Another reason why the efficient market hypothesis is fuzzy

This paper makes use of the performance evaluation to test the validity of the efficient market hypothesis (EMH) in hedge fund universe. The paper develops a fuzzy set based performance analysis and portfolio optimisation and compares the results with those obtained with the traditional probability methods (frequentist and Bayesian models). We consider a data set of monthly investment strategy indices published by Hedge Fund Research group. The data set spans from January 1995 to June 2012. We divide this sample period into four overlapping sub-sample periods that contain different economic market trends. To investigate the presence of managerial skills among hedge fund managers we first distinguish between outperformance, selectivity and market timing skills. We thereafter employ three different econometric models: frequentist, Bayesian and fuzzy regression, in order to estimate outperformance, selectivity and market timing skills using both linear and quadratic CAPM models. Persistence in performance is carried out in three different fashions: contingence table, chi-square test and cross-sectional auto-regression technique. The findings obtained with probabilistic methods contradict the EMH and suggest that the “market is not always efficient,” it is possible to make abnormal rate of returns if one exploits mispricing in the market, and makes use of specific investment strategies. However, the results obtained with the fuzzy set based performance analysis support the appeal of the EMH according to which no economic agent can make risk-adjusted abnormal rate of return. The set of optimal invest strategies under fuzzy set theory results in a well-diversified portfolio of investment with an expected mean return equal to that of the efficient frontier portfolio under the Markowitz’ mean-variance

Solving Large-Scale Fuzzy and Possibilistic Optimization Problems

The semantic and algorithmic differences between fuzzy and possibilistic optimization methods are presented in the context of three methods for solving large fuzzy and possibilistic optimization problems. In particular, an optimization problem in radiation therapy with various orders of complexity,1,000-55,000 constraints, possessing (i) soft constraints, (ii) fuzzy right-hand side values and (iii) possibilistic right-hand side values, are used to illustrate the semantics and to test the performance of the three fuzzy and possibilistic optimization methods. We focus on the uncertainty in the right side which arises, in the context of the radiation therapy problem, from the fact that minimal/maximal radiation tolerances are target values rather than fixed real numbers. The results indicate that fuzzy/possibilistic optimization is a natural way to model various types of optimization under uncertainty problems and large optimization problems can be solved efficiently