Interpreting Factor-Model Regressions for Undiversified Portfolios

Summary

This exchange considers whether CAPM or a multi-factor asset-pricing regression requires the portfolio being analyzed to be efficiently diversified. The answer says statistically significant coefficients can still be interpreted when the portfolio does not satisfy that condition.

The regression is presented as a way to decompose portfolio returns into linear exposures to the included factors and an intercept. The intercept can be viewed as return unexplained by those exposures, while the coefficients describe co-movement with the factors. The answer cautions implicitly against treating that statistical relationship as proof of causation. It gives no empirical example or discussion of estimation assumptions, omitted variables, significance tests, or how an inefficient portfolio may affect risk-adjusted performance comparisons, so those considerations remain outside the exchange's scope.

Key ideas

• Factor-model regressions can estimate exposures for portfolios regardless of whether they are efficiently diversified.
• Coefficients describe the portfolio's linear relationship with the included factors.
• The intercept captures performance not explained by those factor exposures.
• Regression co-movement alone does not establish that factors caused the observed returns.

Tags

# How consequential are violations of the efficient diversification assumption of asset pricing models?


# How consequential are violations of the efficient diversification assumption of asset pricing models?












When using asset pricing models such as the CAPM or the Fama-French four factor model to determine the risk-adjusted return of a portfolio, does this strictly require efficient diversification of the portfolio? How consequential is a violation of this assumption? Do the regression coefficients obtained from estimation of such a model, using the return time series of a portfolio as dependent variable have a meaningful interpretation when the portfolio is far from efficient diversification?

## Answer by Kyle Balkissoon (score 2, accepted)

https://quant.stackexchange.com/a/15897

The coefficients assuming they are statistically significant can be interpreted whether or not the underlying portfolio is efficient.

The CAPM or FF4 simply tries to decompose a portfolio into a series of linear exposures + an intercept (alpha) which can be viewed as constant added value.

In mathematical terms the regression is explaining how much of the performance "coincides" with the four factors (causality is difficult to establish).

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