Using Futures Basis to Compare Futures and Spot Fair Value
Summary
The document considers how a trader who believes futures lead spot price discovery can use futures information to adjust passive spot quotes. The answer identifies the futures–spot difference as the basis and suggests modeling it as a function of time remaining until futures maturity. It offers both an exponential relationship, with a rate-like basis parameter, and a simpler linear approximation, with a carry amount that accrues over time to maturity.
By repeatedly estimating that parameter and tracking it, a trader can compare the current relationship with its historical or smoothed typical level. A deviation may indicate that spot appears cheap or expensive relative to futures, providing a reference for spot quoting. The discussion is conceptual and does not specify how to estimate the fair prices from order books, account for funding, dividends, or transaction costs, or translate a basis signal into quote changes. The suggested mean reversion is described qualitatively, not supported by data or a tested trading rule.
Key ideas
- The difference between futures and spot is called the basis.
- The basis can be modeled as growing with time to maturity, either exponentially or approximately linearly.
- Repeated estimates can provide a typical basis level for comparison with current conditions.
- A basis deviation can help assess whether spot appears cheap or expensive relative to futures.
- The note does not provide a calibrated model or specific market-making rule.
Tags
Full text
# Futures vs. spot forecasting
# Futures vs. spot forecasting
If i have the belief that the futures lead the spot for price discovery, and I am able to forecast the future prices, given this forecast, what would be the best way to back out this number such that it can be used to determine what is the fair value at any given instant?
Would it be easier to just look at the returns of the futures forecast and then just use the spot market to move quotes around. I am mostly executing passive strategies.
For example, the futures LOB looks like this:
Bid Qty | Bid Price | Ask Price | Ask Qty
```
60 | 1189.5 | 1190.0 |90
4 | 1189.0 | 1190.5 |90
1 | 1188.5 | 1191.0 |90
4 | 1188.0 | 1191.5 |90
12 | 1187.5 | 1192.0 |90
```
And the spot exchange looked as follows.
Bid Qty | Bid Price | Ask Price | Ask Qty
```
106 | 1097.5 | 1097.9 |186
405 | 1096.8 | 1098.1 |190
2 | 1096.4 | 1098.7 |100
2 | 1085.3 | 1099.2 |9
15 | 1083.8 | 1099.5 |19
```
If i thought the fair price for the futures just looking at the order book was $1189.2 and the fair price for spot was 1097
Is there a way I can back out the forecast from the futures to trade the spot and vice versa?
How could i use this value to decide if e futures or spot was trading rich/cheap and how should this value affect how I quote in the spot market as a Market maker?
I personally have had issues with massaging this data.
Sorry if naive question.
Thanks
## Answer by nbbo2 (score 3, accepted)
https://quant.stackexchange.com/a/51285
The relationship between S and F is known as "the basis". You can theorize a relationship of the form
$$F=S \exp(c(T-t))$$
or the simpler, approximate $F = S + C (T-t)$. Knowing $F,S$ and $T-t$ (the time to maturity) you can estimate $c$ or $C$ which we might call the "basis per day to maturity". If you constantly estimate it and plot it, you will see that it is mean reverting, with some noise but generally close to a "normal" or "usual" value. You can use the average or smoothed value $\bar{C}$ to see if $S$ seems currently cheap or expensive compared to $F$.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.