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Interpreting CAPM Alpha and R-Squared Across Portfolios

Article Quant Q&A · Author: Priya
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Summary

The document asks how to compare CAPM regressions for two portfolios when their intercept estimates and adjusted R-squared values point in different directions. For P1, the intercept is reported as statistically insignificant and adjusted R-squared as 29%. For P2, the intercept is significant and adjusted R-squared is 85%. The author wonders whether the first portfolio fits CAPM better because its intercept is not significant, or whether the second does because its regression explains more return variation.

The central issue is that these statistics answer different questions: the intercept concerns average returns left unexplained by the market factor, while adjusted R-squared describes the proportion of observed variation accounted for by the regression, adjusted for model size. A high fit does not by itself establish that CAPM is correctly specified, and an insignificant intercept is not proof that alpha is exactly zero. The document poses the interpretive question but provides no regression diagnostics, confidence intervals, sample details, or proposed resolution, so it does not establish which portfolio is better described by CAPM.

Key ideas

  • A CAPM regression intercept measures estimated return unexplained by market exposure.
  • Adjusted R-squared summarizes how much return variation the regression accounts for.
  • An insignificant intercept and a high adjusted R-squared address different aspects of model fit.
  • Neither statistic alone establishes that CAPM is the best model for a portfolio.
  • The comparison lacks sample details and diagnostics needed for a fuller assessment.

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EquitiesStatisticsFactor investing
Full text
# How to interpret CAPM model?


# How to interpret CAPM model?












I want to run CAPM model on two portfolios P1 and P2. Where CAPM is Rt - Rft = λ0 + λ1 (Rmt - Rft) Results which I got: Portfolios Intercept Coefficient of Rm-Rf Adjusted R2 P1 0 i.e not sig. value significant 29% P2 not zero i.e sig. value significant 85%

For the P1 intercept is zero, is this mean CAPM is best model for P1 as it is capable of capturing the variation in the returns. But if we consider adj. R2 it only 29% which is very low which mean this model explain only 29% variation in returns of P1. For P2 intercept is not zero as it is significant, is this mean that this model is not best for P2 as its intercept is not zero. But it has adj. R2 value of 85% which very high in comparision of P1. • How do I interpret these results? CAPM is best for which portfolio? • Should I consider either intercept or adj. R2? • Should I consider both of them. But if I consider both of them, then these results are contradictory. Kindly help me. Thank you Priya

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