Testing CAPM Security Market Line Pricing Errors for Significance

Summary

This question describes a cross-sectional CAPM test using 49 industry portfolios. The author first estimates portfolio betas from time-series data, then regresses mean excess returns on those estimated betas with the intercept constrained to zero to fit a security market line. The main question is how to test in R whether the resulting residuals, interpreted as pricing errors, differ significantly from zero.

The document establishes the test setup and the practical obstacle: the author wants to follow a test demonstrated in a video but lacks the R knowledge to implement it. It does not specify a test statistic, standard-error method, null hypothesis beyond the residual question, or code. In particular, it gives no detail on how uncertainty from the first-stage beta estimates or dependence among portfolio returns should affect inference. It is therefore a request about statistical testing rather than a worked CAPM result or a complete testing procedure.

Key ideas

• The proposed CAPM test estimates portfolio betas in a time-series step.
• The second step regresses mean excess returns on estimated betas with the intercept fixed at zero.
• The residuals from that cross-sectional fit are treated as pricing errors.
• The question asks how to test the pricing errors for statistical significance in R.
• No test method, implementation, or empirical conclusion is provided.

Tags

# Testing pricing errors on the SML for significance with R


# Testing pricing errors on the SML for significance with R












I have been attempting to do a cross-sectional test of the CAPM.

To do this, i have estimated the betas of 49 industry portfolios with time -series data. And then done a cross sectional regression, where i regressed the mean excess returns on the estimated betas, with a forced intercept of 0, to get the security market line.

And i got the following result:

How can i test if the residuals (pricing errors) are significantly different from 0 with R?

EDIT:

I am trying to do what is described in this video: https://www.youtube.com/watch?v=zxTfVIWZg34 but i lack the R knowledge to actually perform the test.

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