The Modigliani‐Miller Propositions After Thirty Years

the event with a retrosjjective look at what we set out to do on that occasion and an appraisal of where the propositions stand today after three decades of intense scrutiny and often bitter controversy. Some of these controversies can be now be regarded as settled. Our Proposition I, holding the value of a firm to be independent of its capital structure (that is, its debt/equity ratio) is accepted as an implication of equilibrium in perfect capital markets. The validity of our then-novel arbitrage proof of that proposition is also no longer disputed, and essentially similar arbitrage proofs are now common throughout finance. Propositions analogous to, and often even called, M and M propositions, have spread beyond corporation finance to the fields of money and banking, fiscal policy and intemational finance. ^ Examples include Cornell and French (1983) on the pricing of stock index futures. Black and Scholes (1973) on the pricing of options and Ross (1976) on the structure of capital asset prices generally. For other, and in some respects, more general proofs of our capital structure proposition, see among others, Stiglitz (1974) for a general equilibrium proof showing that individual wealth and consumption opportunities are unaffected by capital structures; Hirshleifer (1965) and (1966) for a state preference, complete-markets proof; Duffie and Shafer (1986) for extensions to some cases of incomplete markets and Merton (forthcom-ing) for a spanning proof.