MODIGLIANI AND MILLER: THEORY OF INVESTMENT 271 Since we have already shown that arbitrage will also prevent va from being larger than VI, we can conclude that in equilibrium we must have V2=vi, as stated in Proposition I. Proposition II. From Proposition I we can derive the following propo- sition concerning the rate of return on common stock m companies whose capital structure includes some debt the expected rate of return or yield, i, on the stock of any company j belonging to the kth class is a linear function of leverage as follows (8) 讠=p+(p-r)D/S小 That is, the expected yield of a share of stock is equal to the appropriate capitalization rate p for a pure equity stream in the class, plus a premiun related to financial risk equal to the debt-to-equity ratio times the spread between pk and r Or equivalently, the market price of any share of stock is given by capitalizing its expected return at the continuously variable rate i of( 8). 12 A number of writers have stated close equivalents of our Propositio I although by appealing to intuition rather than by attempting a proof and only to insist immediately that the results were not applicable to the actual capital markets.Proposition Il, however, so far as we have been able to discover is new. 4 To establish it we first note that, by definition, the expected rate of return, i, is given b 叉-rD Si From Proposition I, equation we know that. di Substituting in (9)and simplifying, we obtain equation( 8) X=1000, D=4000, =5 per cent and p=10 per cent. These values imply that V=10,000 and S=6000 by virtue of Proposition I. The expected yield or rate of return per share is the 1000-200 1 See, for example, J. B. williams [21, esp. pp. 72-73]; David Durand [3]; and W.A. Morton [15]. None of these writers describe in any detail the keep the average cost of capital constant under changes in cal ever, to be visualizing the equilibrating mechanism in term ks and bonds as the yields of each get out of line with their riskiness. "This is an argu ment quite different from the pure arbitrage mechanism underlying our proof, and the diffe inevita misunderstanding of many factors influencing relative yields such as, for ex- the portfolio composition of financial institutions, See below, esp 4 Morton does make reference to a linear yield function but only .. for the sake of sim plicity and because the particular function used makes no essential difference in my conclu sions"[15, P. 443, note