Asmerilda Hitaj

Optimal Hedge Fund Allocation with Improved Estimates for Coskewness and Cokurtosis Parameters

Since hedge fund returns are not normally distributed, mean–variance optimization techniques are not appropriate and should be replaced by optimization procedures incorporating higher-order moments of portfolio returns. In this context, optimal portfolio decisions involving hedge funds require not only estimates for covariance parameters but also estimates for coskewness and cokurtosis parameters. This is a formidable challenge that severely exacerbates the dimensionality problem already present with mean–variance analysis. This article presents an application of the improved estimators for higher-order co-moment parameters, in the context of hedge fund portfolio optimization. The authors find that the use of these enhanced estimates generates a significant improvement for investors in hedge funds. The authors also find that it is only when improved estimators are used and the sample size is sufficiently large that portfolio selection with higher-order moments consistently dominates mean–variance analysis from an out-of-sample perspective. Their results have important potential implications for hedge fund investors and hedge fund of funds managers who routinely use portfolio optimization procedures incorporating higher moments.

Hedge Fund Portfolio Allocation with Higher Moments and MVG Models

The well-known mean-variance model, see Markowitz (1952), despite its popularity and simplicity, is not able to capture the stylized facts of asset returns such as asymmetry and fat tails, which have an impact on portfolio selection, particularly when hedge funds are included.

Some Empirical Evidence on the Need of More Advanced Approaches in Mortality Modeling

Recent literature on mortality modeling suggests to include in the dynamics of mortality rates the effect of time, age, the interaction of the latter two terms and finally a term for possible shocks that introduce additional uncertainty. We consider for our analysis models that use Legendre polynomials, for the inclusion of age and cohort effects, and investigate the dynamics of the residuals that we get from fitted models. Obviously, we expect the effect of shocks to be included in the residual term of the basic model.

Portfolio Optimization Using Modified Herfindahl Constraint

Modern portfolio theory started with Markowitz (J Financ 7(1):77–91, 1952; Portfolio selection efficient diversification of investments. Wiley, New York, 1959). Early works developed necessary conditions on utility function that would result in mean-variance theory being optimal, see Tobin (Rev Econ Stud 25(2):65–86, 1958). Recently, considering the stylized facts of asset returns, mean-variance model has been extended to higher moments. Despite all, empirical evidence has shown that mean-variance model and its variants often yield overly concentrated portfolios. Portfolio diversification is still an open question. To avoid this problem different constraints have been introduced in the portfolio optimization procedure. In this paper we study from an empirical point of view the impact of imposing a constraint on the Modified Herfindahl index of the portfolio, in case of mean-variance and mean-variance-skewness optimization. We find that imposing a constraint on the level of the portfolio diversification leads to better out of sample performance and significant gains, despite the use of shrinkage estimators for moments and comoments, in particular when long estimation periods are considered.

Sensitivity analysis of Mixed Tempered Stable parameters with implications in portfolio optimization

This paper investigates the use, in practical financial problems, of the Mixed Tempered Stable distribution both in its univariate and multivariate formulation. In the univariate context, we study the dependence of a given coherent risk measure on the distribution parameters. The latter allows to identify the parameters that seem to have a greater influence on the given measure of risk. The multivariate Mixed Tempered Stable distribution enters in a portfolio optimization problem built considering a real market dataset of seventeen hedge fund indexes. We combine the flexibility of the multivariate Mixed Tempered Stable distribution, in capturing different tail behaviors, with the ability of the ARMA-GARCH model in capturing the time dependence observed in the data.

Sensitivity Analysis of the Mixed Tempered Stable Parameters with Implications in Portfolio Optimization

This paper investigates the use, in practical financial problems, of the Mixed Tempered Stable distribution both in its univariate and multivariate formulation. In the univariate context, we study the dependence of a given coherent risk measure on the distribution parameters. The latter allows to identify the parameters that seem to have a greater influence on the given measure of risk. The multivariate Mixed Tempered Stable distribution enters in a portfolio optimization problem built considering a real market dataset of seventeen hedge fund indexes. We combine the flexibility of the multivariate Mixed Tempered Stable distribution, in capturing different tail behaviors, with the ability of the ARMA-GARCH model in capturing the time dependence observed in the data.

VIX Computation Based on Affine Stochastic Volatility Models in Discrete Time

We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. We build this class of models in order to reach two desirable results. Firstly, we have a recursive procedure for the characteristic function of the log price at maturity that allows a semi-analytical formula for option prices as in Heston and Nandi (2000). Secondly, we try to reproduce some features of the VIX Index. We derive a simple formula for the VIX index and use it for option pricing purposes.

Portfolio Allocation Using Omega Function: An Empirical Analysis

It is widely recognized that expected returns and covariances are not sufficient to characterize the statistical properties of securities in the context of portfolio selection. Therefore different models have been proposed. On one side the Markowitz model has been extended to higher moments and on the other side, starting from Sharpe ratio, a great attention has been addressed to the correct choice of the risk (or joint risk-performance) indicator. One such indicator has been proposed recently in the financial literature: the so-called Omega Function, that considers all the moments of the return distribution and whose properties are being investigated thoroughly. The main purpose of this paper is to investigate empirically, in an out-of-sample perspective, the portfolios obtained using higher moments and the Omega ratio. Moreover we analyze the impact of the target threshold (when the Omega Ratio is used) and the impact of different preferences for moments and comoments (when a higher-moments approach is used) on portfolio allocation. Our empirical analysis is based on a portfolio composed of 12 Hedge fund indexes.