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

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.

Simple Unequal Allocation Procedure for Ranked Set Sampling with Skew Distributions

A practical unbalanced Ranked Set Sampling (RSS) model is proposed to estimate the population mean of positively skewed distributions. The gains in the relative precisions of the population mean based on the proposed model for chosen distributions are uniformly higher than those based on balanced RSS and the t-model proposed in Kaur et al. (1997). The relative precisions of the simple unequal allocation model are, with one exception, better than (s, t)-model which is better than t-model. The relative precision of the proposed model is very close or equal to the optimal Neyman allocation model.