Greedy Tracking Error Optimization for Small Futures Portfolios

Summary

The document presents a static optimization approach for choosing tradable futures positions when a small account cannot hold fractional target weights. It minimizes portfolio tracking error relative to an ideal target, while also accounting for trading costs. Rather than searching exhaustively across integer position combinations, a greedy procedure starts from feasible weights and repeatedly adds one contract-sized increment when it improves the objective. The step direction follows the sign of the target position, subject to constraint-related corner cases.

The author compares this approach with rounded positions, selecting a fixed instrument list, and dynamic optimization, reporting estimated Sharpe-ratio penalties and tracking-error tradeoffs for those alternatives. The claims are based on the author’s system and presented performance exhibits; they are not a general guarantee. The method can also be constrained by live-trading rules such as reduce-only, do-not-trade, and maximum-position limits. Greedy search is faster and may be adequate, but can stop at a local minimum, and results will depend on costs, covariance estimates, capital, and the available contracts.

Key ideas

• Small accounts may be unable to represent ideal portfolio weights because futures positions come in contract-sized increments.
• The objective combines tracking error from the target weights with trading costs relative to prior holdings.
• A greedy search adds feasible contract increments that improve the objective, avoiding exhaustive enumeration.
• The document compares dynamic selection, fixed instrument lists, and rounded positions using tracking error and Sharpe-ratio tradeoffs.
• Live constraints can include reduce-only rules, prohibited trades, and maximum positions.
• Greedy optimization can settle at a local minimum, and reported results depend on the author’s system and assumptions.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.