Modeling Growth Stocks via Size Distribution¤

The inability to predict the earnings of growth stocks, such as biotechnology and internet stocks, leads to the high volatility of share prices and di±culty in applying the traditional valuation methods. 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, which 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 in turn is modeled as a birth-death process. In addition, the model gives an explanation to an empirical observation that the market capitalization of internet stocks tends to be a power function of their relative ranks. Issuing stocks is arguably the most important way for growth companies to ̄nance their projects, and in turn helps transfer new ideas into products and services for society. Although the components of growth stocks may change over time (perhaps consisting of railroad and utility stocks in the early 1900's, and biotechnology and internet stocks in 2001), studying the general properties of growth stocks is essential to understand ̄nancial markets and economic growth. However, uncertainty is manifest for growth stocks. For example, (a) growth stocks tend to have low or even negative earnings; (b) the volatility of growth stocks is high (both their daily appreciation and depreciation rates are high); (c) it is di±cult to predict the upward and downward trends. Consequently, it poses a great challenge to derive a meaningful mathematical model within the classical valuation framework, such as the net present value method. Since it appears that as far as growth stocks are concerned, we are only sure about their uncertainty, one may wonder whether there is much more to say about them. The current paper attempts to illustrate that a mathematical model for growth stocks can, nevertheless, be built, mainly by utilizing the high volatility of their share prices. One motivation of the current study comes from a report on internet stocks in the Wall Street Journal1 (Dec 27, 1999): People2 at Credit Suisse First Boston observed that \there is literally a mathematical relationship between the ranking of the (internet) stock and its capitalization". More precisely, it is suggested the emergence of an almost linear downward We are grateful to Professor Morris Cohen at the Wharton School, University of Pennsylvania, to point out the article in the Wall Street Journal during a talk. This observation is summarized later in a research report by Mauboussin and Schay (2000).