270 THE AMERICAN ECONOMIC REVIEW F1≈a(S2+D2) X-raD,- a-X-Ta D3 Comparing (5)with(6)we see that as long as Vi>Vi we must have Yi>Y3, so that it pays owners of company 2's shares to sell their hold ings, thereby depressing Ss and hence Vi; and to acquire shares of com- pany 1, thereby raising SI and thus Vi. We conclude therefore the levered companies cannot command a premium over unlevered com- panies because investors have the opportunity of putting the equivalent leverage into their portfolio directly by borrowing on personal account Consider now the other possibility, namely that the market value of the levered company V, is less than Vi. Suppose an investor holds ini- tially an amount si of shares of company 1, representing a fraction a of the total outstanding stock, Si. His return from this holding is YI Suppose he were to exchange this initial holding for another portfolio also worth si, but consisting of sa dollars of stock of company 2 and of d dollars of bonds, where Ss and d are given by In other words the new portfolio is to consist of stock of company 2 and of bonds in the proportions S /V2 and D3/Va, respectively. The return from the stock in the new portfolio will be a fraction sa/Ss of the total return to stockholders of company 2, which is(X-rD,), and the return from the bonds will be rd. Making use of(7), the total return from the portfolio, Y,, can be expressed as follows S Y2=-(X-rD,+rd =-(X-rDa)+r=51==X=aX (since s1=aSi). Comparing Y with Y we see that, if VI<SI=Vi, then Y, will exceed Y1. Hence it pays the holders of company 1's shares to sell these holdings and replace them with a mixed portfolio containing an appropriate fraction of the shares of company 2 The acquisition of a mixed portfolio of stock of a levered company j and of bonds in the proportion S,/V, and D,/V, respectively, may be regarded as an operation which"undoes" the leverage, giving access to an appropriate fraction of the unlevered return Xj. It is this possibility of undoing leverage which prevents the value of levered firms from be ing consistently less than those of unlevered firms, or more generally prevents the average cost of capital X,/V, from being systematically higher for levered than for nonlevered companies in the same class