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Say, I read a financial statement of a company, and it reports, maybe 20-30 metrics, both generic, like revenue, free cash flow and specific to the company, like iphone sales etc. Is there a reasonable statistical procedure to determine which metrics actually drive the company's performance?

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borrowing from arbitrage pricing model, say we have $R_{t,t+1} = X_tf_{t,t+1} + \epsilon_{t,t+1}$, where $R$ is stock return, $X$ is your estimation universe consisting of numerous factors you mentioned in question, and $\epsilon$ is estimated from residual. Then for each day/any time frequency you have given company stat updated, estimate factor return by OLS (you can also use WLS etc), so under this model we can have a vector of factor return, $(X_t^TX)^{-1}X_t^TR_{t,t+1}$ and explains it as how much each factor contributes to the stock return.

And since it's a linear regression model, each coefficients' (factor returns) statistical significance can be calculated if you assume log of return is normally distributed and error term is normally distributed also (or other distributions that you see fit).

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  • $\begingroup$ Suppose I have 3000 metrics instead of 30. Would you agree, that this approach would just overfit on the historical data and may not have much use for future? $\endgroup$ – LazyCat Oct 12 '18 at 16:45
  • $\begingroup$ @LazyCat I'd say no matter what models you use, if you have 3000 metrics you're going to see the curse of dimensionality. Real question is, why would we use 3000 metrics blindly in the first place? $\endgroup$ – numerairX Oct 12 '18 at 17:52
  • $\begingroup$ I don't want to use all 3000 metrics, but I want to figure out which of them are important. The curse of dimensionality is more of a problem of the approach you suggest. $\endgroup$ – LazyCat Oct 12 '18 at 18:23
  • $\begingroup$ @LazyCat if you're more focused on selecting features, try run the same model in forward or backward selection and see what subsets of features the above methods give $\endgroup$ – numerairX Oct 12 '18 at 19:07

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