Articles

Determining Market-Capitalization Breakpoints
By Andrew Clark

Page 5 of 6

Figures 7-9 detail the results for each "activity" for each country. Since the results were very consistent across the periods (January 2000-February 2012), we show one value per country per activity. Also shown is the goodness of fit.

Log Volume - Log Bid

Log Price x Volume

In the developed-market countries, both volume measures, especially price times volume, have single exponents and excellent fits. The two exceptions are Switzerland and Italy, where volume traded and bid/ ask spread have a moderate goodness of fit, while price times volume has an excellent fit. It needs to be kept in mind that both Switzerland and Italy have a substantially smaller number of stocks in their universe, and this contributes to the lack of fit. However, it may also be the case that for both countries, a power law is not being followed.

For developing-market countries, there is a consistent presence of one scaling exponent, and in general, excellent fits. As mentioned earlier, Malaysia is the country with the consistently poor fit. Although Malaysia is not plagued by a lack of stocks, it clearly does not follow a scaling law. So, in Malaysia's case, we cannot say empirical evidence does not support market-cap breakpoints.