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I understand that time-varying interest rates, “cost of carry” and “convenience yield” will have an effect on forward and futures prices but why would it affect the prices of forwards relative to futures, and how would it effect their relative prices to each other?

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    $\begingroup$ As you know, with a forward you do not make or receive any cash flows until the maturity. With a future you make/receive daily M2M payments and these cash flows are reinvested at whatever i.r. prevails at the moment, which varies stochastically. That's why a difference exists between forward and future, when the i.r. changes are correlated with factors underlying the commodity (if i.r. are correlated to the price of soybeans, the carrying cost of soybeans, etc. then yes it matters: soybean future $\neq$ soybean forward). $\endgroup$ – Alex C Feb 26 '17 at 18:48

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