Turnover: how fast a portfolio's positions actually change

Turnover measures how much of a portfolio's capital is reallocated between rebalances. It is a distinct concept from concentration: a portfolio can hold a small number of large positions and still change very little from one rebalance to the next, or hold many modest positions that shift substantially every period.

Definition

For weights \(w_{i,t}\) and \(w_{i,t-1}\) at consecutive rebalance dates, one-way turnover for that rebalance is

\[\tau_t = \frac{1}{2} \sum_{i} \left| w_{i,t} - w_{i,t-1} \right|.\]

The one-half factor avoids double-counting a dollar that moves out of one position and into another. Annualized turnover sums \(\tau_t\) across all rebalances in a year, or scales a shorter evaluation period to a one-year basis. A value of \(1.0\) means the portfolio's capital was, on net, fully reallocated once over the period measured.

Why turnover is not just a cost line item

Turnover matters directly because trading has cost: every reallocated dollar pays the bid-ask spread and market impact of getting there. It also matters indirectly, because a method that reallocates heavily on small changes in its inputs is telling you something about how sensitive its solution is to estimation noise rather than to a genuine change in the underlying economic signal.

This comparison, from the walk-forward study in robust portfolio optimization, is the counterintuitive case in practice: trailing-ICIR weighting produced by far the highest turnover of the five methods, well above either mean-variance solution, despite holding a similar concentration level to equal weighting. A raw expected-return score can move enough between rebalances to justify a large reallocation on the objective's own terms, even when the resulting portfolio does not look more concentrated by any static measure. Concentration and turnover answer different questions, and a method can score well on one while scoring poorly on the other.

Use in strategynet.ai

The allocator's walk-forward evaluation charges every unit of turnover a fixed transaction-cost assumption, currently 5 basis points, so that turnover differences between methods are reflected in the reported net return rather than left as a footnote. A method's evaluation Sharpe already accounts for how often it trades to achieve that result.

Further reading

• Richard C. Grinold and Ronald N. Kahn, Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk, McGraw-Hill, 2nd edition, 2000 (ISBN 978-0-07-024882-3). Develops the turnover and trading-cost tradeoffs referenced here.
• Roger G. Clarke, Harindra de Silva, and Steven Thorley, “Portfolio Constraints and the Fundamental Law of Active Management”, Financial Analysts Journal, 2002. Examines how position constraints, closely related to turnover under rebalancing, affect achievable information ratios.