Futures and Forward Prices vs interest rates

Question

Textbooks usually state that if an asset's prices are positively correlated with interest rate movements, then its Futures price is going to be greater than its Forward Price assuming the same maturity.

The reasoning is that if you're long futures and the asset's prices increase along with interest rates, then you'll get to re-invest your gains at a higher rate. On the flip side during losses, you'll get to borrow at lower interest rates. This is not possible with forwards since they aren't marked-to-market daily. Hence, futures prices should exceed the forward price.

Does the logic hold from the short's perspective as well?

Answer 1

Consider a short futures vs short forward contract on the same asset. The futures will make profits when the asset prices go down, but would get to re-invest at a lower rate. On the flip side during losses, you'll have to borrow at higher rates. Clearly the short is getting the worse end of the bargain. If $F_{0,T}$ is the futures price at which you entered the short, while $F_{t,T}$ is the price at time at which you're evaluating the position, the profit is given by-

$$F_{0,T}-F_{t,T}$$

The above suggests that the way to compensate the short leg for getting the short end of the stick is by increasing $F_{0,T}$ relatively speaking. This is also what we got for the long leg, and hence futures prices will tend to be higher than the corresponding forward price in case of expected positive correlation with interest rates.

Answer 2

contango or backwardation is just a function of the dividend or coupon on the asset and the financing rate until delivery. If the coupon yield is higher than the financing yield the forward price will be lower and will be in backwardation and financing rate higher than coupon rate will make the futures price higher than spot which is contango. The math comes from cash and carry arbitrage.