Conditional Factor Models for Equity Statistical Arbitrage

Summary

This study builds a statistical arbitrage method around a conditional factor model for a portfolio of US equities. A state space model treats returns as noisy combinations of factor values and latent, time-varying factor risk premia. Online filtering and prediction estimate those premia, producing expected returns that can be compared with observed returns; large deviations are considered candidates for mean reversion.

The authors evaluate a trading strategy that accounts for transaction costs, using both linear and nonlinear versions of the state space model. They report results across a 29-year history and compare performance with simple benchmarks and other published approaches, finding the method competitive. They also report that performance has weakened over time, particularly in recent years, though it remains economically compelling in their analysis. The document provides no details here on asset selection, trading thresholds, cost assumptions, or risk controls, so the reported findings alone are not enough to judge whether the strategy would transfer to another market or period.

Key ideas

• A state space factor model can represent equity returns as noisy exposures to latent factor risk premia.
• Online estimates of time-varying premia adapt the model to changing return behavior.
• Large gaps between observed and filtered returns are treated as potential mean reversion trades.
• The evaluated strategy includes transaction costs and uses linear and nonlinear model variants.
• Reported performance is competitive over a long sample but declines in more recent years.

Tags

# On statistical arbitrage under a conditional factor model of equity returns


# On statistical arbitrage under a conditional factor model of equity returns









We consider a conditional factor model for a multivariate portfolio of United States equities in the context of analysing a statistical arbitrage trading strategy. A state space framework underlies the factor model whereby asset returns are assumed to be a noisy observation of a linear combination of factor values and latent factor risk premia. Filter and state prediction estimates for the risk premia are retrieved in an online way. Such estimates induce filtered asset returns that can be compared to measurement observations, with large deviations representing candidate mean reversion trades. Further, in that the risk premia are modelled as time-varying quantities, non-stationarity in returns is de facto captured. We study an empirical trading strategy respectful of transaction costs, and demonstrate performance over a long history of 29 years, for both a linear and a non-linear state space model. Our results show that the model is competitive relative to the results of other methods, including simple benchmarks and other cutting-edge approaches as published in the literature. Also of note, while strategy performance degradation is noticed through time -- especially for the most recent years -- the strategy continues to offer compelling economics, and has scope for further advancement.

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