Asset pre-selection for a cardinality constrained index tracking portfolio with optional enhancement

Abstract

Index trackers are important passive investments offering the return and risk of the market encapsulated by the index, the largest US index tracker was valued at $900 billion in early 2026. Using a two-stage approach of asset selection followed by estimation on S&P 500 data, we explore the role of cardinality constraints in determining the effectiveness of the tracker's reproduction of market return and risk. We compare eight pre-selection procedures: forward selection or backward elimination; implemented using ordinary least squares or least absolute deviation regression; with or without a regression constant. We show experimentally that out-of-sample tracking errors decrease according to the inverse of the square root of cardinality and out-of-sample tracking error, transaction volume and return-risk ratios all improve as the cardinality constraint is relaxed. By contrast for enhanced returns, cardinalities of the order 10 to 20 are most effective.