Estimating Firm-Specific Risk from Factor-Regression Residuals
Summary
The document explains idiosyncratic risk as the portion of a stock’s return variability left after accounting for systematic market movements. In a market model, beta scales the market’s excess return to estimate the firm’s market-related return; subtracting that fitted component leaves residual returns. The questioner also considers a Fama–French three-factor regression, which adjusts for additional common return factors before residual volatility is measured.
The proposed measure is the annualized standard deviation of daily regression residuals over the firm’s fiscal year. This offers a firm-level volatility measure after factor exposures are removed, rather than treating total stock volatility as entirely firm-specific. The response gives a conceptual explanation of beta and market adjustment, but does not provide Stata syntax or fully specify annualization conventions, regression details, or data requirements. Those choices need to be made consistently when implementing the measure.
Key ideas
- Beta scales the market return to estimate a firm’s systematic market exposure.
- Regression residuals represent returns not explained by the included market or factor variables.
- Idiosyncratic risk can be measured as the standard deviation of daily residuals across a fiscal year.
- Adding Fama–French factors adjusts residual risk for more than market exposure alone.
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Full text
# Calculate Idiosyncratic Risk? # Calculate Idiosyncratic Risk? I have basic finance background but I am trying to calculate idiosyncratic risk as measure for firm risk in my CEO gender research. I have found the following on Alpha architect but I am unsure of how to interpret this and actually calculate the residuals. I am not using Excel, but Stata. For this reason I really need to understand what I am doing so that I can code it in Stata. Importantly, I am trying to calculate Idiosyncratic Risk defined as follows: "the annualized standard deviation of the residuals from the regression of daily returns over the firm's fiscal year". I have some of the inputs already. I have the excess returns of the firm stocks in my dataset, the market excess returns and I have calculated the beta's for my firms. I also have the FF 3 factors. The Alpha Architect link contains an Excel example of which I am basing my questions. Here is a visualization from the Excel. Some of the links in the explanation I have don't work so I am unsure how exactly I need to do the following: 1. what I need the beta for? 2. how to conduct the Fama French 3 Factor regression so that I can extract the residuals of that regression 3. how to calculate Idiosyncratic risk once I have the residuals Links: https://alphaarchitect.com/2014/12/19/a-quick-lesson-in-volatility-measures/ How to calculate unsystematic risk? ## Answer by eSurfsnake (score 0) https://quant.stackexchange.com/a/41189 Simplistically, the risk (volatility or standard deviation) of the stock is composed of two pieces: ``` 1) the market risk, and 2) the idiosyncratic risk of the firm ``` If all firms had the same beta, the market risk would be the same for all firms, and would be the index risk. But, in the CAPM theory, some firms move (on average) more than 1:1 with the market. It is like some boats rising farther when the tide comes in, and dropping lower when it goes out. Thus, the model is that any firm has a systematic risk which is $\beta$ times the move of the market. When you subtract that out (on a daily basis) what is left is the unique, idiosyncratic risk of the firm after adjusting for the market and the beta of the firm.
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