Formula for Commodities that can be stored

1.         It is not possible to predict the price of a commodity at Time “T”.   2.        The future expected price of a commodity at time “T” is denoted with ST. But we do not know what will be the exact price. 3.        Let us assume that price (ST) at time T0. Let this be denoted with E0(ST). E0 refers to the expectations at Time T0. 4.        Therefore, E0(ST) can be discounted to present value, using an appropriate discount rate “α”. 5.        At time T0 :  The present value of the E0(ST), then will be : E0(ST) x e-αT 6.        Now, let F(0, T) be the forward price of the commodity at Time “T”. 7.        Even this can be converted to present value, by discounting at risk free rate. 8.        The present value of the forward price of the commodity is: F(0, T) x e-rT 9.        In the absence of arbitrage, the present value of the forward price of the commodity should be equal to the present value of E0(ST) 10.      In other words: F(0, T) x e-rT =  (should be equal to) E0(ST) x e-αT 11.       Or, when we take the e-rT to the other side, the formula for F(0,T) becomes as: F(0, T) = E0(ST)e(r-α)T According to Robert McDonald, the above formula is  used when a commodity can be stored. 12.      Examples of commodities that cannot be stored is electricity (Once produced should be consumed) 13.      Reasons for non-storability: a.        Seasonal demand and supply b.        Intra-day variation of prices