Consistent and Efficient Dynamic Portfolio Replication with Many Factors

Abstract

Factor investing involves choosing securities to construct portfolios with particular risk–return profiles. With the proliferation of benchmark-tracking exchange-traded funds (ETFs) virtually any risk–return profile can be reconstructed; the challenge is to find the right ETFs because the number of relevant ETFs is very large. This article proposes an innovative modification to the resampling procedure used in many popular machine learning methods for reducing the dimensionality of this problem. The proposed method allows selection of the specific ETFs used to replicate returns, taking the total costs of using the optimal portfolio to dynamically track returns into consideration. Existing variable selection algorithms are not designed to incorporate rebalancing costs, which are accumulated over time. The methodology is illustrated by replicating hedge fund returns with ETFs. The results show that, by selecting the right replication instruments in a way that is consistent with an investor’s economic utility instead of using purely statistical losses, the investor can save around 60 bps per year.

TOPICS: Exchange-traded funds and applications, statistical methods, simulations, big data/machine learning

Key Findings

• • A modified LASSO approach is developed for replication when variables are selected from many potential factors and transaction costs are accounted for in a dynamically consistent way.

• • By accounting for investor’s economic utility instead of purely statistical losses, the improved portfolio optimization procedure saves investors around 60 bps per year out of sample.

• • The new cross validation procedure is applicable for a wide range of problems in a time series context, when overfitting and transaction costs are major concerns of the model user.