Equilibrium Impact of Value - At - Risk ∗

We offer a framework to analyze Value-at-Risk based regulation rules and their possible distortion effects on financial markets. Our model is formulated in a continuous-time economy where investors maximize expected utility subject to some regulatory Value-at-Risk constraint when asset price dynamics are not lognormal and exhibit stochastic volatility. To retain tractability of the optimization problem, we make use of perturbation theory. We show that in partial equilibrium the effectiveness of VaR regulation is closely linked to the “leverage effect”, the tendency of volatility to increase when prices decline. We extend our analysis to a pure exchange economy and explore the implications of VaR regulation on equilibrium quantities such as interest rates and volatilities. Analysis of the general equilibrium model with heterogenous investors indicates that, when economic growth is slow, VaR regulation tends to reduce the level of interest rates and, at the same time, increases volatilities in stock markets. JEL Classification Codes: G11, G12, G28, D92, C60, C61.