Axiomatization of residual income and generation of financial securities

Roberto Ghiselli Ricci and Carlo Alberto Magni

Quantitative Finance, 2014, vol. 14, issue 7, 1257-1271

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.

Date: 2014
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Working Paper: Axiomatization of residual income and generation of financial securities (2009)
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DOI: 10.1080/14697688.2012.717415

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