A Nonlinear Interval Portfolio Selection Model and Its Application in Banks
- 115 Downloads
In classical Markowitz’s Mean-Variance model, parameters such as the mean and covariance of the underlying assets’ future return are assumed to be known exactly. However, this is not always the case. The parameters often correspond to quantities that fall within a range, or can be known ambiguously at the time when investment decision must be made. In such situations, investors determine returns on investment and risks etc. and make portfolio decisions based on experience and economic wisdom. This paper tries to use the concept of interval numbers in the fuzzy set theory to extend the classical mean-variance portfolio selection model to a mean-downside semi-variance model with consideration of liquidity requirements of a bank. The semi-variance constraint is employed to control the downside risk, filling in the existing interval portfolio optimization model based on the linear semi-absolute deviation to depict the downside risk. Simulation results show that the model behaves robustly for risky assets with highest or lowest mean historical rate of return and the optimal investment proportions have good stability. This suggests that for these kinds of assets the model can reduce the risk of high deviation caused by the deviation in the decision maker’s experience and economic wisdom.
KeywordsDownside-risk management interval return portfolio selection semi-variance simulation
Unable to display preview. Download preview PDF.
- Markowitz H, Portfolio selection, The Journal of Finance, 1952, 7(1): 77–91.Google Scholar
- Chi G T, Chi F, and Yan DW, The Three factors optimization model of mean-deviation-skewness on loans portfolio, Operations Research & Management Science, 2009, 18(4): 98–111.Google Scholar
- Muller G E and Witbooi P J, An optimal portfolio and capital management strategy for Basel III compliant commercial banks, Journal of Applied Mathematics, 2014, 130(3): 343–376.Google Scholar
- Liu S T, A fuzzy modeling for fuzzy portfolio optimization, Expert Systems with Applications, 2011, 38(11): 13803–13809.Google Scholar
- Tien F and Seow E, Asset allocation in a downside risk framework, Journal of Real Estate Portfolio Management, 2000, 6(3): 213–223.Google Scholar
- Hanna S D, Gutter M S, and Fan J X, A measure of risk tolerance based on economic theory, Journal of Financial Counseling and Planning, 2001, 12(2): 53–60.Google Scholar
- Zhao Y M and Chen H Y, Interval number linear programming model of portfolio investment, Operations Research & Management Science, 2006, 15(2): 124–127.Google Scholar
- Chi G T, Sun X Y, and Dong H C, A portfolio optimization model of banking asset based on the adjusted credit grade and the Semivariance absolute deviation, Systems Engineering — Theory & Practice, 2006, 26(8): 1–16.Google Scholar
- Rose P S and Hudgins S C, Bank Management & Financial Services, Beijing, China Machine Press, 2008.Google Scholar