Evolution of Firm Size

Gonon, Lukas and Rogers, L. C. G. (2014): Evolution of Firm Size. In: International Journal of Theoretical and Applied Finance, Vol. 17, No. 05, 1450031

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Workgroup Financial Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0219-0249
• Language: English