Equity and debt in the form of a bond

We start with a company with a simple capital structure consisting of equity and debt in the form of a bond. When the bond matures the bond investor normally gets the nominal value of his investment back. In case the company is not able to repay the bond, the company’s asset will be liquidated and paid out to the bondholder. The value of the corporate bond (C) is therefore the minimum of the debt (D, equivalent to nominal value of the bond) and the value of the assets of the company (A). C = min(D, A) = D + min(A – D, 0).

If we look at the nominal debt value as the strike price and the value of the assets as the value of the underlying, the equation above can be rewritten as C = D – max(D + A, 0). Thus a corporate bond is a combination of a risk-free bond and a short put on the company’s assets. The risk of default can be extracted from the price of the put. The put price in turn depends on the asset value of the firm (price of the underlying) and its debt (strike price of the option), interest rate, maturity of the debt and the volatility of the company value. This is where the link between implied volatility and corporate spreads originates, as the implied volatility of the stock can help to estimate the volatility of the firm’s asset value. Based on this relationship Galai and Masulis (1976) derive a formal link between the degree of debt financing and equity risk.

With constant operational risk, equity risk rises when debt financing goes up. This link was confirmed in a number of studies and extended to operational leverage, the fact that fixed costs cannot be reduced very fast when demand turns weak, as Schwert (1989), Ferguson (1994) and Franks and Schwartz (1988) point out.