# Equilibrium-based volatility models of the market portfolio rate of return (peacock tails or stotting gazelles)

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## Abstract

We introduce a theoretical and empirical method of studying equilibrium-consistent volatility models. We implement it with the market portfolio’s return, which is central to financial risk management. Within an equilibrium framework, we study two families of such models. One is deterministic volatility, represented by current popular models. The other 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## References

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