Portfolio optimisation models

Abstract

In this thesis we consider three different problems in the domain of portfolio optimisation. The first problem we consider is that of selecting an Absolute Return Portfolio (ARP). ARPs are usually seen as financial portfolios that aim to produce a good return regardless of how the underlying market performs, but our literature review shows that there is little agreement on what constitutes an ARP. We present a clear definition via a three-stage mixed-integer zero-one program for the problem of selecting an ARP. The second problem considered is that of designing a Market Neutral Portfolio (MNP). MNPs are generally defined as financial portfolios that (ideally)exhibit performance independent from that of an underlying market, but, once again, the existing literature is very fragmented. We consider the problem of constructing a MNP as a mixed-integer non-linear program (MINLP) which minimises the absolute value of the correlation between portfolio return and underlying benchmark return. The third problem is related to Exchange-Traded Funds (ETFs). ETFs are funds traded on the open market which typically have their performance tied to a benchmark index. They are composed of a basket of assets; most attempt to reproduce the returns of an index, but a growing number try to achieve a multiple of the benchmark return, such as two times or the negative of the return. We present a detailed performance study of the current ETF market and we find, among other conclusions, constant underperformance among ETFs that aim to do more than simply track an index. We present a MINLP for the problem of selecting the basket of assets that compose an ETF, which, to the best of our knowledge, is the first in the literature. For all three models we present extensive computational results for portfolios derived from universes defined by S&P international equity indices with up to 1200 stocks. We use CPLEX to solve the ARP problem and the software package Minotaur for both our MINLPs for MNP and an ETF.