Hamada’s equation and the beta of debt under CAPM

David Johnstone and Steve Tulig

Accounting and Finance, 2022, vol. 62, issue 2, 2385-2399

Abstract: The Hamada equation based on Miller–Modigliani (MM) Proposition I shows the ‘no arbitrage’ relationship between the firm’s levered and unlevered beta. This relationship can be obtained from a capital asset pricing model (CAPM). MM is not required because asset prices under CAPM are inherently additive under any arbitrary slicing or securitisation of the firm’s cash flows (the size of the pie is unaffected by how it is cut). Our CAPM theory shows why the market rate of return on debt increases when the firm takes risks that increase its probability of default, even when the risk is idiosyncratic and unconnected to market conditions.

Date: 2022
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