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Reinvestment rates do matter in the choice between futures and forwards.
When there is a positive correlation between interest rates and the underlying asset price, gains from increases in the asset price (the excess balance on the margin account) can be reinvested at a higher rate (positive correlation: asset price rose, so interest rates rose as well). In this case the investor will have a preference for futures as opposed to forwards.
When there is a positive correlation between interest rates and the underlying asset price, gains from increases in the asset price (the excess balance on the margin account) can only be reinvested at a lower rate (negativecorrelation: asset price rose, so interest rates fell). In this case the investor will have a preference for forwards as opposed to futures.
This explains price differences between forwards and futures prior to expiration.

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