 cents per bushel

The present value of  E₀(S_T) = 785 x e^{-α T}; using alpha = 3.1%, it can also be equated to 760 cents per bushel.

This means, the trader is expecting more than the risk free rate of 2.35% in the forward prices. The additional rate expected by the trader is 3.1% - 2.35% = 0.75%.

An additional yield of 0.75% is expected by the trader more than the risk-free rate. The reasons are many reasons to include this 0.75%. It may be due to demand and supply or due to cost of carry or for any other reasons.

What we need to understand here in this discussion is:

According to McDonald, the forward price formula for storable commodities is given by:

F_{(0, T)} = E₀(S_T)e^(r-α)T  (In the yesterday’s discussion, “exp” was missing in the formula, today rectified. I am sorry)

Here ‘r’ is the risk free rate and alpha is the discount rate used to convert the future expected price of the commodity to present value. In reality, risk free rate is lower than the appropriate discount rate “α”. Because, the traders include other factors like cost of carry, convenience yield or other factors in the forward price. Assuming that the forward prices quoted using the risk-free rate would lead to wrong assumptions.