Production
https://prod.org.br/doi/10.1590/0103-6513.208816
Production
Research Article

Portfolio optimization using Mean Absolute Deviation (MAD) and Conditional Value-at-Risk (CVaR)

Lucas Pelegrin da Silva; Douglas Alem; Flávio Leonel de Carvalho

http://dx.doi.org/10.1590/0103-6513.208816 Production, vol.27, p.0, 2017
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Abstract

This paper investigates the efficiency of traditional portfolio optimization models when the returns of financial assets are highly volatile, e.g., in financial crises periods. We also develop alternative optimization models that combine the mean absolute deviation (MAD) and the conditional value at risk (CVaR), attempting to mitigate inefficient, low return and/or high-risk, portfolios. Three methodologies for estimating the probability of the asset’s historical returns are also compared. By using historical data on the Brazilian stock market between 2004 and 2013, we analyze the efficiency of the proposed approaches. Our results show that the traditional models provide portfolios with higher returns, but our propose model are able to generate lower risk portfolios, which might be more attractive in volatile markets. In addition, we find that models that do not use equiprobable scenarios produce better results in terms of return and risk.

Keywords

Portfolio optimization, Mean Absolute Deviation, Conditional Value-at-risk, Brazilian stock market

References

Albuquerque, G. U. V. (2009). Um estudo do problema de escolha de portfólio ótimo (Master’s thesis). Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos.

Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7), 1285-1297. http://dx.doi.org/10.1016/j.cor.2009.09.009.

Aouni, B., Colapinto, C., & La Torre, D. (2014). Financial portfolio management through the goal programming model: current state-of-the-art. European Journal of Operational Research, 234(2), 536-545. http://dx.doi.org/10.1016/j.ejor.2013.09.040.

Babaei, S., Sepehri, M. M., & Babaei, E. (2015). Multi-objective portfolio optimization considering the dependence structure of asset returns. European Journal of Operational Research, 244(2), 525-539. http://dx.doi.org/10.1016/j.ejor.2015.01.025.

Charnes, A., Cooper, W. W., & Ferguson, R. O. (1955). Optimal estimation of executive compensation by linear programming. Management Science, 1(2), 138-151. http://dx.doi.org/10.1287/mnsc.1.2.138.

Charnes, A., & Cooper, W. W. (1957). Management models and industrial applications of linear programming. Management Science, 4(1), 38-91. http://dx.doi.org/10.1287/mnsc.4.1.38.

Chen, W. (2015). Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica A, 429, 125-139. http://dx.doi.org/10.1016/j.physa.2015.02.060.

Kolm, P. N., Tütüncü, R., & Fabozzi, F. J. (2014). 60 years of portfolio optimization: practical challenges and current trends. European Journal of Operational Research, 234(2), 356-371. http://doi:10.1016/j.ejor.2013.10.060.

Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5), 519-531. http://dx.doi.org/10.1287/mnsc.37.5.519.

Lee, S. M. (1972). Goal programming for decision analysis (pp. 15-39) Philadelphia: Auerbach Publishers.

Mansini, R., & Speranza, M. G. (2005). An exact approach for portfolio selection with transaction costs and rounds. IIE Transactions, 37(10), 919-929. http://dx.doi.org/10.1080/07408170591007821.

Mansini, R., Ogryczak, W., & Speranza, M. G. (2014). Twenty years of linear programming based portfolio optimization. European Journal of Operational Research, 234(2), 518-535. http://dx.doi.org/10.1016/j.ejor.2013.08.035.

Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91. http://dx.doi.org/10.1111/j.1540-6261.1952.tb01525.x.

Mashayekhi, Z., & Omrani, H. (2016). An integrated multi-objective Markowitz–DEA cross-efficiency model with fuzzy returns for portfolio selection problem. Applied Soft Computing, 38, 1-9. http://dx.doi.org/10.1016/j.asoc.2015.09.018.

Pouya, A. R., Solimanpur, M., & Rezaee, M. J. (2016). Solving multi-objective portfolio optimization problem using invasive weed optimization. Swarm and Evolutionary Computation, 28, 42-57. http://dx.doi.org/10.1016/j.swevo.2016.01.001.

Saborido, R., Ruiz, A. B., Bermúdez, J. D., Vercher, E., & Luque, M. (2016). Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection. Applied Soft Computing, 39, 48-63. http://dx.doi.org/10.1016/j.asoc.2015.11.005.

Sandoval Junior, L., & Franca, I. P. (2012). Correlation of financial markets in times of crisis. Physica A: Statistical Mechanics and its Applications, 391(1-2), 187-208. http://dx.doi.org/10.1016/j.physa.2011.07.023.

Sharpe, W. F. (1971). A linear programming approximation for the general portfolio analysis problem. Journal of Financial and Quantitative Analysis, 6(05), 1263-1275. http://dx.doi.org/10.2307/2329860.

Verma, R., & Soydemir, G. (2006). Modeling country risk in Latin America: a country beta approach. Global Finance Journal, 17(2), 192-213. http://dx.doi.org/10.1016/j.gfj.2006.05.003.

Young, M. R. (1998). A minimax portfolio selection rule with linear programming solution. Management Science, 44(5), 673-683. http://dx.doi.org/10.1287/mnsc.44.5.673.

Zanini, F. A. M., & Figueiredo, A. C. (2005). As teorias de carteira de Markowitz e de Sharpe: uma aplicação no mercado brasileiro de ações entre julho/95 e junho/2000. Revista de Administração Mackenzie, 6(2), 37-64.
 

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