An application of Microsoft Excel's evolutionary solver based on a novel chromosome encoding scheme to the 1/N portfolio tracking problem

摘要

The 1/N portfolio is an equally-weighted portfolio composed of all N stocks from a given investment universe. This portfolio offers an attractive risk-return profile but causes substantial management costs if N is large. Therefore, we consider the problem of optimally tracking the 1/N portfolio by constructing an equally-weighted portfolio composed of a subset of the N stocks. This problem can be formulated as a binary quadratic program that, however, becomes computationally expensive to solve for mathematical programming solvers if N is large. In this paper, we present a novel chromosome encoding scheme based on a string of unique integers representing the indices of the selected stocks. We implement this scheme on a spreadsheet and apply Microsoft Excel's evolutionary solver to devise tracking portfolios. We demonstrate that, by using our novel encoding scheme instead of an existing one, the solver determines considerably better solutions.