Time-scale effects on the gain-loss asymmetry in stock indices

Abstract

The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over 2%, and it is the result of the non-Pearson type auto-correlations in the index. These non-Pearson type correlations can be viewed also as functionally dependent daily volatilities, extending for a finite time interval. A generalized time-window shuffling method is used to show the existence of such auto-correlations. Their characteristic time-scale proves to be smaller (less than 25 trading days) than what was previously believed. It is also found that this characteristic time-scale has decreased with the appearance of program trading in the stock market transactions. Connections with the leverage effect are also established.

A Bayesian analysis of gain-loss asymmetry

“…n draw 1 + 2 ∞ t=0 ρ t (15) where ρ t is the autocorrelation at lag t ≥ 0. Roughly speaking, the ESS corresponds to the number of independent samples with the same estimation power as the n draw autocorrelated samples so that the estimation error is proportional to 1/ √ ESS.…”

“…Roughly speaking, it consists of the fact that the drawdowns observed in stock prices and stock index values are not as large as the upward movements. This effect was widely studied in the literature to analyze stocks [13], indices [14,15] as well as stocks in emerging markets [16]. Many attempts to deal with this effect have been considered, such as an analysis of the clustering on the asymmetry properties in financial time series [17], symmetry breaking mechanisms [18], or by using empirical and agents modeled studies [19,20].…”

Multifractal analysis of financial markets

“…An analysis in the frequency space based on the discrete wavelet transform showed that the gain-loss asymmetry is introduced mainly by the low-frequency content of the price series and the asymmetry disappears if enough of the low-frequency content is removed [218]. Alternatively, the gain-loss asymmetry is found to be caused by the non-Pearson-type autocorrelations in the time series [220]. Furthermore, the gain-loss asymmetry vanishes if the temporal dependence structure is destroyed by shuffling the time series [221].…”

A multi-scale symmetry analysis of uninterrupted trends returns of daily financial indices

“…Initially, most of the market symmetry or gain/loss asymmetry studies relied on studying the third standardized moment of the price or index variations or other similar measurement. More recently, symmetry of financial variations or related problems has been approached by very ingenious methodologies, as for example, the analysis of the returns distribution of stocks ensembles during crash and rally days [9]; the study of large fluctuation dynamics under time reversal (TR) symmetry (large fluctuations dynamics at daily scale are not TR symmetric, but at the scale of high frequency data they are) [10]; study of the investment horizons distribution [11,12]; empirical analysis of the clustering on the asymmetry properties in financial time series [13]; symmetry break mechanisms [14]; symmetry in trading volume [15]; analysis related to time-scale effects on gain/loss asymmetry in stock indices [16]; the use of the non-extensive formalism of Physics [17], or focusing in searching possible symmetry points of returns [18] and many more interesting empirical and agents modeled studies [19,20].…”

“…For instance, [21,22] have analyzed returns of a large sample of diverse financial indices without finding important symmetry deviations or fully rejecting the symmetry hypothesis. On the other hand, many studies under different conditions and points of view have reported the emergence of asymmetries in the financial returns distribution [9][10][11][12][13][14][15][16][17][18][19][20].…”