Empirical Evidences on the Interconnectedness between Sampling and Asset Returns’ Distributions

Giuseppe Orlando,Michele Bufalo

doi:10.3390/risks9050088

Abstract

The aim of this work was to test how returns are distributed across multiple asset classes, markets and sampling frequency. We examine returns of swaps, equity and bond indices as well as the rescaling by their volatilities over different horizons (since inception to Q2-2020). Contrarily to some literature, we find that the realized distributions of logarithmic returns, scaled or not by the standard deviations, are skewed and that they may be better fitted by t-skew distributions. Our finding holds true across asset classes, maturity and developed and developing markets. This may explain why models based on dynamic conditional score (DCS) have superior performance when the underlying distribution belongs to the t-skew family. Finally, we show how sampling and distribution of returns are strictly connected. This is of great importance as, for example, extrapolating yearly scenarios from daily performances may prove not to be correct.

Highlights

We empirically perform a number of analyses across asset classes, markets and for several sampling frequencies
To confirm evidence on the graphical analysis resulting from the (Q-Q) plot, we use the Kolmogorov–Smirnov normality (K-S) test Kolmogorov (1933); Stephens (1992)
In order to understand whether returns follow a t-skew distribution, we investigate about the presence of unitary roots, i.e., about the absence of stationarity, and the persistence of fat tail, that is in contrast with the normal distribution

Summary

Introduction

Our finding holds true across asset classes, maturity and developed and developing markets This may explain why models based on dynamic conditional score (DCS) have superior performance when the underlying distribution belongs to the t-skew family. The aim of this article was to investigate the interconnectedness between sampling and asset returns’ distributions To this end, we empirically perform a number of analyses across asset classes, markets and for several sampling frequencies. The t-skew distribution can be seen as a mixture of skew-normal distributions Kim (2001) which generalize the normal distribution thanks to an extra parameter regulating the skewness By construction, they can model heavy tails and skews that are common in financial markets.

Objectives

Methods

Results