Annals of the University of Oradea: Economic Science (Dec 2019)
TRADITIONAL VS. FUZZY INDICATORS OF MODERN PORTFOLIO THEORY
Abstract
This paper offers another perspective upon the well-known indicators of Modern Portfolio Theory (created by Harry Markowitz): arithmetic mean or geometric mean for return on financial assets, standard deviation or variance for financial risk, and covariance or correlation between the assets included in the portfolio. This perspective consists of modelling these statistical indicators, using the triangular fuzzy numbers, due to the advantages they have. The first advantage of the fuzzy approach is the returns on financial assets, and the financial asset risks are expressed in intervals with minimum and maximum values, called the triangular fuzzy numbers. This advantage makes the decision of investment more accurate, especially considering the volatility of financial assets. Using triangular fuzzy numbers in estimating the returns based on history of trading, can overcame the fact that past performance is no guarantee for future results, due to the different possibilities of fuzzification. In this paper, the returns will be fuzzified considering the mode value (the most frequent value in a given period of time) of the returns from the past period. This statistical value will help the investors to evaluate the frequency of the last returns and to estimate the most probably frequent value of the returns for the next period. So, the estimation, not only the decision, will be more reliable. The second advantage of using the triangular fuzzy numbers in modelling the financial return and the financial risk is their membership function, which allows the investors to evaluate their investments, depending on the membership degree. The returns of the assets that are closer to the mode return, will be most likely the returns for the next period. The returns that are closer to the limits of the fuzzy intervals, will be less probably the returns for the next period. This assumption has its own gap: the market should have the same conditions as the last period.
