Why a Single Stock Can Have a Low Fama–French Regression R-Squared

Summary

The document considers why a regression of an individual stock’s returns on the Fama–French three factors produces a lower R-squared than expected from the original factor-model paper. The questioner describes aligning monthly stock returns with monthly factor data and regressing returns on the market, size, and value factors, while wondering whether date conventions or using one stock explains the result.

The answer reports a similar R-squared for Apple and attributes the modest fit to stock-specific, idiosyncratic risk, which the factors do not explain. It distinguishes this single-stock exercise from the paper’s portfolio regressions. The example supports the point that a lower R-squared does not by itself show that factor dates are misaligned or that the regression is incorrect. The discussion is brief: it does not systematically audit the data merge, excess-return construction, or other regression choices, so those details still matter when reproducing a specific study.

Key ideas

• The three-factor model may explain less variation in an individual stock than in a diversified portfolio.
• Idiosyncratic stock risk contributes to residual variation and lowers regression R-squared.
• A result similar to the reported Apple regression is presented as consistent with this explanation.
• A low R-squared alone does not establish that monthly factor dates were aligned incorrectly.
• Exact replication still depends on matching the paper’s portfolio, excess-return, and data conventions.

Tags

# Large price adjustment for capitalization-weighted index


# Large price adjustment for capitalization-weighted index












Assume we are calculating a value-weighted index of a set of stocks that have more or less the same capitalization. However, one of the stocks has substantially larger price than others (although market cap is still on the same level). For example:

```
Stock A: price 10, market cap 100 000
Stock B: price 15, market cap 120 000
Stock C: price 10000, market cap 110 000
```

Then value weighted index will be:

```
10 * (100 000/330 000) + 15 * (120 000/330 000) + 10000 * (110 000/330 000) = 3342
```

Now if Stock C gets excluded from the index and is replaced by Stock D with price 18 and market cap 110 000, then new value of the index is:

```
10 * (100 000/330 000) + 15 * (120 000/330 000) + 18 * (110 000/330 000) = 14.5
```

So the index would drop by 99.6% without any changes to the market cap. Am I missing something here ? Is there a way to adjust for that ? Fundamentally the index should represent average return on a universe of stocks and should not be affected so much by inclusion/exclusion of a single stock.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.