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A Study on Multi-Constraint Portfolio Optimization Based on Lagrange Multiplier Method in Financial Market Risk Management Framework

By: Mengrui Bao1
1Economics and Management Faculty, Cangzhou Normal University, Cangzhou, Hebei, 061000, China

Abstract

With the improvement of economic development and consumption level, the portfolio problem has become a concern of more and more people. Under the financial market risk management framework, this topic is based on the classical portfolio MV model, and the generalized MV model with multi-conditional constraints is established by introducing a variety of trading constraints existing in the real trading, which is solved by using the Lagrange multiplier method. Collecting trading data from the Chinese securities market for empirical study of the model, it is found that the portfolio returns of securities in industries with small correlation are higher than those of securities in industries with large correlation, and the risk-to-investment ratios of securities in different industries and the same industry are 0.834-1.057 and 0.823-1.038 in the multi-group test, and diversification of investment in different industries can reduce investment risk. The model in this paper performs better in all indicators of portfolio performance, its cumulative return is higher than the comparison method by 0.118~0.213, and the yield curve is stable at -0.024~0.025.The results show that the proposed multi-constraint portfolio model is not only reasonable and effective, but also can better guide investors to choose the optimal and robust investment program.