سرخوردگی محور پویایی بازار سهام: اثر اهرم و عدم تقارن

By applying inverse statistics to financial data it has recently been found from empirical studies that indices exhibit a pronounced gain-loss asymmetry [M.H. Jensen, Phys. Rev. Lett. 83 (1999) 76; I. Simonsen, M.H. Jensen, A. Johansen, Eur. Phys. J. B 27 (2002) 583; M.H. Jensen, A. Johansen, I. Simonsen, Physica A 324 (2003) 338]. This gain-loss asymmetry appears to have some similarities with the stylized fact leverage effect and we investigate if they could be of same origin. For this purpose we introduce the Frustration Governed Market model which includes correlations in time between a model index and its individual stocks. It is shown that the model reproduces very well the empirical findings with respect to gain-loss asymmetry and leverage. In special cases, however, the model may produce leverage without a pronounced gain-loss asymmetry.

All investors share one major concern: optimization of profit. Though simplistic, this viewpoint has subtle details to it due to the different approaches that can be applied to reach this goal. For instance, one could risk all for what one believes to be the most profitable investments or alternatively pay attention to minimization of portfolio risk. The first strategy may be a fruitful, but also very hazardous one. As known, investments with high profit potential also inherit high risk. The alternative amounts to calculate realistic measures of risk and to find other assets that may cover up possible losses created by the initial investment—a very celebrated method known as hedging [1]. Recently the concept of fear as a driving mechanism for the stock market was introduced and investigated in Ref. [2]. The empirical work leading to the so-called Fear Factor model showed the existence of an inherent gain-loss asymmetry in stock indices, while the constituting stocks show little, or no, sign of a similar effect [3]. The Fear Factor model [2] has brought knowledge about the importance of collective behavior in the stock market and its consequences concerning the asymmetry. The gain-loss asymmetry share common features with another stylized fact—the leverage effect [4] and [5]—which is also most pronounced for indices. Still it is an open question if the asymmetry and leverage effect are measures of the same property: The Fear Factor model has shown that leverage is not necessary to produce the observed gain-loss asymmetry. To shed light on this discussion, we shall in the following introduce a model constructed to incorporate the leverage effect; this model we term the Frustration Governed Market model.

We have briefly reviewed the stylized facts gain-loss asymmetry and leverage that both seem to result from collective behavior in stock market dynamics. We have presented the new Frustration Governed Market model that conceptually ascribe these stylized facts to frustrated investors. It is shown that the model is capable of reproducing the empirical findings, but also that leverage within this framework does not necessarily imply the existence of well-pronounced gain-loss asymmetry. Future studies are called upon to resolve this question.