Teoría moderna de portafolio: desarrollos fundamentales, extensiones y enfoques robustos

Modern Portfolio Theory: Fundamental Developments, Extensions, and Robust Approaches

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En este trabajo se presentan los principales desarrollos teóricos de la teoría moderna de portafolios. Inicialmente, se introducen los elementos fundamentales del modelo media-varianza (MV) de Markowitz, su formulación y solución del problema de optimización, así como sus limitaciones. Luego, se presentan diferentes extensiones del MV al introducir medidas alternativas de riesgo, así como los ajustes del modelo de construcción de portafolios. En este ámbito, se expone el enfoque de downside risk. Finalmente, se introducen los enfoques robustos de portafolio teniendo en cuenta los enfoques: bayesiano, de optimización robusta y de paridad de riesgo. Desde estos nuevos enfoques se resaltan aquellos ajustes que permiten superar las principales limitaciones del modelo MV. También, se introducen desarrollos recientes que extienden las formulaciones originales del modelo de portafolio para tratar nuevos desafíos y problemáticas actuales.

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Acerbi, C. y Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking

and Finance, 26(7), 1487-1503. https://doi.org/10.1016/S0378-4266(02)00283-2 DOI: https://doi.org/10.1016/S0378-4266(02)00283-2

Artzner, P., Delbaen, F., Eber, J. y Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203-228. https://doi.org/10.1111/1467-9965.00068 DOI: https://doi.org/10.1111/1467-9965.00068

Bellman, R. (1957). A Markovian decision process. Journal of Mathematics and Mechanics, 679-684. DOI: https://doi.org/10.1512/iumj.1957.6.56038

Ben-Tal, A. y Nemirovski, A. (1998). Robust convex optimization. Mathematics of Operations Research, 23(4), 769-805. https://doi.org/10.1287/moor.23.4.769 DOI: https://doi.org/10.1287/moor.23.4.769

Berstein, P. (1992). Capital Ideas: The Improbable Origins of Modern Wall Street. The Free Press.

Best, M. y Grauer, R. (1991). Sensitivity analysis for mean-variance portfolio problems. Management Science, 37(8), 980-989. https://doi.org/10.1287/mnsc.37.8.980 DOI: https://doi.org/10.1287/mnsc.37.8.980

Bertsimas, D., Brown, D. y Caramanis, C. (2011). Theory and applications of robust optimization. SIAM Review, 53(3), 464-501. https://doi.org/10.1137/080734510 DOI: https://doi.org/10.1137/080734510

Black, F. y Litterman, R. (1991). Global Asset Allocation with Equities, Bonds, and Currencies. Goldman, Sachs & Co Fixed Income Research, 1-44. DOI: https://doi.org/10.3905/jfi.1991.408013

Black, F. y Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48(5), 28-43. https://doi.org/10.2469/faj.v48.n5.28 DOI: https://doi.org/10.2469/faj.v48.n5.28

Carmona, D. y Gamboa, J. (2022). Optimización robusta de portafolio empleando métodos Bayesianos. ODEON, 21, 81-104. https://doi.org/10.18601/17941113.n21.05 DOI: https://doi.org/10.18601/17941113.n21.05

Cesarone, F., Martino, M. y Carleo, A. (2022). Does ESG impact really enhance portfolio profitability? Sustainability, 14(4), 20-50. https://doi.org/10.3390/su14042050 DOI: https://doi.org/10.3390/su14042050

Chopra, V. y Ziemba, W. (1993). The effects of errors in means, variances, and covariances on optimal portfolio choice. Journal of Portfolio Management, 19(2), -11. https://doi.org/ 10.1142/9789814417358_0021 DOI: https://doi.org/10.3905/jpm.1993.409440

Choueifaty, Y. y Coignard, Y. (2008). Toward maximum diversification. The Journal of Portfolio Management, 35(1), 40-51. DOI: https://doi.org/10.3905/JPM.2008.35.1.40

Constantinides, G. y Malliaris, A. (1995). Portfolio theory. Handbooks in Operations Research and Management Science, 9(1), 1-30. https://doi.org/10.1016/S0927-0507(05)80045-3 DOI: https://doi.org/10.1016/S0927-0507(05)80045-3

Coqueret, G. (2022). Perspectives in Sustainable Equity Investing. CRC Press. DOI: https://doi.org/10.1201/9781003215257

De Finetti, B. (1940). The problem of ‘full-risk insurances’. Journal of Investment Management, 4(1), 19-43.

