Black’s Leverage Effect is Not Due to Leverage
Lo and Hasanhodzic challenge the theory.
BY Andrew W. Lo and Jasmina Hasanhodzic | February 17, 2011
(SSRN) One of the most enduring empirical regularities of equity markets is the fact that stock-return volatility rises after price declines, with larger declines inducing greater volatility spikes. In a seminal paper, Black (1976) provides a compelling explanation for this phenomenon in terms of the firm’s financial leverage: a negative return implies a drop in the value of the firm’s equity, increasing its leverage which, in turn, leads to higher equity-return volatility. This explanation has been so tightly coupled with the empirical phenomenon that the inverse relation between stock returns and volatility is now commonly known as the “leverage effect”. This effect, and the leverage-based explanation, have been empirically confirmed by a number of studies since Black (1976), e.g., Christie (1982), Cheung and Ng (1992), and Duffee (1995), using linear regressions of returns on subsequent changes in volatility for individual stocks and stock portfolios, and arguing that these relationships become stronger as the firms’ debt- to-equity ratios increase. However, the validity of the leverage explanation has been called into question more recently by Figlewski and Wang (2000), who document several empirical anomalies associated with it.
In this paper we provide clear evidence that the leverage effect is not due to financial leverage. Using the returns of all-equity-financed companies from January 1972 to December 2008, and the specifications of Black (1976), Christie (1982), and Duffee (1995), we find just as strong an inverse relationship between returns and the subsequent volatility changes as for their debt-financed counterparts. This finding suggests that we must look elsewhere for an explanation of this empirical regularity, e.g., time-varying expected returns, endogenous volatility, or path-dependent cognitive risk perceptions.
In Section 2 we provide a review of the literature in which the stock-return/volatility relationship is documented, focusing on a few key regression-based studies that we replicate using the sample of all-equity-financed companies described in Section 3. In Section 4 we present our empirical results, and we conclude in Section 5 with a discussion of some possible interpretations. (Read the full paper here)