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I'm having trouble understanding how Futures are worth more than Forwards when price and interest rates are positively correlated but both declining.

For instance, a Future with losses of -5 at T(n-1) and -5 at T(n) vs. a Forward with losses of -10 at T(n). How is the Future more valuable? Most textbooks I've read explain it as "losses derived from a falling futures price can be financed at a lower interest rate", but you're still having to borrow 5 at T(n-1) and paying back 5(1+r) at T(n). So total losses for the Future are 5+5(1+r) which is greater than 10 for the forward.

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Call $G_t$ the price of the future, and $F_{t,T}$ the price of a forward at time t with maturity T. You know that by NA $F_{t,T}=R_{t,T}E_t[S_T]=R_{t,T} S_t$ where $R_{t,T}$ is the gross return on a risk free bond with maturity T and $E_t[ \cdot ]$ is a risk neutral expectation. One day before maturity the price of the future will be such that $$G_{T-1}=R_{T-1,T}E_{T-1}[S_T]$$ and two days before maturity $$G_{T-2}=R_{T-2,T-1}E[G_{T-1}]=E_{T-2}[R_{T-2,T-1}R_{T-1,T}S_T]=\\E_{T-2}[R_{T-2,T-1}R_{T-1,T}]E_{T-2}[S_T]+Cov_{T-2}[R_{T-2,T-1}R_{T-1,T},S_T]$$ You can also rewrite $E_{T-2}[S_T]=\frac{F_{T-2,T}}{R_{T-2,T}}$ and if $\frac{R_{T-2,T-1}R_{T-1,T}}{R_{T-2,T}}\approx 1$ then $$G_{T-2}\approx F_{T-2,T}+Cov_{T-2}[R_{T-2,T-1}R_{T-1,T},S_T]$$

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Your comparison is not quite apples to apples. You should compare one futures contract at (n-2) with (1+r) forward contracts. That makes them equal in terms of equity exposure. If you do this, you find that you borrow 5 and pay back 5(1+r1) at n where r1 is less than r if rates have gone down. hence the futures is better if this correlation holds.

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