Empirical Evidence on Student-tLog-Returns of Diversified World Stock Indices

Abstract

The aim of this paper is to document some empirical facts related to log-returns of diversified world stock indices when these are denominated in different currencies. Motivated by earlier results, we have obtained the estimated distribution of log-returns for a range of world stock indices over long observation periods. We expand previous studies by applying the maximum likelihood ratio test to the large class of generalized hyperbolic distributions, and investigate the log-returns of a variety of diversified world stock indices in different currency denominations. This identifies the Student-t distribution with about four degrees of freedom as the typical estimated log-return distribution of such indices. Owing to the observed high levels of significance, this result can be interpreted as a stylized empirical fact.

The risk–return tradeoff: A COGARCH analysis of Merton's hypothesis

“…Klüppelberg et al, 2006). Thus the COGARCH distribution tails are "heavy", consistent with recent extensive empirical evidence of Platen and Sidorowicz (2007). For more details on the theoretical properties of G and ρ 2 , we refer to Klüppelberg et al (2004) and Klüppelberg et al (2006).…”

On the performance of the minimum VaR portfolio

“…As noted previously, a Student's t 4 distibution has been found to be appropriate for world stock indices (Platen and Sidorowicz, 2008), and Jagannathan and Ma (2003) found the standard normal distribution to be appropriate for portfolios with short sales disallowed. 18 We repeated the analysis in Figure 3 for the iShares data; as the corresponding diagrams convey the same impression as those for the FF5×5 dataset, we have not included them in this paper.…”

“…They then extend their results to the multivariate Student's t distribution (Section 3, p.1177), and in fact to any distribution for which the VaR can be written as a linear function of the expectation and standard deviation of the returns. A Student's t distribution assumption has notable relevance in that the heavy-tailedness of returns distributions is an empirically-observed fact: in a recent study, Platen and Sidorowicz (2008) show that a Student's t distribution with four degrees of freedom provides a good fit to the returns of a large sample of widely varying world stock indices.…”

Distributionally Robust Reward-Risk Ratio Optimization with Moment Constraints

“…Note that compared to normal distributions, t-distributions have been widely used to model return of financial assets whose distributions are usually fat-tailed. We refer the readers to Hu and Kercheval [23] and Platen and Sidorowicz [37] for recent developments and empirical evidences.…”