Stock Price Volatility in a Multiple Security Overlapping Generations Model

A number of empirical studies have reached the conclusion that stock price volatility cannot be fully explained within the standard dividend discount model. This paper proposes a resolution based upon a model that contains both a random supply of risky assets and finitely lived agents who trade in a multiple security environment. As the analysis shows there exist 2K equilibria when K securities trade. The low volatility equilibria have properties analogous to those found in the infinitely lived agent models of Campbell and Kyle (1991) and Wang (1993, 1994). In contrast, the high volatility equilibria have very different characteristics. Within the high volatility equilibria very large price variances can be generated with very small supply shocks. Using previously established empirical results the model can reconcile the data with supply shocks that are less than 10% as large as observed return shocks. The multiple security analysis also shows that within the economy some securities may trade under high volatility conditions, while others trade in low volatility conditions. Switching the economy from a high to a low volatility equilibrium for any single security may be very difficult. Depending upon the variance-covariance structure of the economy, an equilibrium change may require simultaneous control over the trading environment of every single security in the economy.