Optimal trend-following portfolios

Sebastien Valeyre

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We propose a a unifying theory for portfolio optimisation, following from the work of Markowitz and Capital Fund Management.
We emphasize the importance of modelling correlation matrix between trends, not solely the the correlation matrix between small-scale returns in determining the optimal trend-following portfolio.
Implied correlation matrices between trends, which are needed in the formulation of some very particular portfolios, are derived.

Abstract

This paper derives an optimal portfolio based on a trend-following signal. Building on the previous literature, we provide a unifying theoretical setting to introduce an autocorrelation model with a covariance matrix of trends and risk premiums. We specify practically relevant models for the covariance matrix of trends. The optimal portfolio is decomposed into four basic components that yield four basic portfolios: Markowitz, risk parity, agnostic risk parity and trend-following on risk parity. The overperformance of the proposed optimal portfolio, when applied to a cross-asset trading universe, is confirmed by empirical backtests. We thus provide a unifying framework to describe and rationalize previously developed portfolios.

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