An Aggregation Theorem for the Valuation of Equity Under Linear Information Dynamics

Abstract

We state an Aggregation Theorem which shows that the recursion value of equity is functionally proportional to its adaptation value. Since the recursion value of equity is equal to its book value plus the expected present value of its abnormal earnings, it follows that the adaptation value of equity can normally be determined by a process of simple quadrature. We demonstrate the application of the Aggregation Theorem using two stochastic processes. The first uses the linear information dynamics of the Ohlson (1995) model. The second uses linear information dynamics based on the Cox, Ingersoll and Ross (1985)'square root' process. Both these processes lead to closed form expressions for the adaptation and overall market value of equity. There are, however, many other processes which are compatible with the Aggregation Theorem. These all show that the market value of equity will be a highly convex function of its recursion value. The empirical evidence we report for UK companies largely supports the convexity hypothesis. Copyright Blackwell Publishers Ltd, 2003.

Searching for value relevance of book value and earnings: a case of premium versus discount firms

“…The empirical accounting research asserts that the roles of earnings and book value in equity valuation are affected by firm-level conditions such as the sign of earnings, financial strength of the firm, and relative levels of earnings and book values (Collins et al 1999;Barth et al 1998;Ashton et al 2003;Burgstahler and Dichev 1998). The prior literature stresses the importance of accounting for these conditions both in analytical modelling and empirical testing, as the relationship between equity market value and accounting numbers is complex.…”

“…The association studies typically model these relationships either in the spirit of residual income (Ohlson 1995;Rees 1997;Hand and Landsman 2005), or the option-style valuation framework (Burgstahler and Dichev 1997;Wysocki 1998;Ashton et al 2003).…”

“…A large body of empirical market-based accounting research demonstrates that the relative valuation roles of book values, earnings and dividends are fundamentally affected by firm characteristics. The influential and welldocumented characteristics include (i) the sign and permanence of earnings (Hayn 1995;Collins et al 1999Jefferson et al 2000, (ii) the relative levels of earnings and book value (Burgstahler and Dichev 1997), and (iii) the financial health of the firm (Barth et al 1998;Ashton et al 2003).…”

‘Equity smirks’ and embedded options: the shape of a firm's value function

“…This paper examines the methodology and assumptions of Ashton, D., Cooke, T.,Tippett, M., Wang, P. (2004) employing recursion value η as an explanatory single-variable in a model of the firm, first introduced by Ashton, D., Cooke,T.,Tippett in (2003). A qualitative analysis of all of their numerical findings is given together with an indication of how more useful is the tool of special function theory, here requiring confluent hypergeometric functions associated with the Merton-style valuation equation…”

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AbstractThis paper examines the methodology and assumptions of Ashton, D., Cooke, T.,Tippett, M., Wang, P. (2004) employing recursion value η as an explanatory single-variable in a model of the firm, first introduced by Ashton, D., Cooke,T.,Tippett in (2003). A qualitative analysis of all of their numerical findings is given together with an indication of how more useful is the tool of special function theory, here requiring confluent hypergeometric functions associated with the Merton-style valuation equation

A justification and a wider interpretation of their model and findings is offered: these come from inclusion of strictly convex dissipating frictions arising either as insurance costs, replacement costs of funds paid out, or of debt service, and from the inclusion of alternative adaptation options embedded in the equity value of a firm; these predict not only a J-shaped equity curve, but also, under the richer modelling assumption, a snakelike curve that may result from financial frictions like insurance.

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