El Ghaoui, L. y Lebret, H. (1997). Robust solutions to least-squares problems with uncertain data. SIAM Journal on Matrix Analysis and Applications, 18(4), 1035-1064. https://doi.org/10.1137/S0895479896298130 DOI: https://doi.org/10.1137/S0895479896298130

El Ghaoui, L., Oustry, F. y Lebret, H. (1998). Robust solutions to uncertain semidefinite programs. SIAM Journal on Optimization, 9(1), 33-52. https://doi.org/10.1137/S1052623496305717 DOI: https://doi.org/10.1137/S1052623496305717

Elton, E., Gruber, M. y Padberg, M. (1976). Simple criteria for optimal portfolio selection. Journal of Finance, 11(5), 1341-1357. https://doi.org/10.2307/2326684 DOI: https://doi.org/10.1111/j.1540-6261.1976.tb03217.x

Fisher, I. (1907). The Rate of Interest: Its nature, determination and relation to economic phenomena. MacMillan.

Fabozzi, F., Focardi, S., Kolm, P. y Pachamanova, D. (2007). Robust portfolio optimization and management. John Wiley & Sons. DOI: https://doi.org/10.3905/jpm.2007.684751

Gasser, S. M., Rammerstorfer, M. y Weinmayer, K. (2017). Markowitz revisited: Social portfolio engineering. European Journal of Operational Research, 258(3), 1181-1190. https://doi.org/10.1016/j.ejor.2016.10.043 DOI: https://doi.org/10.1016/j.ejor.2016.10.043

Georgantas, A., Doumpos, M. y Zopounidis, C. (2021). Robust optimization approaches for portfolio selection: A comparative analysis. Annals of Operations Research, 1-17. https://doi.org/10.1007/s10479-021-04177-y DOI: https://doi.org/10.1007/s10479-021-04177-y

Goldfarb, D., Iyengar, G. (2003). Robust portfolio selection problems. Mathematics of Operations Research, 28(1), 1-38. https://doi.org/10.1287/moor.28.1.1.14260 DOI: https://doi.org/10.1287/moor.28.1.1.14260

He, G. y Litterman, R. (1999). The intuition behind Black-Litterman model portfolios. Goldman Sachs - Investment Management Research, Technical report, 1-18.

Henriksson, R., Livnat, J., Pfeifer, P. y Stumpp, M. (2019). Integrating ESG in portfolio construction. The Journal of Portfolio Management, 45(4), 67-81. https://doi.org/10.3905/ jpm.2019.45.4.067 DOI: https://doi.org/10.3905/jpm.2019.45.4.067

Hirschberger, M., Steuer, R., Utz, S., Wimmer, M. y Qi, Y. (2013). Computing the nondominated surface in tri-criterion portfolio selection. Operations Research, 61(1), 169-183. https://doi.org/10.1287/opre.1120.1140 DOI: https://doi.org/10.1287/opre.1120.1140

James, W., y Stein, C. (1961). Estimation with quadratic loss. Proceedings Fourth Berkeley Symposium of Math. Statis. Prob., 1, 361-380.

Kim, J. H., Kim, W. C., Kwon, D. G. y Fabozzi, F. J. (2018). Robust equity portfolio performance. Annals of Operations Research, 266(1), 293-312. https://doi.org/10.1007/ s10479-017-2739-1 DOI: https://doi.org/10.1007/s10479-017-2739-1

Kolm, P., Tütüncü, R., y Fabozzi, F. (2014). 60 years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356-371. https://doi.org/10.1016/j.ejor.2013.10.060 DOI: https://doi.org/10.1016/j.ejor.2013.10.060

Krokhmal, P., Palmquist, J. y Uryasev, S. (2002). Portfolio optimization with conditional value-at-risk objective and constraints. Journal of Risk, 4(1), 43-68. DOI: https://doi.org/10.21314/JOR.2002.057

Ledoit, O. y Wolf, M. (2003). Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance, 10(5), 603-621. https://doi.org/10.1016/S0927-5398(03)00007-0 DOI: https://doi.org/10.1016/S0927-5398(03)00007-0

Ledoit, O. y Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2), 365-411. https://doi.org/10.1016/S0047-259X(03)00096-4 DOI: https://doi.org/10.1016/S0047-259X(03)00096-4

León, B. y Zapata, C. (2023). Gestión moderna de portafolio: una guía cuantitativa con aplicaciones en R y Python. Colegio de Estudios Superiores de Administración (CESA).

Lintner, J. (1965). Security prices, risk, and maximal gains from diversification. The Journal of Finance, 20(4), 587-615. https://doi.org/10.2307/2977249 DOI: https://doi.org/10.1111/j.1540-6261.1965.tb02930.x

Maillard, S., Roncalli, T. y Teiletche, J. (2010). The properties of equally weighted risk contribution portfolios. Journal of Portfolio Management, 36(4), 60–70. https://doi.org/10.3905/jpm.2010.36.4.060 DOI: https://doi.org/10.3905/jpm.2010.36.4.060

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

Markowitz, H. (1959). Portfolio selection: Efficient diversification of investments. Yale University Press.

