Fractal analysis of market (in)efficiency during the COVID-19

Abstract

Using the multifractional Brownian motion as a model of the price dynamics, we analyze the impact of the COVID-19 pandemic on the efficiency of fifteen financial markets from Europe, US and Asia. We find that Asian markets (Hang Seng, Nikkei 225, Kospi) have recovered full efficiency, while European and US markets - after an initial rebound - have not yet returned to the pre-crisis level of efficiency. The inefficiency that currently characterizes US and European markets originates moderately high levels of volatility.

Keywords: COVID-19 pandemic; Efficient markets; Multifractional Brownian motion; Pointwise regularity exponent.

Fig. 1

Relation between the estimated standard deviation and the Hölder exponent. The standard deviation $\sigma \left(t\right)$ was estimated on a rolling window of 30 data along the path of an mBm of assigned functional parameter $H\left(t\right)$. The values of $H\left(t\right)$ were averaged in the same window to make the comparison possible. The Figure displays the average of 100 simulations of length 8,192 (dots) and the fitting curve (red line). The two plots are virtually undistinguishable since it is an almost perfect match, as revealed by the fitting parameters in the legend (the values in parentheses are the coefficients of the fitting curve at 95% bounds).

Fig. 2

Top panel: Surrogate mBm with functional parameter $H\left(t\right)=0.5+0.25*\sin (4·\pi ·t)$ with time support [0,1], Mid panel: Increment process $Y(t,a)=B_{H(t+a),K}(t+a)-B_{H\left(t\right),K}\left(t\right)$; Bottom panel: Functional parameter $H\left(t\right)$ (red continuous line) and estimates ${\widehat{H}}_{30,1,8192}(t,(-1,1))$ (dots).

Fig. 3

Top panel: S&P500, log-index variations from January 3rd, 2000 to June 10th, 2020 (5127 daily stock quotes); Bottom panel: ${\widehat{H}}_{30,1,5127}(t,(-1,1)),$ the area in green indicates $E^{\alpha },$ with $\alpha =0.05$. All times such that the corresponding $H\left(t\right)$ fall outside $E^{\alpha }$ indicate periods in which market experiences inefficiencies. The impact of COVID-19 crisis reflects in the large negative inefficiency that appears in the far-right.

Fig. 4

Pointwise regularity dynamics before and after the major crashes of $2007-2009$ global systemic crisis (blue line) and COVID-19 crisis (red line). Time 0 is the date of the major downturns recordered during the two crises. Notice the different patterns: while in $2007-2009$ crisis the recovery was slow but somewhat univocal, in the case of the COVID-19 after an immediate recovery, the pointwise regularity of most European and US indexes has flattened below of the lower threshold of efficiency, what indicates that a subtle antipersistence characterizes US and Europe-based financial markets.