Using Regression to Identify Company Metrics Associated With Stock Returns

Summary

The document asks how to identify which company financial or operational metrics help explain its stock performance. The response proposes a linear factor model in which the stock return is regressed on a set of candidate metrics, treated as explanatory variables. At each chosen observation frequency, ordinary least squares can estimate coefficients that represent each metric’s conditional contribution to returns; weighted least squares is mentioned as an alternative.

The response suggests evaluating coefficient significance under distributional assumptions for returns and model errors, while allowing other suitable distributions. It does not provide data, a worked example, or evidence that this procedure reliably isolates causal business drivers. Results would depend on the metric set, timing, sample size, and model assumptions; correlated predictors and changing financial disclosures can also complicate interpretation. The method is therefore a starting point for statistical attribution, rather than proof that a metric causes company performance.

Key ideas

• A linear factor model can relate stock returns to candidate company metrics.
• Ordinary least squares estimates coefficients that describe each metric’s contribution within the model.
• Weighted least squares is offered as another estimation approach.
• Coefficient significance depends on assumptions about return and error distributions.
• The response gives no empirical validation or method for establishing causality.

Tags

# selecting key performance indicators for a stock


# selecting key performance indicators for a stock












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?

## Answer by numerairX (score 1)

https://quant.stackexchange.com/a/42168

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).

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.