Mathematical and Statistical Methods for Actuarial Sciences and Finance

Optimal dynamic asset allocation in a non–Gaussian

world

Gianni Pola

Abstract.Asset Allocation deals with how to combine securities in order to maximize the

investor’sgain. We consider the Optimal Asset Allocation problem in a multi-period investment

setting: the optimal portfolio allocation is synthesised to maximise the joint probability of the

portfolio fulfilling some target returns requirements. The model does not assume any particular

distribution on asset returns, thus providing an appropriate framework for a non–Gaussian

environment. A numerical study clearly illustrates that an optimal total-return fund manager is

contrarianto the market.

Key words:asset allocation, portfolio management, multi-period investment, optimal control,

dynamic programming

1 Introduction

In the finance industry, portfolio allocations are usually achieved by an optimiza-

tion process. Standard approaches for Optimal Asset Allocation are based on the

Markowitz model [15]. According to this approach, return stochastic dynamics are

mainly driven by the first two moments, and asymmetry and fat-tails effects are as-

sumed to be negligible. The model does not behave very well when dealing with

non–Gaussian-shaped asset classes, like Hedge Funds, Emerging markets and Com-

modities. Indeed it has been shown that sometimes minimizing the second order

moment leads to an increase in kurtosis and a decrease in skewness, thus increasing

the probability of extreme negative events [3, 10, 22]. Many works have appeared

recently in theliterature that attempt to overcome these problems: these approaches

were based on an optimization process with respect to a cost function that is sensitive

to higher-order moments [2, 11, 12], or on a generalisation of the Sharpe [21] and

Lintner [14] CAPM model [13, 16].

The second aspect of the Markowitz model is that it is static in nature. It permits the

investor to make a one-shot allocation to a given time horizon: portfolio re–balancing

during the investment lifetime is not faced. Dynamic Asset Allocation models address

the portfolio optimisation problem in multi-period settings [4, 7, 17, 20, 23].

M. Corazza et al. (eds.), Mathematical and Statistical Methodsfor Actuarial Sciencesand Finance
© Springer-Verlag Italia 2010