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CAPM and significance of low value of R-square in regression

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Capital Asset Pricing Model (CAPM) is used to calculate the required return from a stock. To calculate the required return from ABC stock, a regression was run between the S&P Index daily retun over risk free rate and ABC daily returns over risk free rate on the historical data for 500 days. The R square value of the regression is 20%. What does this value represent. What does a low value of R square mean. Could you find some possible reasons for low R sqaure. Since the R square value is only 20%, can we conclude CAPM is not a good model to calculate the required rate of return.

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Solution Summary

This posting explains how to interpret the value of r-square obtained in a regression analysis mainly in the context of beta calculations for using CAPM. Whether a low value of R-square is always bad or a higher value of r-square is always good? Such questions are answered.

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See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

No. R square of the time series regression is really irrelevant. It is a bit meaningful in that low R square leads to imprecisely estimated alphas and betas, but we have separate t statistics to evaluate that question. High R2 only matters if you are interpreting the regression as an APT, but then we'd have other factors and not the market on the right hand side, and portfolios on the left.

R2 is a statistic that measures the percentage of variation in the dependent variable that is explained for by all the explanatory variables in the model. Thus, R2 provides a measure of the overall goodness-of-fit of the regression model. The R2 ...

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