Are Securities Also Derivatives?

Abstract

This paper has used the Arbitrage Theorem (Gordan Theorem) to show that first, all securities are derivatives for each other, and they are priced by the same risk neutral probability measure. Second, after the firm changes its debt-equity ratio, the equityholders can always combine the new equity with other existing securities to create a home-made equity which will give exactly the same time-1 payoff of the old equity. That is, we have a capital structure irrelevancy proposition: changes in firms' debt-equity ratios will not affect equityholders' wealth (welfare), and equityholders' preferences toward variance are irrelevant. Third, when the firm moves from a more certain project to a more uncertain one, the time-0 price of equity will increase, but (because the time-1 payoff of common bond has an upper bound) the time-0 price of common bond will decrease. Fourth, different labor contractual arrangements will not affect the time-0 price of labor input. When the firm moves from a more certain project to a more uncertain one, the time-0 price of labor input will increase if it is under the share or the mixed contract.