Portfolio allocation under general return distribution

Modern Portfolio theory, developed by Markowitz (1952), is based on finding the best trade-off between risk and expected return. This model assumes that returns are normally distributed. In real life, for the majority of the assets this assumption is not true, as generally the distribution of returns has negative skewness and fat tails. This is more evident in case of hedge funds, commodities or emerging markets portfolios. Therefore, in these cases, a portfolio allocation based on the first two moments does not seem to be the right procedure, because we cannot ignore the higher moments. So, we need to find a way to incorporate the higher moments in the portfolio allocation decision. This is the reason why in this dissertation we will extend the Markowitz model to the higher moments and we will analyze the impact that skewness and kurtosis have on portfolio allocation. To introduce the higher moments in the portfolio allocation, we will approximate the expected utility by a fourth order Taylor expansion and we will compare the portfolio allocation based on four moments with the portfolio based on the first two moments. To compare two different optimal portfolios we will use a measure called, Monetary Utility Gain/Loss (MUG) . Furthermore, in the issue of constructing the optimal portfolio allocation, we will consider different approaches for the estimation of the co-moments. We will describe in more details three different approaches: i. Sample approach ii. Constant Correlation approach iii. Shrinkage approach In the empirical part, we will use a fix-mixed rolling window strategy with different calibrations periods, sample periods and levels of risk aversion.