Articles

Determining Market-Capitalization Breakpoints
By Andrew Clark

Page 6 of 6

Conclusion
We have shown that in most of the countries examined, there is good-to-excellent evidence that empirical data such as volume, bid/ask spread and price times volume do not support commonly used market-cap breakpoints. These results are in line with other work that looked at other "activities" on both a daily and intraday basis. Again, our conclusions do not invalidate current market conventions. What our research shows is that in most cases, empirical measures of stock activity do not support the common market-cap breakpoints.

Works Cited
1. Plerou, V. et al. "Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series," Physical Review Letters. 1999, vol. 83, 7.
2. Plerou, V. et al. "Random Matrix Approach to Cross Correlation in Financial Data," Physical Review E. 2002, vol. 65.
3. Zumbach, G. "How the Trading Activity Scales with the Company Size in the FTSE 100," Quantitative Finance. 2004, vol. 4, 4.
4. Li, W. et al. "Financial Factor Influence on Scaling and Memory of Trading Volume in Stock Markets," Physical Review E. 2011, vol. 84.
5. Kertesz, J. and Eisler, Z. "Limits of Scaling and Universality in Stock Market Data," (Online) Dec. 21, 2005. (cited: Jan. 12, 2012) http://arxiv.org/abs/physics/0512193v1.
6. Stumpf, M.P.H. and Porter, M.A. "Critical Truths about Power Laws," Science. 2012, 335.
7. Bouchaud, J-P and Potters, M. "Theory of Financial Risk and Derivative Pricing," Cambridge University Press, 2000.

Endnotes
¹ Mega-cap stocks are considered to be part of the group comprising the 70 percent. While this article does not specifically work with mega-cap stocks, the conclusions it
draws about market-cap breakpoints apply to mega-cap stocks as well.
² Most market-capitalization schemes that are tripartite in nature, such as the one above, do not tend to include micro-cap stocks. Market participants who are interested
in micro-cap stocks typically make an estimate as to where small-caps end and micro-caps begin. This article shows that such estimates may suffer from the same problem
that makes other market-cap breakpoints hard to justify empirically.
³ The usual least squares (LSQ) estimate assumes a variance in the y variable but none in the x variable, which is assumed to be known exactly. However, market capitalization
is a time series and therefore has its own variance. To account for this, we have to use a more sophisticated LSQ estimate with an error in both variables. Zumbach
used an LSQ estimator that is more complex to compute, since it involves a minimization problem (to find the best parameters) to find the roots of a one-dimensional
function (to compute the error on the parameters). The values of the minimum (slope and intercept) and the errors on the parameters (standard deviations of the slope
and intercept) are fairly insensitive to the choice for the standard deviation (s1 vs. s2), but the goodness of fit depends directly on the choice for the standard deviation.
Since s1 is lower than s2, this produces systematically worse goodness of fit. For this reason, we use the more conservative standard deviation s1.