Mean-variance investing with factor tilting

Factor analysis proposes an alternative approach to standard portfolio theory: the latter is optimisation based, while the former is estimation based. Also, in standard portfolio theory, returns are only explained by the portfolio volatility factor, while factor analysis proposes a multiplicity of factors, which the managers can choose from to tilt their portfolios. In attempting to reconcile these alternative worlds, we propose a penalised utility function, incorporating both the Markowitzian risk-return trade-off and the manager’s preferences towards factors, and discriminating among losses and gains relative to a reference asset. The penalisation affects the optimisation process, favouring the selection of portfolios with less variance and more tilted towards the chosen risk factors. Penalty levels set by the manager generalise the traditional notion of risk aversion. We test our model by building an investment portfolio based on a combination of asset classes and selected investing factors, focussed on the eurozone. To identify the optimal portfolio, we adopt a set of three metaheuristic optimisation algorithms: the fitness function stochastic maximization using genetic algorithms, differential evolution algorithm for global optimisation, and the particle swarm optimisation, and dynamically choose the best solution. In this way, we can improve the Markowitzian optimisation by tilting the asset allocation with managers’ expectations and desired exposures towards designated factors.