An optimisation approach to constructing an exchange-traded fund

In this paper we consider the problem of deciding the portfolio of assets that should underlie an exchange-traded fund (ETF). We formulate this problem as a mixed-integer nonlinear program. We consider ETFs which have positive leverage with respect to their benchmark index and ETFs which have negative leverage (inverse, short, ETFs). Our formulation is a flexible one that incorporates decisions as to both long and short positions in assets, as well as including rebalancing and transaction cost. Computational results are given for problems, derived from universes defined by S&P international equity indices, involving up to 1,200 assets.