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I was going through the proof about the equality of forward and futures price (assuming constant interest rate) in a book. Somewhere, the authors used the fact that suppose we start with two capitals - say A and B and we end up with the same final capital S, then A=B otherwise there will be arbitrage opportunity. Why arbitrage arises if A and B are not same?

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Say for example A>B. Then you would sell strategy A versus buying strategy B, collecting A-B initially. At the end you will have S-S, which is zero. So you have a risk free profit.

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