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The basis risk which we calculate by subtracting the spot rate from the futures rate will not be the same in reality for the expected futures price (lets say 3 months) right? The transaction is to be paid in 2 months but the futures contract is for 3 months
Firstly what you are referring to is the basis (not the basis risk).
Indeed the basis will change over the 2 months.
We assume that the basis falls linearly to zero over the life of the future (and so in your example would have fallen to 1/3 of what it is now).
The basis risk is due to the fact that in real life the basis will fall, but there is no reason why it should fall linearly.
All of this is explained in my free lectures on foreign exchange risk management 🙂
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