International portfolio optimisation under uncertainty

Abstract

Portfolio optimisation problems are generally concerned with allocating funds to investments. The goal is to find an allocation that minimises risk subject to some certain constraints. To attain robust solutions from the optimisation, it is vital to ensure that the model is able to properly represent the underlying uncertainty in portfolio management. The main source of uncertainty in managing portfolios is from asset returns fluctuation. Typically, it is depicted through scenarios or return distributions which are commonly assumed to be normal. Such assumption, however, does not illustrate the true characteristics of financial asset returns and thus distorts the representation of returns, risks and interrelationship of assets in a portfolio. This thesis presents novel approaches to represent the uncertainty in international portfolio management in order to mitigate risks associated. Three main issues are covered in our studies. The first issue deals with an approach to hedge risk from exchange rates of a multi-currency portfolio. A hedging mechanism is incorporated into a portfolio optimisation model to produce a portfolio that is optimal in terms of asset and currency exposure. Costs associated to exchange rate hedging are also included into the model to improve accuracy in calculating risk and return of the portfolio. The second issue is about representing the uncertainty of multiple assets in a portfolio through scenarios. Under the assumption of normality, some risk and return characteristics of assets are omitted from standard scenario generation method. We present a novel approach to extract more accurate information from assets to generate realistic scenarios. A two-stage stochastic international portfolio optimisation model is formulated accordingly to create portfolios that are expected to be more efficient than portfolios optimised with scenarios generated from the standard approach. The last issue is associated with an approach to keep portfolio's efficiency over its investment horizon through continual reallocation, known as portfolio rebalancing. Since the uncertainty regarding changes in financial market conditions diminishes the efficiency of conventional rebalancing strategies, we propose a new rebalancing method and formulate it as a stochastic optimisation problem. The proposed rebalancing strategy aims to reallocate the portfolio to attain a high probability of positive returns and low probability of negative returns under second-order stochastic dominance criteria. A portfolio implementing the new rebalancing strategy is expected to outperform a portfolio that follows traditional rebalancing methods in terms of portfolio returns. Overall, the thesis aims to create a richer portfolio optimisation model as well as to extract the correct information from financial markets to better cope with the underlying uncertainty in portfolio management