Published in Wilmott Magazine, Mar/Apr 2008, pp. 62-68


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Incorporating Default Risk into Hamada's Equation for Application to Capital Structure

Ruben D. Cohen (e-mail)




Implemented widely in the area of corporate finance, Hamadaís Equation enables one to separate the financial risk of a levered firm from its business risk.The relationship, which results from combining the Modigliani-Miller capital structuring theorems with the Capital Asset Pricing Model, is used extensively in practice, as well as in academia, to help determine the levered beta and, through it, the optimal capital structure of corporate firms.


Despite its regular use in the industry, it is acknowledged that the equation does not incorporate the impact of default risk and, thus, credit spread - an inherent component within every levered institution.Several attempts have been made so far to correct this, but, for one reason or another, they all seem to have their faults.†† This, of course, presents a major setback, as there is a strong need, especially by practitioners, to have in place a solid methodology to enable them to assess a firmís capital structure in a consistent manner.This work addresses the issue and provides a robust modification to Hamadaís Equation, which achieves this consistency.