Risk indicators in equity markets ⋆ Leonard MacLean 1 , Giorgio Consigli 2 , Yonggan Zhao 1 , and William Ziemba 3 1 School of Business Administration, Dalhousie University, 6100 University Avenue, Halifax, Canada B3H 3J5, l.c.maclean@dal.ca {l.c.maclean, yonggan.zhao}@dal.ca 2 Department of Mathematics, Statistics and Computer Science, University of Bergamo, Via dei Caniana, 24127 Bergamo, Italy giorgio.consigli@unibg.it 3 Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, British Columbia V6T 1Z2, Canada ziemba@interchange.ubc.ca Abstract. The distribution of securities prices in financial markets is known to exhibit heavy tails, and furthermore the time trajectory has occasional extreme swings or reversals in direction. The modelling of heavy tails has been achieved with the addition of a homogeneous point process to a diffusive process. However, the timing of the jumps in the point process should capture the price reversals. In this paper a non- homogeneous point process is introduced, so that the intensity and size of jumps are state dependent. The state is characterized by stress mea- sures, which are composed from combinations of risk factors. The factors considered are the bond-stock yield differential and the volatility index. The parameters in the model are estimated from data on the US market from 1990 - 2007. An out-of-sample test is performed for 2008 - 2009. The model captures the swings in equities prices and provides a basis for anticipating reversals from risk factors. Keywords. Cox process, endogenous instability, stress factors, extreme equity risk, maximum likelihood. M.S.C. classification. 62F25, 91B24, 91B30. J.E.L. classification. C13, C52, G12. 1 Introduction The short and medium term dynamics of equity markets in developed economies have in recent years (e.g. last two decades) increasingly shown evidence of fun- damental imbalances associated with frequent volatility regime switching and occasional prolonged periods of one-sided tail events. The development of new ⋆ Supported by Natural Sciences and Engineering Council of Canada and the Canada Research Chairs program.