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Deriving the arbitrage pricing theory when the number of factors is unknown

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  • L. P. Middleton
  • S. E. Satchell

Abstract

This paper examines the use of proxies (or reference variables) for the true factors in the arbitrage pricing theory (APT). It generalizes other authors' existing work and shows that, when there are more reference variables than the true factors, the APT still holds. The possibility of fewer reference variables than the true factors is also considered, but the APT is not shown to hold, in the same sense, for this case. This work builds on an earlier paper by Ingersoll (Ingersoll J 1984 J. Finance39 1021-39), and our propositions can be thought of as specializations of his theorems. Similar to Nawalkha (Nawalkha S 1997 J. Financial Economics46 357-81), our work does not use the mathematics of Hilbert and Banach spaces and, thus, is open to a much wider audience. The practical implication of our results is that model builders should be generous with the number of factors they use, as excessively parsimonious models suffer from inaccuracy.

Suggested Citation

  • L. P. Middleton & S. E. Satchell, 2001. "Deriving the arbitrage pricing theory when the number of factors is unknown," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 502-508.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:5:p:502-508
    DOI: 10.1088/1469-7688/1/5/302
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    Cited by:

    1. Szczygielski, Jan Jakub & Brzeszczyński, Janusz & Charteris, Ailie & Bwanya, Princess Rutendo, 2022. "The COVID-19 storm and the energy sector: The impact and role of uncertainty," Energy Economics, Elsevier, vol. 109(C).
    2. Blanka Francová, 2018. "An Analysis of the Impact of Selected Factors on the Bond Market," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 66(6), pages 1451-1458.

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