|
Traditional approaches of Markowitz's portfolio theory are of the crisp-stochastic category, which means that data and parameters are determined as crisp (real) numbers or unique distribution functions. However, in financial markets, the information is incomplete and complex, resulting to the impossibility to predict the future return and the actual risk of a portfolio precisely.
In this paper, we investigate the minimum variance possibility portfolio assuming that the expected rate of returns is a fuzzy number, represented by a Gaussian membership function. As an application, the Brazilian equity market is considered in the numerical experiments.
Zadeh (1978) states that possibilistic distributions were meant to provide a graded semantics to natural language statements. In Zhang and Nie (2003) was proposed the notions of upper and lower possibilistic mean and possibilistic variances and covariances of fuzzy numbers. Due to this, several works have suggested the construction of efficient portfolios using possibilistic theory.
This paper evaluates the performance of minimum variance fuzzy possibilistic portfolio in the Brazilian equity market in the case that assets return is a Gaussian fuzzy variable. Its results are compared to those of the following benchmarks: minimum variance portfolio estimated by real (crisp) numbers, the IBOVESPA equity index, an equally-weighted portfolio, and the maximum Sharpe ratio portfolio.
In terms of annualized return, the minimum variance fuzzy possibilistic portfolio provided better results than all remaining portfolios. The same results were found considering the cumulative return metric.The fuzzy possibilistic portfolio provides the better combination of return and risk, since it is the more conservative approach (lowest level of annualized volatility). The suggested approach provides better results than all alternative techniques with a few number of assets.
|
