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Evolution Of Firm Size

Author

Listed:
  • LUKAS GONON

    (ETH Zürich, Department of Mathematics, Rämistrasse 101, 8092 Zürich, Switzerland)

  • L. C. G. ROGERS

    (Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK)

Abstract

In this paper, we develop the idea that firm sizes evolve as log Brownian motions dSt = St(σdWt + μdt) where the constants μ, σ are characteristics of the firm, chosen from some distribution, and that the firms are wound up at some random time. At any given time, we see a firm of a given size. What can we say about its characteristics given its size? How would we invest in such a market? What do these assumptions imply about the distribution of sizes? By making simple and well-chosen modeling assumptions, we are able to develop quite concrete forms of the dependence of firm characteristics on size, from which we are able to deduce optimal investment weights as a function of size alone. As in the approach of Fernholz [2002, Stochastic Portfolio Theory. Springer], this avoids the need to estimate growth rates of stocks in order to decide on investment strategy.

Suggested Citation

  • Lukas Gonon & L. C. G. Rogers, 2014. "Evolution Of Firm Size," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1-15.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:05:n:s0219024914500319
    DOI: 10.1142/S0219024914500319
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