An Arbitrage Model for Calculating Firm Beta at Different Leverage Levels

Abstract

Traditionally, the Hamada Equation is used to estimate a firm’s levered beta. However, a major drawback of the Hamada Equation is its assumption that the cost of debt is equal to the risk free rate at all levels of debt. In this paper, we develop an alternative model that could be applied by practitioners to estimate levered betas. The primary advantage of our approach is that it does not require Hamada’s assumption that the cost of debt is equal to the risk free rate. Our model is based on the concept that the target or proposed debt level for the firm being evaluated can be replicated via a stock portfolio. In an efficient market where arbitrage can occur, the beta for the firm at the target debt level may be derived from the beta of the replicated stock portfolio.