EVOLUTION OF FIRM SIZE

Lukas Gonon () and L. C. G. Rogers ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2014, vol. 17, issue 05, 1-15

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.

Keywords: Firm size; Black–Scholes model; optimal investment; growth rate estimation uncertainty; generalized hyperbolic distribution (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0219024914500319

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