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

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  • David Ashton
  • Terry Cooke
  • Mark Tippett

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.

Suggested Citation

  • David Ashton & Terry Cooke & Mark Tippett, 2003. "An Aggregation Theorem for the Valuation of Equity Under Linear Information Dynamics," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(3‐4), pages 413-440, April.
    • Handle: RePEc:bla:jbfnac:v:30:y:2003:i:3-4:p:413-440
    DOI: 10.1111/1468-5957.00003
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    References listed on IDEAS

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    Cited by:

    1. Denise A. Jones, 2018. "Using real options theory to explain patterns in the valuation of research and development expenditures," Review of Quantitative Finance and Accounting, Springer, vol. 51(3), pages 575-593, October.
    2. Adam Ostaszewski, 2004. "‘Equity smirks’ and embedded options: the shape of a firm's value function," Accounting and Business Research, Taylor & Francis Journals, vol. 34(4), pages 301-321.
    3. Beattie, Vivien, 2005. "Moving the financial accounting research front forward: the UK contribution," The British Accounting Review, Elsevier, vol. 37(1), pages 85-114.
    4. Juana Aledo Martínez & Juan Manuel García Lara & María T. González Pérez & Christos A. Grambovas, 2020. "An empirical assessment of proposed solutions for resolving scale problems in value relevance accounting research," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 60(4), pages 3905-3933, December.
    5. David Ashton & Terry Cooke & Mark Tippett & Pengguo Wang, 2004. "Linear information dynamics, aggregation, dividends and ‘dirty surplus’ accounting," Accounting and Business Research, Taylor & Francis Journals, vol. 34(4), pages 277-299.
    6. Mark Aleksanyan & Khondkar Karim, 2013. "Searching for value relevance of book value and earnings: a case of premium versus discount firms," Review of Quantitative Finance and Accounting, Springer, vol. 41(3), pages 489-511, October.
    7. Arturo Leccadito & Stefania Veltri, 2015. "A regime switching Ohlson model," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(5), pages 2015-2035, September.
    8. Victoria L. Hodgson & Allan Hodgson, 2008. "Marketing Communication Expenditures and Financial Capital—The Impact of Marketing as an Option," Australian Journal of Management, Australian School of Business, vol. 33(2), pages 333-353, December.

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