I just stuck this question
supopose that the future index for s&p 500 delivery one year from now is selling for $ 960.000, whereas the stocka are selling for $900.000. If the one year Treasurey bill rate is %5 , is it possible to use index arbitrage to make a profit?

If you buy the stock now for $900K, and sell a call option for $960K, it looks like you’ve made $60K.
But in fact, you’ve simply sold away all the up-side risk, but keep all the down-side risk.

If the stock goes up, then the guy who bought the call option exercises it. You give him the stock that you’ve been holding, and keep the $60K plus $3K in interest. He (not you) will realize the gain on the stock that you had been holding.

But if the stock goes down, then the guy who bought the call option will choose not to exercise it. You may have the $63K, but now you can’t use the option to dump the stock; you’d have to sell it and eat the loss.

the deifintions of hedging,speculation and arbitrage?

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