A multiscale view on inverse statistics and gain/loss asymmetry in financial time series

Abstract

Researchers have studied the first passage time of financial time series and observed that the smallest time interval needed for a stock index to move a given distance is typically shorter for negative than for positive price movements. The same is not observed for the index constituents, the individual stocks. We use the discrete wavelet transform to illustrate that this is a long rather than short time scale phenomenon -if enough low frequency content of the price process is removed, the asymmetry disappears. We also propose a new model, which explain the asymmetry by prolonged, correlated down movements of individual stocks.

Persistent collective trend in stock markets

“…This asymmetry is expressed by negative return levels being reached sooner than those corresponding to positive levels (of the same magnitude of ρ). This effect was termed the gain-loss asymmetry [7] and has later been observed for many major stock indices [7,8,18,19,23,25]. It is here important to note that the gain-loss asymmetry is not a consequence of the generally long-term positive trend (or drift) of the data since this was removed by considering an average with a suitable window size on the prices.…”

“…This is consistent with the findings of Kahneman and Tversky [31], reported in the economics literature, that demonstrate that the utility loss of negative returns is larger than the utility gain for positive returns in the case of most investors. Recently, the idea of the fear-factor model [24] was reconsidered and generalized by Siven et al [25] by allowing for longer time periods of stock co-movement (correlations). These authors also find that the gain-loss asymmetry is a long timescale phenomena [25], and that it is related to some correlation properties present in the time series [21].…”

“…Recently, the idea of the fear-factor model [24] was reconsidered and generalized by Siven et al [25] by allowing for longer time periods of stock co-movement (correlations). These authors also find that the gain-loss asymmetry is a long timescale phenomena [25], and that it is related to some correlation properties present in the time series [21]. It was also proposed that the gain-loss asymmetry is in close relationship with the asymmetric volatility models (E-GARCH) used by econometricians [26].…”

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

“…11 in Appendix). All these results suggest a much reduced characteristic time-scale for the non-Pearson type auto-correlations that are responsible for the gain-loss asymmetry than that reported in [33].…”

“…Contrary to indices, stock prices show a smaller degree of asymmetry [22][23][24]. The asymmetry of the inverse statistics of stock markets is still a central problem of applied mathematics, econophysics and economics [19,26,33,34].…”