MODIGLIANI AND MILLER: THEORY OF INVESTMENT 269 its capital structure and is equal to the capitalisation rate of a pure equity stream of认 s class. To establish Proposition I we will show that as long as the relations (3)or(4)do not hold between any pair of firms in a class, arbitrage will take place and restore the stated equalities. We use the term arbitrage advisedly. For if Proposition I did not hold, an investor could buy and ell stocks and bonds in such a way as to exchange one income stream for another stream, identical in all relevant respects but selling at a lower price. The exchange would therefore be advantageous to the inves- tor quite independently of his attitudes toward risk. As investors exploit these arbitrage opportunities, the value of the overpriced shares will fall and that of the underpriced shares will rise, thereby tending to eliminate the discrepancy between the market values of the firms By way of proof, consider two firms in the same class and assume for simplicity only, that the expected return, X, is the same for both firms Let company 1 be financed entirely with common stock while company levered firm, Va, to be larger than that of the unlevered one, V1.Con sider an investor holding Ss dollars'worth of the shares of company 2, representing a fraction a of the total outstanding stock, S2. The return rom this portfolio, denoted by Y,, will be a fraction a of the income available for the stockholders of company 2, which is equal to the total return Xi less the interest charge, rD Since under our assumption of homogeneity, the anticipated total return of company 2, X2, is, under all circumstances, the same as the anticipated total return to company 1, X1, we can hereafter replace X2 and Xi by a common symbol X Hence, the return from the initial portfolio can be written as Y2=a(X-rD, Now suppose the investor sold his aS2 worth of company 2 shares and acquired instead an amount si=(Sr+D,of the shares of company 1 He could do so by utilizing the amount as, realized from the sale of his initial holding and borrowing an additional amount ad, on his own credit, pledging his new holdings in company 1 as a collateral. He would thus secure for himself a fraction si/ S1=a(S+D /S1 of the shares and earnings of company 1. Making proper allowance for the interest pay ments on his personal debt aD, the return from the new portfolio, Y, is given b 1 In the language of the theory of choice, the exchanges points in the interior to eficient points on the not movements between eficient points along the boundary. Hence for this part of the analysis nothing is involved in the way of specific assumptions about investor attitudes or behavior other than that investors behave