Financial Return Distributions: Past, Present, and COVID-19

Abstract

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.

Cryptocurrency Market Consolidation in 2020–2021

“…Over the past few years, two processes have had a particularly strong impact on financial markets: the emergence of the cryptocurrency market [ 1 , 2 , 3 , 4 , 5 ] and the COVID-19 pandemic [ 6 , 7 , 8 , 9 , 10 , 11 , 12 ]. Each of these processes alone has already been a topic in numerous pieces of the scientific literature, but they also were studied together [ 5 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 ]. Of particular interest in this context is how the ongoing pandemic is changing the cryptocurrency market and how this market position among the other financial and commodity markets undergoes an accelerated evolution.…”

Radical Complexity

“…Here again, thinking about the problem before blindly applying standard recipes is of paramount importance to get it right. Furthermore, of course, if the “inverse-cubic law” is indeed universal, as again recently advocated in [ 25 ], we should try to understand why. Despite many efforts in that direction, it is fair to say that there is no consensus on the underlying mechanism responsible for such a critical-like behaviour, see Section 1 and Section 4 .…”

“…As an illustration related to the topic of copulas, let me consider the following question: is the univariate distribution of standardised stock returns universal , i.e., independent of the considered stock? In particular, is the famous “inverse-cubic law” [ 24 , 25 ] for the tail of the distribution indeed common to all stocks?…”

“…Our conjecture: markets are intrinsically unstable and have always been so. As noted in Section 1 above, this chronic instability may lie at the heart of the turbulent, multiscale nature of financial fluctuations and the universal power-law of the distribution of returns [ 24 , 25 ].…”

Collective correlations, dynamics, and behavioural inconsistencies of the cryptocurrency market over time

“…In recent years, substantial research has focused specifically on the unique dynamics of cryptocurrencies. Various topics of interest include Bitcoin and other cryptocurrencies’ price dynamics [ 46 – 50 ], fractal patterns, [ 51 – 54 ], cross-correlation and scaling effects [ 55 – 60 ]. A great deal of this work has addressed how these dynamics have changed over time, in particular during market crises such as the COVID-19 market crash [ 61 – 73 ].…”