Comparison analysis of copula-based and Markowitz portfolio methods - Tupko, Olha; Tupko, Natalia; Vasil'eva, Nataliia (Technology audit and production reserves, 2016)
In this paper, the objects of study are securities (stocks) and portfolio. The main problem of the study is portfolio optimization. One of the first portfolio methods was presented by Henry Markowitz with his Modern Portfolio Theory (MPT), which is considered as a classic and the most popular one in modern investing. MPT provides the following assumptions: variance is used as a measure of risk, portfolio stock returns distribution is considered as a normal one. However, these assumptions do not represent real processes in the modern economy. First, in terms of modern volatile economy portfolio stock returns distribution curve has heavy tails, which is not typical for normal distribution. Secondly, in case of variance as a measure of risk probability of extreme events, such as a simultaneous increase or decrease of stock prices, are not taken into account. So Markowitz method no longer meets the requirements of the modern financial market and there is a need to study alternative and more valid portfolio methods. In this paper, copula-based approach is considered in contrast to the classical one. In the method assumption about the normality of stock returns is rejected and Value-at-Risk (VaR) is considered as a valid risk measure. VaR assessment is based on an information about random distribution. Since the normality assumption was rejected, to assess portfolio stock returns distribution need to be defined. To do these copula-functions was used. Stochastic optimization problem using VaR was solved with a modified Nelder-Mead method. As a result of the dynamic optimization return of copula-based portfolio for 2015 was 12,1 % of the initial investment sum, while the portfolio, constructed with the classical method, showed losses of 4,1 %. Since in copula-based approach incorrect normality assumption is rejected and a valid risk measure is chosen, copula-based portfolio is much more effective than the Markowitz one.