Optim Lett DOI 10.1007/s11590-014-0779-x ORIGINAL PAPER An optimisation approach to constructing an exchange-traded fund C. A. Valle · N. Meade · J. E. Beasley Received: 4 January 2014 / Accepted: 4 August 2014 © Springer-Verlag Berlin Heidelberg 2014 Abstract 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. Keywords ETF · Exchange-traded fund · MINLP · Mixed-integer nonlinear program · Optimisation 1 Introduction An exchange-traded fund (henceforth ETF) is, as the name suggests, a fund (portfolio of assets) on which shares have been issued. These shares are traded on the open C. A. Valle · J. E. Beasley (B ) Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, UK e-mail: john.beasley@brunel.ac.uk C. A. Valle e-mail: cristiano.arbexvalle@brunel.ac.uk N. Meade Business School, Imperial College, London SW7 2AZ, UK e-mail: n.meade@imperial.ac.uk J. E. Beasley JB Consultants, Morden SM4 4HS, UK e-mail: john.beasley@jbconsultants.biz 123