Implied Penalties for Financial Leverage: Theory versus Empirical Evidence

Article excerpt


This study takes a new look at an old issue - the relationship between financial leverage and beta and, hence, between financial leverage and required return. Our motivation for returning to this question is based on three concerns: the conflicting results in extant empirical work, the recent controversy in the validity of beta as a discriminating measure of security risk (Fama and French, 1992), and the use of Hamada (1972) and similar techniques for unlevering and relevering betas for purposes of estimation of the cost of equity.

The theoretical literature dictates a positive and linear relationship between required return and leverage, as formulated by Modigliani and Miller (1858, 1963) within a constant risk class framework. Modigliani and Miller show, on both a no tax and after corporate tax basis, that the required return on equity of a levered firm increases in proportion to the debt-to-equity ratio. Hamada (1969, 1972) rederives the Modigliani and Miller propositions within a portfolio theoretic framework and shows that parallel relationships hold between equity betas and leverage as well. The major implication of the above works is that frans with the same asset risk but different degrees of leverage should have different costs of equity, with the market requiring higher returns on the more highly levered firm.

Opposing such paradigms is the traditionalist view. The traditionalists maintain that the market does not require higher returns for more highly levered frans until some critical leverage point is reached. At that point, required return will increase more dramatically with increases in financial leverage than that suggested by the later models of Modigliani and Miller and Hamada. Thus, within this framework, the cost of equity for frans within a given risk class will be constant across firms as long as critical leverage is not reached. [For one discussion of the traditionalist position, see Barges (1963).] While the arguments for the traditionalist position lack strong theoretical support (Brealey and Myers, 1988, pp. 396-397), the position nonetheless may reflect the perceptions of investors and analysts and the workings of financial markets. Surprisingly, while there has been a plethora of empirical research relating beta to financial leverage and a host of other variables, little research has tested how closely the actual Hamada relationships hold or has tested the Hamada relationship vis-a-vis the traditional position.

This article examines this issue from several perspectives. First, using ordinary least squares regression, we consider the Hamada proposition of a linear relationship between beta and financial leverage. Consistent with other studies, we find inconclusive results using this fairly simple test. We then relax the linearity assumption, and we use switching regime regressions to test for the nonconstant relationship between leverage and required return posited by traditionalist theories. Again, we find inconsistencies in the results of the switching regime models. Given the inconsistent results in tests of both the Hamada and the traditionalist models, we attempt to disentangle these mixed results by constructing a carefully controlled matched pair sample.

Examination of this issue is important for several reasons. Most managerial finance texts emphasize that a firm's equity risk arises from two components - operating risk and financial risk - and that market measures of equity risk, such as beta, should be delevered (typically with the Hamada adjustment) from the effects of financial risk in order to determine the asset risk premium applicable to the average firm project. To the extent that the Hamada adjustment for leverage fails to hold in practice, asset betas will be biased, leading to incorrect divisional costs of capital and capital budgeting decisions. Additionally, in the event the traditionalists are correct, firms that strive for a target beta would want to monitor more closely changes in operating risk over changes in financial risk. …