Testing Modigliani-Miller for Banks

Chapter 3 uses data on 51 large US banks in 2001-13 to test the M&M the­orem. With assets ranging from about $6 billion to $2.4 trillion, these banks accounted for about 75 percent of the total assets of US banks (including noncommercial bank subsidiaries of bank holding companies) in 2013.

The discussion begins with the question of whether the banking sector is special. The ratio of total assets to equity capital has typically been only about 3:1 for the nonfinancial sector but about 10:1 or higher for banking. In their analysis of equity returns, Fama and French (1992, 429) specifically excluded financial firms, because they judged that the high leverage normal for the sector did not have the same meaning of distress as in nonfinancial firms. The major product of banks—liquid deposit services to customers— constitutes debt, making them inherently different from nonbanks with re­spect to the ratio of debt to equity (Herring 2011, DeAngelo and Stulz 2013).

Those empirical tests of M&M for banking that have been conducted, moreover, have typically sought to identify the influence of the capital structure irrelevance theorem by calculating the relationship of bank “beta” coefficients to leverage ratios (capital relative to assets).^[5] In the capital asset pricing model (CAPM), the unit cost of equity equals the risk-free rate plus the firm's beta coefficient multiplied by the excess of the diversified market yield over the risk-free rate (equity premium). Although tests do tend to find that bank beta coefficients are related to leverage, the underlying CAPM framework is known to perform poorly in explaining cross-section stock returns (Fama and French 1992). In any event, the original model of Modigliani and Miller (1958) provides a much more direct estimating form, and the tests in chapter 3 apply this form.

In those tests the cost of equity capital is estimated as a linear function of the ratio of debt to equity.

The tests in chapter 3 apply two alternative measures of equity cost: the inverse of the price-to-earnings ratio and the ratio of net earnings to the book value of equity. For both the data are constrained to force the observed equity cost to no less than the risk-free rate plus 100 basis points, so that negative earnings instances (concentrated in 2007-10) do not give misleading signals of returns demanded by investors. Although about 8 percent of bank-year observations show negative earnings, only 1 percent of the sample had losses exceeding 3 percent of bank assets, suggesting a lower needed seawall than typically perceived.

The estimates show a statistically significant coefficient of equity cost on leverage for one of the specifications (net earnings relative to book value of equity). Using the average coefficients estimated for the two specifica­tions, and considering the base levels of equity cost and likely levels for in­terest rates on debt, a 15 percentage point increase in the ratio of equity capital from an illustrative base level of 10 percent (as proposed by Admati and Hellwig 2013) would raise the average cost of capital to banks by a central estimate of 62 basis points. If there were no M&M effect at all, the corresponding increase would be 112 percent, so the estimated M&M offset amounts to 0.45. Slightly less than half of the cost impact of higher capital requirements would thus be offset by the lower unit cost of equity thanks to lower risk.