The Betting Against Beta Anomaly: Fact or Fiction?
A new related paper has been added to:
#77 – Beta Factor in Stocks
Authors: Buchner, Wagner
Title: The Betting Against Beta Anomaly: Fact or Fiction?
This paper suggests an alternative explanation for the recently documented betting against beta anomaly. Given that the equity of a levered firm is equivalent to a call option on firm assets and option returns are non-linearly related to underlying stock returns, linear CAPM-type regressions are generally misspecified. We derive theoretical expressions for the pricing error and analyze its magnitude using numerical examples. Consistent with the empirical findings of Frazzini and Pedersen (2014), our pricing errors are negative, increase with leverage, and become economically significant for higher levels of firm leverage.
Notable quotations from the academic research paper:
"In this paper, we suggest a possible alternative explanation for the betting against beta phenomenon. We propose that the betting against beta phenomenon is due to pricing errors, which arise given that the CAPM does not take non-linearities in stock returns into account. Our rationale is as follows. As highlighted by the classic Black-Scholes-Merton model of corporate debt and equity valuation, the equity of a levered firm is equivalent to a call option written on the underlying value of the firm’s assets. As is known, option returns are highly skewed and non-linearly related to the returns of the underlying. Therefore, linear CAPM-type regressions of equity returns may suffer from model misspecification. Using the Black-Scholes-Merton model, we derive expressions for the model pricing error under the standard CAPM and analyze its magnitude using numerical examples.
Our analysis highlights that the pricing error is negative and becomes economically large as firm leverage increases. That is, consistent with the empirical findings of Frazzini and Pedersen (2014), our theoretical analysis predicts that a portfolio that is long low-beta stocks and short high-beta stocks generates a positive CAPM alpha. However, since the equity is correctly priced under our Black-Scholes-Merton framework, the observed positive alpha is due to the pricing error that is induced by the inadequate linearity assumption of the CAPM. This result questions whether the betting against beta phenomenon is indeed an asset pricing anomaly or whether it is due to the fact that the standard CAPM is an inappropriate setting for analyzing the equity returns of highly levered firms. As the analysis presented in this paper is purely theoretical, our aim here is not to assert that the documented betting against beta phenomenon can fully be attributed to the pricing error that we point out. Such detailed empirical tests are beyond the scope of the present paper. Nonetheless, our findings highlight that care must be taken when we interpret the negative alphas of high-beta stocks as an asset pricing anomaly"
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