Marschak, J. (1938). Money and the Theory of Assets. Econometrica, Journal of the Econometric Society, 311-325. https://doi.org/10.2307/1905409 DOI: https://doi.org/10.2307/1905409

Michaud, R. (1989). The Markowitz optimization enigma: Is optimization optimal? Financial Analysts Journal, 45(1), 31-42. DOI: https://doi.org/10.2469/faj.v45.n1.31

Michaud, R. (1998). Efficient asset management: A practical guide to stock portfolio optimization and asset allocation. Oxford University Press.

Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34(4), 768-783. https://doi.org/10.2307/1910098 DOI: https://doi.org/10.2307/1910098

Pachamanova, D. y Fabozzi, F. (2012). Equity portfolio selection models in practice. Encyclopedia of Financial Models, 1(1), 61-87. https://doi.org/10.1002/9781118182635.efm0046 DOI: https://doi.org/10.1002/9781118182635.efm0046

Qian, E. (2005). Risk parity portfolios: Efficient portfolios through true diversification. Panagora Asset Management, Technical Report.

Qian, E. (2006). On the financial interpretation of risk contribution: Risk budgets do add up. Journal of Investment Management, 4(4), 1-11. DOI: https://doi.org/10.2139/ssrn.684221

Qian, E. (2011). Risk parity and diversification. The Journal of Investing, 20(1), 119-127. Rockefellar, R. y Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of Risk, 2(3), 21-41. https://doi.org/10.21314/JOR.2000.038 DOI: https://doi.org/10.21314/JOR.2000.038

Rockafellar, R. y Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. https://doi.org/10.1016/S0378-4266(02)00271-6 DOI: https://doi.org/10.1016/S0378-4266(02)00271-6

Romero, C. (2010). La Teoría Moderna de Portafolio: un ensayo sobre sus formulaciones originales y sus repercusiones contemporáneas. ODEON, 5, 103-118.

Roncalli, T. (2014). Introduction to Risk Parity and Budgeting. CRC Press. DOI: https://doi.org/10.2139/ssrn.2272973

Roy, A. (1952). Safety first and the holding of assets. Journal of the Econometric Society, 20(3), 431-449. https://doi.org/10.2307/1907413 DOI: https://doi.org/10.2307/1907413

Rubinstein, M. (2006). Bruno de Finetti and mean-variance portfolio selection. Journal of Investment Management, 4(3),1-19.

Sharpe, W. (1963). A simplified model for portfolio analysis. Management science, 9(2), 277-293. https://doi.org/10.1287/mnsc.9.2.277 DOI: https://doi.org/10.1287/mnsc.9.2.277

Sharpe, W. (1964). Capital Asset Prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425-442. https://doi.org/10.1111/j.1540-6261.1964.tb02865.x DOI: https://doi.org/10.1111/j.1540-6261.1964.tb02865.x

Sharpe, W. (1971). A linear programming approximation for the general portfolio analysis problem. Journal of Financial and Quantitative Analysis, 6(5), 1263-1275. https://doi.org/10.2307/2329860 DOI: https://doi.org/10.2307/2329860

Sortino, F. y Price, L. (1994). Performance measurement in a downside risk framework. Journal of Investing, 3(3), 59-64. https://doi.org/10.3905/joi.3.3.59 DOI: https://doi.org/10.3905/joi.3.3.59

Tobin, J. (1958). Liquidity preference as behavior towards risk. Review of Economic Studies, 25(1), 68-85. DOI: https://doi.org/10.2307/2296205

Treynor, J. (1961). Toward a theory of market value of risky assets. Working paper.

Tütüncü, R. y Koenig, M. (2004). Robust asset allocation. Annals of Operations Research, 132(1), 157-187. https://doi.org/10.1023/B:ANOR.0000045281.41041.ed DOI: https://doi.org/10.1023/B:ANOR.0000045281.41041.ed

Uryasev, S. y Rockafellar, R. T. (2001). Conditional value-at-risk: Optimization approach. Stochastic optimization: Algorithms and Applications, 411-435. https://doi.org/10.1007/978-1-4757-6594-6_17 DOI: https://doi.org/10.1007/978-1-4757-6594-6_17

Utz, S., Wimmer, M., Hirschberger, M. y Steuer, R. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491-498. https://doi.org/10.1016/j.ejor.2013.07.024 DOI: https://doi.org/10.1016/j.ejor.2013.07.024

Von Neumann, J. y Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.

Zapata, C. (2021a). Optimización robusta de portafolios: conjuntos de incertidumbre y contrapartes robustas. ODEON, 20, 93-121. https://doi.org/10.18601/17941113.n20.04 DOI: https://doi.org/10.18601/17941113.n20.04

Zapata, C. (2021b). Modelo Media-Varianza y criterios ASG: de Markowitz al portafolio socialmente responsable. ODEON, 21, 55-79. https://doi.org/10.18601/17941113.n21.04 DOI: https://doi.org/10.18601/17941113.n21.04

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