Axiomatization of residual income and generation of financial securities

Abstract

This paper presents an axiomatization of residual income, also known as excess profit, and illustrates how it can univocally give rise to fixed-income or variable-income assets. In the first part it is shown that, depending on the relations between excess profit and the investor's excess wealth, a well-specified theory of residual income is generated: one is the standard theory, which historically traces back to Hamilton and Marshall and is a deep-rooted notion in economic theory, finance, and accounting. Another is the systemic value added or lost-capital paradigm: first introduced by Magni, the theory is enfolded in Keynes's notion of user cost and is naturally generated by an arbitrage-theory perspective. In the second part, the paper inverts the usual analysis: instead of computing residual incomes from a pattern of cash flows, residual incomes are fixed first to derive vectors of cash flows. It is shown that variable- or fixed-income assets may be constructed on the basis of either theory starting from pre-determined growth rates for residual income. In particular, zero-coupon bonds and coupon bonds traded in a capital market are shown to be deduced as equilibrium vectors of residual-income-based assets.