BERND PAPE Asset Allocation, Multivariate Position Based Trading ...

50 ACTA WASAENSIAto check their adequacy for modelling financial returns. In their study it turns out thatmany common distributions, such as the Student t, EPD, and the logistic distributionare strongly rejected for daily returns, whereas at least the Student t and the logisticdistributions appear acceptable for the description of weekly and monthly returns.I am not aware of any study that would compare Tukey’s (g × h) distribution to any ofthe above mentioned distributions, nor any study comparing the best fitting model ofthe EGB and SGT families with generalized hyperbolic distributions or distributionsof the VG type. As said above, there appears no coherent picture from the empiricalfinance literature regarding the superiority of any one model, except that both thenormal and the stable model appear to be inappropriate.However, it has been pointed out e.g. by Lux & Ausloos (2002), that there is an efficientway to sort out uneligible models by simply considering the behavior of their tails 75 .Discrete mixutes of normals, including the compound events and the jump diffusionmodel, the VG and the generalized hyperbolic families, Tukey’s (g × h) distribution,as well as TLF have all exponentially declining tails and do thus not qualify as modelsfor stock prices, when a correct description of extremal returns is required.Ruling out Lévy stable distributions, as they imply infinite variance 76 , points to continuousmixtures of normals, such as the Student t distribution and its skewed gerneralizationswithin the SGT family. This provides, however, only a statistical description,but no economic explanation beyond the mixture interpretation as reaction to incomingnews 77 . As such, the success of the statistical approach in identifying an appropriatedescription of stock returns, even when confined to the unconditional distribution only,appears to be quite limited despite about half a century of intensive research.75 see section 2.4.76 see section 3.2.1.77 see secton 3.2.3.