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How to hedge short contracts through forward prices?

Are you doing spot hedging or cross-contract or cross-market hedging?

Futures and spot hedging is mainly for basis difference hedging, locking in a stable basis difference. If you do forward hedging, you can expect the basis difference to shrink;

Cross-market or cross-contract hedging is mainly for price difference hedging. , lock in a stable price difference, and if you do forward hedging, expect the price difference to return;

What you said about using forward short contracts to form a hedging is to require forward hedging. The specific method is as mentioned above.