FORMATION AND OPTIMIZATION OF VARIOUS PORTFOLIOS MODELS ON THE VaR INDICATOR BASIS
This article describes a formation of various portfolios models based on H. Markovitz portfolio theory. The portfolios which can include instruments with fixed profitability and common stock are considered. As a risk measure VaR indicator is used. In the research historical data on the stock prices included in the Dow30 market index were used. The profitability of all shares was analyzed in the period from 01.09.2015 to 01.09.2016 on one day basis. Companies included in the surveyed portfolios were selected using factor analysis method. They are considered as a portfolio consisting of a uniform distribution of shares and optimization portfolios.
In these optimization models maximization of portfolio efficiency at the set risk level and risk minimization at the set level of efficiency can act as criterion functions. In some optimization tasks efficiencies of risky assets are calculated considering market changes. For portfolios of different profitability, the optimal curves "Profitability-Risk" are constructed. Comparison of the results is providing. Portfolios consisting of shares of various companies are explored. Depending on the investor's attitude to risk, appropriate portfolios can be chosen.
Numerical results of effective assets distribution within the portfolio for various optimization problems statements are shown.
Basak, S. & Shapiro, A. (2001). Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices. Review of Financial Studies, 14, 371-405.
Blanchett, D., & Ratner, H. (2015). Building Efficient Income Portfolios. The Journal of Portfolio Management, 41(3), 117-125.
Good, D. (2000). Value-at-risk trade off: Accuracy vs. computational time. Commodities Now, 4, 63-68.
Jorion, P. (2003). Portfolio Optimization with Tracking-Error Constraints. Financial Analysts Journal, 59(1), 31-42.
Lintner, J. (1965).The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47(1), 13-37.
Lobanov, A. A., & Chugunov, A. V. (2003). Encyclopedia finansovogo risk-managmenta. Moskva: Alpina Pablisher.
Markovitz, H. (1952). Portfolio selection. Journal of Finance, 7, 77-91.
Rockafellar, R., & Uryasev, S. (2002).Conditional Value-at-Risk for General Loss Distributions. The Journal of Banking & Finance, 26, 1443-1471.
Rubinstein, M. E. (1973). A comparative statics analysis of risk premiums. Journal of Business, 46, 605-615.
Shalit, H., & Yitzhaki, S.(1984). Mean-Gini, Portfolio Theory, and the Pricing of Risky Assets. Journal of Finance, 39, 1449-1468.
Shapkin, A. S., & Shapkin, V. A. (2005). Risk-Menedzhment: Theoriia riska i modelirovanie riskovykh situatsii. Moskva: Dashkov& K.
Sharp, W. F. (1963). A simplified model for portfolio analysis. Management Sci, 9, 277-291.
Sharp, W. F., Alexander., G. J., & Bailey, J. V. (1995). Investments. New Jersey: Prentice Hall.
Tobin, J. (1958). Liquidity Preference as Behavior Towards Risk. The Review of Economics Studies, 25(2), 65-86.
GOST Style Citations
Basak, S. Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices [Text] / S. Basak, A. Shapiro // Review of Financial Studies. – 2001. – № 14.– P. 371–405.
Blanchett, D. Building Efficient Income Portfolios [Text] / D. Blanchett, H. Ratner // The Journal of Portfolio Management – 2015. – № 41 (3). – P. 117–125.
Good, D. Value-at-risk trade off: Accuracy vs. computational time [Text] / D. Good // Commodities Now. – 2000. – V. 4 (1). – P. 63–68.
Jorion, P. Portfolio Optimization with Tracking-Error Constraints [Text] / P. Jorion // Financial Analysts Journal. – 2003. – № 59 (1). – P. 31–42.
Lintner, J. The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets [Text] / J. Lintner // Review of Economics and Statistics. – 1965. – V. 47 (1). – P. 13–37.
Лобанов, А. А. Энциклопедия финансового риск-менеджмента [Текст] / А. А. Лобанов, А. В. Чугунов. – Москва : Альпина Паблишер, 2003. – 768 с.
Markovitz, H. Portfolio selection [Text] / H. Markovitz // Journal of Finance. – 1952. – № 7. – P. 77–91.
Rockafellar, R. Conditional Value-at-Risk for General Loss Distributions [Text] / R.Rockafellar, S. Uryasev // The Journal of Banking & Finance. – 2002. – № 26. – P. 1443–1471.
Rubinstein, M. E. A comparative statics analysis of risk premiums [Text] / M. E. Rubinstein // Journal of Business. – 1973. – № 46. – P. 605–615.
Shalit, H. Mean-Gini, Portfolio Theory, and the Pricing of Risky Assets [Text] / H. Shalit, S. Yitzhaki // Journal of Finance. – 1984. – № 39. – P. 1449–1468.
Шапкин, А. С. Риск-менеджмент: теория риска и моделирование рисковых ситуаций [Текст] / А. С. Шапкин, В. А. Шапкин. – Москва : Дашков и К, 2005. – 880 с.
Sharp, W. F. A simplified model for portfolio analysis [Text] / W. F. Sharp // Management Sci. – 1963. – V. 9. – P. 277–291.
Sharp, W. F. Investments [Text] / W. F. Sharp, G. J. Alexander, J. V. Bailey. – New Jersey : Prentice Hall, 1995. – 1058 p.
Tobin, J. Liquidity Preference as Behavior Towards Risk. [Text] /J. Tobin // The Review of Economics Studies. – 1958. – V. 25 (2). – P. 65–86.
Copyright (c) 2017 Viktor Oliinyk, I. Bielova
This work is licensed under a Creative Commons Attribution 4.0 International License.
ISSN (print) 2306-4994, ISSN (on-line) 2310-8770