Price an index through another index when they have a high correlation

AI & Machine learning
1

There are two indices (Index A and Index B) that are very similar. Index B is a new index, while Index A is an old index with large volumes. The correlation of the returns between the two indices is 97%. I want to price and trade Index B using the price of Index A.



I am considering calculating the price of index B at time t using the following formula: Pb(t) = Pb(t-1) * [Pa(t) / Pa(t-1)].



To determine the most correlated pair among all indices:

  1. Should I calculate the correlation of the log returns?
  2. Should I calculate the intraday correlation (considering multiple days?) or the daily correlation (the last)?




  3. Am I correct in my approach to pricing Index B?
  4. Is there a better way to price Index B? Linear regression model approach is it better?



    Thank you very much
2

Hello elhanan,



You can calculate the correlation of the log returns. You can also test for co-integration using the close prices of the two indices. 



If you are interested in short-term trading or intraday movements, calculating intraday correlation might be more suitable. On the other hand, if you have a longer-term perspective, calculating the daily correlation based on closing prices could be sufficient.



Your approach is fine and could be used, but seems simple. Using the formula can provide a rough estimate, but it may not accurately reflect the true value or dynamics of Index B.

With linear regression, you can analyse the historical relationship between the two indices and estimate the parameters that best describe the relationship. This can provide more accurate pricing estimates, but please note that even linear regression is not 100% accurate.



Hope this helps.

3

Rekhit, thank you very much for your detailed answers.

About linear regression model is it better to run the regression every day again, on the previous day's data and therefore have new parameters every day?

4

Hi,



There is no one size fits all approach here. Some traders prefer to update their model regularly, i.e. daily, to capture the most recent market information. Others may use rolling windows, updating the model every week or month. The point here is we do not want to wait for the program to finish computation and then take the trade. Alternatively, you could define a criteria, based on time (find parameters every week or mont), or based on strategy performance (strategy gave returns below a certain threshold).



Hope this helps.

5

Thanks Rekhit