Multi-Period Portfolio Optimization: Translation of Autocorrelation Risk to Excess Variance

TL;DR

This paper extends growth-optimal portfolio strategies to account for autocorrelation in asset returns, showing how autocorrelation risk can be incorporated into the covariance matrix to improve short-term risk management.

Contribution

It introduces a method to incorporate autocorrelation risk into portfolio optimization by adjusting the covariance matrix, extending previous models that assumed uncorrelated returns.

Findings

Autocorrelation risk can be absorbed into the covariance matrix.

Portfolio strategies can be adapted to account for market autocorrelations.

The approach improves short-term risk control in growth-optimal portfolios.

Abstract

Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors' beliefs about market movements. Moreover, we prove that the risk incurred by such autocorrelations can be absorbed by modifying the covariance matrix of asset returns.