Estimating Company-Specific Stock Risk from Index Regressions
Summary
The document explains how to estimate stock movement that is specific to a company rather than shared with a broad index. It proposes regressing each stock’s returns on index returns, then examining the residuals. A low regression R-squared indicates that a larger share of the stock’s total variation is unexplained by the index, but it does not by itself show which stocks have the greatest absolute company-specific risk.
For comparisons across stocks, the answers recommend measuring residual variance, such as mean squared residuals, or the standard deviation of residuals over a chosen interval. These measures capture the magnitude of the movement left after accounting for the index. The document gives a variance decomposition into market-related and specific components. Its discussion is an initial method rather than a full empirical study: results depend on the regression setup, return frequency, and sample period, and residual risk is an estimate rather than proof that movement came from company news.
Key ideas
- Regress each stock’s returns on index returns to separate index-related movement from residual movement.
- A low R-squared indicates a high specific-risk share of total variation, not necessarily high absolute specific risk.
- Compare stocks’ residual variance or residual standard deviation to estimate the magnitude of company-specific movement.
- The estimated residual risk depends on the chosen data frequency, model, and observation period.
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# Correlation or r-squared to determine if a stock has specific movement relative to an index?
# Correlation or r-squared to determine if a stock has specific movement relative to an index?
In Excel you have the daily prices of all the stocks in the S&P 500 for 3 years; and the index itself.
Using all the data how might you determine which stocks had company specific movement during the 3 year period?
The simplest thing I can think of is to regress each stock against the index and then filter down to those with r-squared closest to `0`. Another option is to use the correlation and filtering for those closest to `-1`, but negative beta isn't necessarily company specific movement.
I'm trying to make this first iteration as simple as possible and easily visible using Excel. Is there a better approach?
## Answer by Gustavo Amarante (score 2)
https://quant.stackexchange.com/a/36551
Short answer: to find the companies with the higher specific risk, look for the regressions with higher mean squared residuals.
Long Answer: If you are interested in company specific risk, what you are doing is kind of right. The lower the $R^{2}$ is, the higher the ratio of company specific risk to total risk is.
Looking at the $R^{2}$ alone is not sufficient to compare company specific risks between companies, because some of them might have very different levels of total risk. After each regression you should compute the company specific risk (which is just the Mean squared residuals).
The risks are connected by following equation:
$$\sigma^{2}_{total}= \beta^{2} \sigma^{2}_{market}+ \sigma^{2}_{specific} $$
## Answer by user28909 (score 1)
https://quant.stackexchange.com/a/36549
Company specific movement can be estimated as the standard deviation of monthly residuals. So, regress each firm with the index and estimate the monthly residuals. Calculate the standard deviation of monthly residuals for each firm. Then use residual risk as an estimate of the magnitude of firm specific movement.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.