Subject Within the theory of portfolio investment, specialists often discuss the issue related to the lack of spatial dimension of investment opportunities. Only two measures are assumed to be sufficient to describe portfolio investing, i.e. profitability and risk. On the one hand, the prevailing practice of using these two characteristics is in line with the goal of reducing the computational complexity of portfolio analysis procedures and making it easier to formalize a number of related tasks. On the other hand, the forced refusal to reproduce the real processes of the stock market multidimensionality clearly constrains the application of methods that would greatly expand the possibilities of modern portfolio analysis. Objectives The study aims to develop an econometric analogue model of random wandering and an application in the task of choosing an efficient Markowitz portfolio. Methods I employ data analysis and machine learning techniques. Results The paper shows the results of portfolio solutions in a random environment of alternative opportunities of the stock market. The linear nature of relationship between the return on equity and the yield of the market is replaced by non-linear, which is reproduced by a separate regression model with a discrete dependent variable. On its basis, I present an econometric model of return on equity, which uses the probability of positive return. Under this model, preferences may simultaneously lead to higher returns and reduced risk. Conclusions Stochastic volatility regression in portfolio analysis can significantly improve the efficiency of portfolio solutions.
Keywords: risk, random variable, Bernoulli distribution
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