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A hybrid approach combining iterated greedy heuristics and quadratic programming to track the 1/N portfolio
No full textInvestors who apply the 1/N portfolio strategy invest an equal amount of their investment budget in all N stocks from a given investment universe. It was empirically shown that this simple strategy compares favorably in terms of risk and return to other, more sophisticated investment strategies like the mean-variance approach and extensions thereof. However, if N is large, the 1/N portfolio strategy causes substantial management costs. Therefore, we consider the problem of optimally tracking the returns of the 1/N portfolio by selecting a small subset of the N stocks and by determining each selected stock's weight in the tracking portfolio. This problem can be formulated as a mixed-integer quadratic program (MIQP) that uses the weights of the stocks in the 1/N portfolio, i.e., 1/N, as input. However, this MIQP becomes computationally expensive when N grows large. In this paper, we therefore develop a hybrid approach that combines an iterated greedy heuristic for selecting the subset of the N stocks and a quadratic program for determining the optimal weight of each selected stock. We demonstrate in a computational experiment that our hybrid approach outperforms a commercial MIQP solver in terms of solution quality and CPU time. Moreover, the portfolios we construct compare advantageously with well-known index-tracking approaches, which can be used to replicate the returns of any portfolio, in terms of tracking accuracy
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