Abstract
| Analysing return distributions of assets are in great interest of finance. It
is a common practice to assume normality of the return distributions, even
though there are numerous empirical studies, indicating that the return
distributions are not normal in general. Theoretical distribution can be assumed
or approximated from the return time series in many ways, developed over
decades. With such assumptions or approximations, some information on returns of
assets can be lost. Hence, quantities, computed directly from the return series
are invaluable. For example, it is known that stochastic dominance is
theoretically superior to mean-variance analysis, as it considers the entire
return distribution. However, it can not be used for more than two assets. With
this point of view, we develop a new non-parametric robust method to order the
performances of multi-assets, based purely on their transformed cumulative
returns. The metric measure used in the method is an extension of the square
root of Topsoe distance from probability density functions to real number series
between zero and 1. We study the properties and bounds of the extended Topsoe
distance. We derive a critical-value test to decide whether two return series
can be `distinguishable' or not. |