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The Betting Against Beta Anomaly: Fact or Fiction?

Last Updated on 10 February, 2024 by Rejaul Karim

The Betting Against Beta Anomaly: Fact or Fiction?” by Axel Buchner and Niklas Wagner, provides an innovative perspective on the recently identified betting against beta anomaly.

The study proposes that conventional linear CAPM-type regressions are usually misrepresentative, given the non-linear relationship between the returns of an option and the underlying stock returns, and the fact that a levered firm’s equity is comparable to a call option on firm assets.

The authors construct theoretical equations for the pricing error and conduct an in-depth examination using numerical illustrations.

The paper’s findings align with earlier empirical research by Frazzini and Pedersen (2014), showing that pricing errors increase with leverage and become economically crucial at higher levels of firm leverage.

Abstract Of Paper

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.

Original paper – Download PDF

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Author

Axel Buchner
ESCP Business School

Niklas Wagner
Passau University

Conclusion

In conclusion, “The Betting Against Beta Anomaly: Fact or Fiction?” offers an alternate perspective on the betting against beta anomaly. The authors highlight that linear CAPM-type regressions are potentially misspecified, considering the non-linearity of the relationship between option returns and underlying stock returns.

They propose theoretical expressions for the pricing error and back their claims through rigorous numerical analyses. The observable pricing errors corroborate with Frazzini and Pedersen’s empirical findings, revealing negative errors that escalate with leverage, and gain economic significance at higher leverage levels.

This conclusion updates the understanding of asset pricing, specifically regarding the betting against beta anomaly and systematic risk.

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FAQ

What is the main focus of the paper “The Betting Against Beta Anomaly: Fact or Fiction?” by Axel Buchner and Niklas Wagner?

The main focus of the paper is to provide an alternative explanation for the betting against beta anomaly. The authors argue that conventional linear CAPM-type regressions are often misrepresentative due to the non-linear relationship between option returns and underlying stock returns, particularly in the context of leveraged firms.

What is the key argument presented in the paper regarding linear CAPM-type regressions and the betting against beta anomaly?

The key argument is that linear CAPM-type regressions are potentially misapplied in the context of the betting against beta anomaly. The authors argue that considering the non-linear relationship between option returns and underlying stock returns, especially for leveraged firms, is crucial for a more accurate representation of the anomaly.

How do the authors support their argument, and what theoretical expressions do they propose?

The authors support their argument by deriving theoretical expressions for the pricing error, emphasizing the need to account for the non-linear nature of option returns in relation to underlying stock returns. These theoretical expressions provide a framework for understanding the potential misrepresentation that can occur when linear CAPM-type regressions are applied to analyze the betting against beta anomaly.

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