|Title||A metric defined on transformed cumulative return series|
|Presenter||Ilknur Tulunay (University of Technology, Sydney)|
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.
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