This is a summary of "Leverage and the Cross-Section of Equity Returns," by Hitesh Doshi, Kris Jacobs, Praveen Kumar, and Ramon Rabinovich, published in the Journal of Finance.
Unlevered market beta is more critical in explaining the cross-section of unlevered equity returns than levered equity returns, even after controlling for size and the book-to-market ratio. The size effect weakens, whereas the value premium and the volatility puzzle substantially vanish for unlevered returns. Leverage creates multiplicative heteroskedasticity in the data, which makes statistical inference challenging. Unlevering returns mitigates the problem of heteroskedasticity.
What Is the Investment Issue?
The authors explore whether the size discount, value premium, and volatility puzzle (i.e., the negative cross-sectional relationship between volatility and returns) anomalies result partly from financial leverage risk. Although there is general consensus that these three anomalies exist, there is little agreement about their interpretation.
How Did the Authors Conduct This Research?
The authors create and investigate hypotheses regarding the cross-section of unlevered equity returns. For a large class of linear asset pricing models of levered stock returns, systematic (levered) equity risk can be decomposed into systematic unlevered risk and non-linear representations of leverage risk. This decomposition provides testable hypotheses for the cross-section of unlevered returns. The most important of these hypotheses is that the asset market beta should be priced into the cross-section of unlevered equity returns.
The authors obtain the number of shares outstanding and stock returns from CRSP while limiting attention to non-financial firms. The risk-free rate is procured from Kenneth French’s website. For most of the study, the face value of the firm’s debt is proxied with total liabilities. Quarterly data on the firm’s debt and liabilities from 1971 to 2012 are obtained from Compustat.
Stock returns for 25 size and book-to-market ratio (BTM) portfolios are reported, and the results demonstrate that small firms and high-BTM firms have higher stock returns. The authors use a regression approach to consider how size and BTM affect the cross-section of expected stock returns. Regressors include the firm’s levered market beta, the logarithm of the firm’s market capitalization, and the logarithm of book value over market value.
The presence of leverage in returns is addressed in two related approaches: by scaling returns using the leverage ratio and by unlevering returns using a parametric model.
What Are the Findings and Implications for Investors and Investment Professionals?
The results confirm that two anomalies exist in the sample: The size discount and value premium are economically and statistically significant in the cross-section of stock returns; and levered market beta is not statistically significant when controlling for size and BTM.
The authors confirm the existence of the volatility puzzle, the size effect, and the BTM effect in levered returns and conclude that levered market beta is not priced. Their analysis of unlevered returns provides two key results. First, a relatively simple model explains the data and shows that the value premium and volatility puzzle weaken significantly for unlevered returns. Size is priced into the cross-section of unlevered returns, but its effect weakens. The results demonstrate that BTM, size, and volatility likely affect the cross-section of stock returns partly through their connection with financial leverage–related risk. Second, leverage produces heteroskedasticity, which makes modeling the non-linear relationship between leverage and stock returns difficult.