Why a Portfolio Can Have Negative Returns and Positive Factor Alpha

Summary

The document asks how a portfolio can have negative or nearly flat realized returns during a period while reporting positive Fama–French three-factor alpha. It presents the familiar regression relationship between excess portfolio returns, market excess returns, size and value factor exposures, and an intercept. The author’s proposed interpretation is that alpha is the portion of the portfolio’s return not explained by the factor contributions, so it can be positive even when the portfolio’s total return is negative.

The numerical illustration supposes a negative market excess return, zero size and value factor returns, and a portfolio loss that is smaller than the market loss. Under those conditions and the stated equation, the residual contribution would be positive. The document does not provide the cited paper’s data, factor loadings, estimation method, or time aggregation details, so it does not verify the reported result. Its example is a conceptual check, not a full assessment of the paper’s alpha estimate.

Key ideas

• Alpha is the regression intercept representing returns not explained by the included factor contributions.
• A portfolio can lose money while earning positive alpha if its return exceeds the factor model’s predicted return.
• The example illustrates this possibility when market excess returns are negative and other factor contributions are zero.
• The document does not provide enough information to validate the cited paper’s reported alpha.

Tags

# How can a stock have negative returns but positive 3-factor alpha?


# How can a stock have negative returns but positive 3-factor alpha?












I've come across a research paper where for a specific period of time, the portfolio has negative returns (or roughly flat returns). During this same period of time, the portfolio's Fama-French 3-factor alpha is fairly positive.

Here is a photo of the returns from the paper, I'm looking at the 2000-2007ish time frame. My understanding is as such, but I'm not completely sure if this is right:

$$ R-R_f = B_1 (R_m-R_f) +B_2 (SMB) + B_3 HML + alpha $$

If in a given year $R_m - R_f$ was -5%, and SMB and HML were zero, but my particular stock (or portfolio) was -2%, I would have +3% alpha. In this way, I would have positive alpha while having negative returns.

Is this understanding correct, or something else?

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