The Impact of Different Distributional Hypotheses on Returns in Asset Allocation

A: This paper discusses and analyzes some portfolio allocation problems with autoregressive processes. Firstly, we examine the distributional behavior of some international indexes. Then, we propose an AR(1)-GARCH(1,1) model to describe the evolution of the portfolio returns over time. In particular, we assume that investors wish to maximize some expected utility functionals of =nal wealth and we evaluate the impact of di>erent distributional hypotheses on investor's choices. Finally, we describe the properties of some optimal choices. Many of the concepts developed in theoretical and empirical =nance over the past decades rest upon the assumption that asset returns follow a normal distribution. In particular, this distributional assumption was applied to the one period strategic allocation problem in order to justify the mean variance analysis. Such an approach, called myopic, was partially motivated by Samuel-son [31] and Merton [21] who proved that when we assume a perfect market, the investors with constant relative risk aversion maintain constant their portfolio compositions independently of the temporal horizon. On the other hand, since the space of feasible consumption bundles is generally a linear space (as Ross [29], Cox and Leland [8], Rubinstein [30] and many others have emphasized), the original dynamic problem can be replaced with an equivalent one-period problem which has appropriate terminal state prices, if consumption takes place at the end. More generally, if preferences are time separable and if we treat consumption at each date separately, the analysis is unchanged. However, the myopic approach presents several drawbacks. First of all, it does not consider the return predictability empirically observed. Secondly, this approach cannot be used for long term approaches when transaction costs are allowed. In order to evaluate how the investors' choices change when the return predictability is modeled, Wilkie [34], [35], Hodrick [13], Boender et al. [5] have proposed several autoregressive models to describe the evolution of the asset returns over time. However, most of these models assume that returns or their stochastic innovations are Gaussian distributed. This distributional assumption is against the empirical evidence. The excess kurtosis, found in Mandelbrot's [19], [20]and Fama's [12] investigations, led them to reject the normal assumption and to propose the stable Paretian distribution as a statistical model for asset returns. In addition, many other empirical analyses (see Rachev and Mit-tnik [28] and the references therein) have shown that residuals of autoregressive models applied to daily =nancial series are not Gaussian distributed. In this paper …