# Why is future price process defined to be a martingale under the risk neutral measure?

In Shreve's book, future process is defined to be a stochastic process that satisfies the following two conditions:

(1) $Fut_s(T,T) = S(T)$ where $Fut_s(T,T)$ is the future price at expiration and S(T) is the price of the underlying.

(2) At any time $t_k$, the value of the (daily settlement) payment to be received at time $t_{k+1}$ and indeed all future times is zero.

As a consequence of the second condition, the book claims that the future price process has to follow the following equation:

I understand that the expectation of the right hand side should be zero by condition (2). Can anyone explain why is it not zero under the true probability measure instead of the risk neutral measure?

Note: This is question is from page 243 of Shreve's Stochastic Calculus for Finance

• The use of the Risk Neutral Expectation is warranted when the P&L can be hedged. What is the hedge here? Aug 6, 2016 at 15:00
• That is essentially what I am asking. Aug 6, 2016 at 16:28
• What happens if you sell the future and buy the commodity in the spot market at time 0, then hold this position until time T? Aug 6, 2016 at 22:24
• Is it not a portfolio of two forward contracts $For(t, S_t) - For(t+1, S_{t+1})$? Aug 7, 2016 at 14:37
• @user1559897 Hi, would you give me feedback on the answer I have just posted? Sep 28, 2022 at 18:17