Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices

Abstract

This paper analyzes optimal, dynamic portfolio and wealth/consumption policies of utility maximizing investors who must also manage market-risk exposure using a given risk-management model. We focus on the industry standard, the Value-at-Risk (VaR) based risk management, and find that VaR risk managers often optimally choose a larger exposure to risky assets than non risk managers, and consequently incur larger losses, when losses occur. We suggest an alternative risk management model, based on the expectation of a loss, to remedy the shortcomings of VaR. A general-equilibrium analysis reveals that the presence of VaR risk managers in a pure-exchange economy amplifies the stock-market volatility at times of down markets (and low output) and attenuates the volatility at times of up markets.