# Choice of factor model based on correlation

I have a portfolio of assets. Each assets have been discretionally (based on investment manager experience) related to economic factors like (like exchange rate inflation spread etc). Now for each asset I want to see if effectively those fator are relevant in order to make a regression and find the betas (coefficient of regression). My question is: what correlation should I use? Pearson which is only a linear based approach or Spearman which can also deal (I am right) with non linear relations and outliers? I did both but clearly I get different results so I need to choose among them. Thanks.Luigi

Indeed Pearson correlation coefficients measure only linear relationships. Spearman correlation coefficients measure only monotonic relationships

There is a comprehensive article there.

• Thanks. Indeed i am aware of the characteristics of both, but my question was more: based on the financial literature on this subject, and considering that a factor model based on macroeconomic factor is not something new but instead well known, what is the typical approach? choosing factor based on high Pearson or high spearman? Also taking into account that some regression like lasso already set some coefficient to.zero based on correlation, my way of proceed is correct or is better to take all the factors and let the lasso the job of removing some of them? – Luigi87 Jul 11 at 17:09

Assuming you're going to be fitting a linear regression, creating a correlation (Pearson) matrix of all assets is a common first step to filter endogenous (or multicollinear) variables from your test set.

• thanks for confirmation. However, if I use a Lasso, is this correlation step redundant? as the lasso drops some features to zero or not? – Luigi87 Jul 14 at 6:55
• @Luigi87, maybe not exhaustively but if you're using LASSO you likely don't need the correlation matrix as well – Chris Jul 15 at 3:54