THE INFLUENCE OF THE COVID-19 PANDEMIC ON ALLOCATION OF ASSETS IN INVESTORS PORTFOLIO
Keywords:Markowitz model, Robust optimization, Data filtering, Covid-19, crisis, Risk aversion
Investing during a pandemic is very challenging. Even in these difficult times, the investor must appropriately allocate assets into his portfolio. In this article, we discuss investing in the stock market. We are interested in creating portfolios of shares that consist of financial assets. The individual methods we use are designed to provide an allocation of funds in between individual shares. In the modern portfolio theory, the Markowitz model (Markowitz, 1952) is being used to solve these problems. The paper's main goal is to propose an efficient, robust approach to solve the Markowitz optimization problem adjusted for periods of a global decline in financial markets. In our research, we focus on robust optimization. Instead of precisely given input parameters, we propose a set of parameters from which we always select the worst possible parameter (so-called worst-case optimization). The robustness of optimization is achieved using so-called filter matrices. These matrices are used to modify historical data directly during optimization. The proposed model modifies the data by using different lengths of historical returns. Our proposed model is then compared with the original Markowitz non-robust model. We compare these two models using the properties of the second derivative of the optimization problem. Our results are visualized for different levels of investor’s risk aversion. We present our methods on historical price data of five randomly selected companies traded on the US market. By comparing the proposed robust approach with the non-robust one, we show that different lengths of historical returns capture volatility changes earlier. The investor can thus reduce his risk aversion and increase his expected returns.
Bobulský, M. (2018). Properties of the value function of a parametric quadratic programming problem. Comenius University in Bratislava, Master thesis, pp. 1-55.
Bobulský, M., Bohdalová, M. (2019). Robust Optimization Methods in Modern Portfolio Theory. European Financial Systems 2019: Proceedings of the 16th International Conference, Brno, Masaryk University, pp. 49-56.
Boyd, S., Kim, S.J. (2007, November). Robust Efficient Frontier Analysis with a Separable Uncertainty Model
Boyd, S., Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press, New York
Kilianová, S., Ševčovič, D. (2013). A Transformation Method for Solving the Hamilton–Jacobi–Bellman Equation for a Constrained Dynamic Stochastic Optimal Allocation Problem. The ANZIAM Journal, 55(1), pp.14-38. doi:10.1017/S144618111300031X.
Kilianová, S., Trnovská, M. (2014). Robust portfolio optimization via solution to the Hamilton–Jacobi–Bellman equation. International Journal of Computer Mathematics, vol. 93(5), pp. 725-734, https://doi.org/10.1080/00207160.2013.871542.
Lan, W., Wang, H., Tsai, Ch. L. (2012). A Bayesian Information Criterion for Portfolio Selection. Computational Statistics & Data Analysis, vol. 56(1), pp. 88-99, https://doi.org/10.1016/j.csda.2011.06.012.
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7, pp. 77–91.
Mirzapour Al-e-hashem, S.M.J., Malekly, H., Aryanezhad, M.B. (2011). A multiobjective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty, Int. J. Prod. Econ. 134, 28–42.
Pishvaee, M.S., Rabbani, M., Torabi, S.A. (2011). A robust optimization approach to closed-loop supply chain network design under uncertainty, Appl. Math. Model. 35, pp. 637-649.
Tütüncü, R., Koenig, M. (2004). Robust asset allocation. Ann. Oper. Res. 132, pp. 157-187. http://blogs/psychologytoday.com/blog/digital-children
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