Modeling Growth Stocks via Size Distribution

Abstract

Since growth stocks tend to have low or even negative earnings and high volatility, it is a great challenge to derive a meaningful mathematical model within the traditional valuation framework. This paper attempts to demonstrate that the high volatility of share prices can nevertheless be used in building a model that leads to a particular size distribution. The result can then be applied to price a growth stock relative to its peers. The model focuses on both transient and steady state behavior of the market capitalization of the stock, which can in turn be either modeled as a birth-death process or a diffusion process. The model not only has some economic interpretations for its parameters, but also leads to some interesting economic insight --- the model postulates mean reversion (with a high mean reverting level) for growth stocks, which may be useful in understanding the recent boom and burst of the ``internet bubble''. In addition, the model provides an explanation to an empirical puzzle reported in the Wall Street Journal about internet stocks.