An Iterated Greedy Heuristic for the 1/N Portfolio Tracking Problem

Abstract

The 1/N portfolio represents a simple strategy to invest money in the stock market. Investors who follow this strategy invest an equal proportion of their investment budget in each stock from a given investment universe. Empirical results indicate that this strategy leads to competitive results in terms of risk and return compared to more sophisticated strategies. However, in practice, investing in all N stocks from a given investment universe can cause substantial transaction costs if N s large or if the market is illiquid. The optimization problem considered in this paper consists of optimally replicating the returns of the 1/ N portfolio by selecting a small subset of theN stocks, and determining the respective weight for each selected stock. For the first time, we apply the concept of iterated greedy heuristics to this novel portfolio-optimization problem. For analyzing the performance of our heuristic approach, we also formulate the problem as a mixed-integer quadratic program (MIQP). Our computational results indicate that, within a limited CPU time, our heuristic approach outperforms the MIQP, in particular when the number of stocks N grows large.