Turnover: measuring portfolio reallocation

A backtest can show attractive returns while quietly replacing most of the portfolio at every rebalance. Once spreads, market impact, and taxes are included, that apparent edge may be too expensive to trade.

Turnover measures the share of portfolio capital reallocated between rebalances. It is different from concentration: a stable concentrated portfolio can have low turnover, while frequent changes to a diversified portfolio can produce high turnover.

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.

Trading costs and allocation stability

Each reallocated dollar incurs bid-ask spread and market impact. Turnover also measures weight stability across rebalance dates. Large reallocations following small changes in estimated returns or covariances indicate a sensitive allocation method.

The walk-forward study in robust portfolio optimization reports annualized turnover of 1.64 for trailing-ICIR weighting, compared with 0.06 for nominal mean-variance and 0.26 for the CVaR-robust variant. Trailing ICIR had an average HHI of 0.172, close to equal weighting at 0.167. Changes in its estimates produced frequent reallocations. Average concentration remained close to equal weighting.

Transaction-cost treatment

The allocator's walk-forward evaluation applies a 5-basis-point transaction cost to each unit of turnover. Reported net returns and Sharpe ratios include the cost of rebalancing.

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.