The problem is you ignore the financing cost. At t<T, if you borrow St at r and buy St and hold it to T, your debt at time T will accumulate to Stexp(r*(T-t)), while you can only get Ft from selling St to the long party. Which means you loss Stexp(r*(T-t))-Ft (given r>0 and St=Ft). You can only say while Ft>Stexp(r*(T-t)) you will have arbitrage opportunity.

While doing arbitrage, you can not ignore the financing cost because you either borrow the money or you have the opportunity cost because you can earn r by just putting the money in the bank. Only when the arbitrage profit is higher than your financing cost, we consider this is an arbitrage because you take no risk but earn more than the risk free rate.

谢谢 明白了