Measuring the Stability of a Dynamic System: The Case of the Stock Market Turmoil 2007-2008

The aim of this paper is to demonstrate how the change in actual and potential market risks in the Dow Jones Industrial Average (DJIA) during the two-year period 2007-2008 can be analyzed with the help of (lambda,sigma-2)-analysis. In the empirical analysis, the average of the Lyapunov exponents for the dynamic system generating DJIA returns is used as the stability measure, lambda, whereas the squared DJIA return is used as the variability measure, sigma-2. The main findings are as follows: (i) the potential market risk in the DJIA did not fluctuate that much during 2007, with the exceptions of early fall and near the end of the year; (ii) the potential market risk fluctuated a lot during 2008, especially in early August and in the middle of September; and (iii) the actual market risk in the DJIA was considerably higher near the end of 2008, especially in October, compared with the rest of the period.