Sparse Mean-Reverting Portfolios: Metrics and Construction Methods
Summary
This article explains why a multi-asset mean-reverting portfolio may be easier to trade when it uses a small number of assets. Sparse baskets can improve interpretability and reduce trading costs; they also avoid the ambiguity that can arise when combining overlapping cointegrated pairs. It frames portfolio selection as balancing mean-reversion strength against the number of nonzero asset weights.
The article reviews the Ornstein–Uhlenbeck mean-reversion speed and alternative proxies: predictability, portmanteau statistics, and zero-crossing rates. Lower predictability and portmanteau values, and higher crossing rates, are associated with stronger mean reversion. It outlines greedy selection, convex relaxation, and covariance or structured VAR preprocessing to identify candidate baskets. An ETF illustration is mentioned, but the supplied text is incomplete and does not provide enough detail to assess the construction methods empirically. Mean-reversion metrics alone do not establish tradability or account for execution costs and short-sale constraints.
Key ideas
- Sparse portfolios seek mean reversion with fewer active asset weights.
- Mean-reversion speed is conceptually useful but difficult to optimize directly over portfolio weights.
- Lower predictability and portmanteau statistics, and higher zero-crossing rates, indicate stronger mean reversion under the stated assumptions.
- Greedy selection and convex relaxation are proposed ways to construct sparse portfolios.
- Short-sale access, transaction costs, and practical tradability remain important limitations.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.