Futures vs. spot forecasting

Question

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 1

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 $F$.