Temporal structure and gain-loss asymmetry for real and artificial stock indices

Abstract

Previous research has shown that for stock indices, the most likely time until a return of a particular size has been observed is longer for gains than for losses. We demonstrate that this so-called gain-loss asymmetry vanishes if the temporal dependence structure is destroyed by scrambling the time series. We also show that an artificial index constructed by a simple average of a number of individual stocks display gain-loss asymmetry-this allows us to explicitly analyze the dependence between the index constituents. We consider mutual information and correlation-based measures and show that the stock returns indeed have a higher degree of dependence in times of market downturns than upturns.

Persistent collective trend in stock markets

“…However, empirically one finds that the waiting times of indices are shortest for negative return levels -the opposite of what is to be expected from the long term trend effect. In passing we note that recently it has been found that also single stocks may show some degree of gain-loss asymmetry when the level of return, |ρ|, is getting sufficiently large [21,22]. However, it still remains true that for not too large return levels, e.g.…”

“…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

“…Gains are made in the following days when the asset price readjusts itself to its intrinsic value [36]. It should be mentioned that stochastic volatility models are also successful to explain the leverage effect (see for example [19,25,41]). …”

“…It could be attributed for example to the cross-correlations, spanning several days, between the stocks forming the index. As a result, the fear-factor model [14,22] still shows asymmetry after shuffling the returns, however this asymmetry disappears in the generalized asymmetric synchronous market model [19], where the falling stock prices stay synchronized for multiple days.…”

“…This approach is motivated by the fact that dynamics of turbulent fluids is similar to the behavior of stock markets: after longer resting periods abrupt bursts can appear intermittently [2,6]. Although the intermittency between resting periods and burst was modeled with success also by stochastic volatility models [7], and such models were also appropriate to approach several other stylized facts like: fat-tails and the leverage effect [8][9][10], the use of inverse statistics allows for a further understanding of various single stocks and market indices, as well as foreign exchange data and even artificial markets [5,[11][12][13][14][15][16][17][18][19][20]. The method of inverse statistics revealed an intriguing gain-loss asymmetry [21], that generated a lot of discussion concerning its origin and the timescale of the auto-correlations in the index, responsible for this effect [14,[22][23][24][25][26].…”