How Interest-Rate Correlation Affects Futures and Forward Prices
Summary
The document explains why futures prices can exceed forward prices when the underlying asset is positively correlated with interest rates. Daily settlement gives a futures position cash flows along the way: a long can reinvest gains at higher rates and faces losses when borrowing costs are lower. The answer checks the same effect from the short’s perspective: a short tends to receive gains when prices fall, when reinvestment rates are lower, and faces losses when rates are higher. It argues that the entry futures price adjusts upward to compensate for this disadvantage to the short.
A second response distinguishes this marking-to-market effect from the usual cash-and-carry relationship between spot, financing, and asset income such as dividends or coupons, which influences whether prices are in contango or backwardation. These are related but distinct considerations. The discussion is qualitative and gives no quantitative pricing derivation; the futures-forward comparison depends on the assumed positive correlation and does not establish a universal ordering for all assets or market conditions.
Key ideas
- Daily settlement makes futures cash flows sensitive to the interest rate prevailing when gains or losses occur.
- With positive asset-price and interest-rate correlation, the reinvestment effect favors the futures long.
- The short experiences the opposite cash-flow timing effect, which also supports a higher futures entry price relative to a forward.
- Dividends, coupons, and financing costs influence forward levels and contango or backwardation through cash-and-carry pricing.
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Full text
# Futures and Forward Prices vs interest rates
# Futures and Forward Prices vs interest rates
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 by Amrit Prasad (score 2)
https://quant.stackexchange.com/a/40454
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 by Edward Watson (score 0)
https://quant.stackexchange.com/a/46942
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.