Equilibrium-Based Volatility Models of the Market Portfolio Rate of Return (Peacock Tails or Stotting Gazelles)

Abstract

Volatility models of the market portfolio’s return are central to financial risk management. Within an equilibrium framework, we introduce an implementation method and study two families of such models. One is deterministic volatility, represented by current popular models. Another is in the “constant elasticity of variance” family, in which we propose new models. Theoretically, we show that, together with constant expected returns, the latter family tends to have better ability to forecast. Empirically, our proposed models, while as easy to implement as the popular ones, outperform them in three out-of-sample forecast evaluations of different time periods, by standard predictability criteria. This is true particularly during high-volatility periods, whether the market rises or falls.

Keywords: Market Risk, Volatility Model, Systematic Risk, Market Portfolio, Predictive Power, Equilibrium, GARCH, RiskMetrics, Piecewise Constant Volatility, Constant Elasticity of Variance

JEL Classification: G17, G12, C58