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How to calculate the correlation coefficient between spot price and futures price?
Spot price+storage fee+insurance premium+interest = futures price.

Unless you do cross-market arbitrage, you should not include transportation fees.

Correlation coefficient: β

Set spot = x;; Futures =Y

n∑xy -∑x∑y

- = β

Square root (n∑x*x-∑x*∑x) × square root (n ∑ y * y-∑ y * ∑ y)