Firms reveal private information about the value of investment through their investment decisions. As a consequence they may have ex post regret once they see other firms ’ investments. We define a notion of rational expectations equilibrium for games which imposes a “no-regret ” property. In this equilibrium, all firms make the same investment decision, but despite the absence of ex post regret, the investment herd can be inefficient. In addition equilibrium might not exist. We introduce a notion of probabilistic existence, and identify conditions under which, if the number of firms is large, enough information comes out so that investment herds are firstbest efficient with high probability, and equilibrium exists with high probability.

This paper applies graphical modelling to the S&P 500, Nikkei 225 and FTSE 100 stock market indices to trace the spillover of returns and volatility between these three major world stock market indices before, during and after the 2008 financial crisis. We find that the depth of market integration changed significantly between the pre-crisis period and the crisis and post- crisis period. Graphical models of both return and volatility spillovers are presented for each period. We conclude that graphical models are a useful tool in the analysis of multivariate time series where tracing the flow of causality is important.