Risk-allocation-based index tracking. (June 2023) - Anis, Hassan T.; Costa, Giorgio; Kwon, Roy H.
Abstract: Index tracking (IT) is a passive investment strategy where a portfolio is created to replicate the performance of a benchmark portfolio. This work reframes the IT problem to be more risk-centric, positing that matching the risk make-up of the tracking portfolio to that of the benchmark's should be a primary importance in IT. To that end, a novel risk-allocation based index tracking (RABIT) framework is proposed where the risk profile of the benchmark is tracked by minimizing the difference between its sectors' percentage risk contribution and tracking portfolio's. The RABIT framework is formulated as a non-convex, quadratically-constrained, quadratic mixed integer program. The formulation is solvable to global optimality by the latest off-the-shelf solvers, which is verified in small-scale experiments. An exploration–exploitation heuristic utilizing nonlinear programming (NLP) and genetic algorithms (GA) is developed to solve larger scale problems which are computationally burdensome to the latest solvers. Computational experiments on synthetic and real-world financial data support the need of the RABIT framework, its use for both nominal and enhanced IT, and validate the use of the proposed heuristic to solve the problem. Empirical experiments show that by matching the risk contributions, the RABIT framework tilts the portfolios towards the benchmark, bringing it closer in terms of in-sample characteristics. The out-of-sample performance of the RABIT framework is also shown to be closer to the benchmark's in terms of risk-adjusted return across all cardinality sizes and auxiliary objective functions. Highlights: A new index tracking approach based on matching risk profiles of sectors is proposed. Better in-sample and out-of-sample tracking results. An effective heuristic is developed to scale to larger index tracking problems.