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Does Marginal VaR Lead to Improved Performance of Managed Portfolios: A Study of S&P BSE 100 and S&P BSE 200

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Abstract

In order to improve upon the performance of a managed portfolio, we propose the use of Marginal Value-at-Risk (MVaR) to ascertain the desirability of assets for inclusion in the managed portfolio, prior to obtaining the optimal managed portfolio. In particular, this is applied on a larger index which comprises of a greater number of assets than a benchmark index and the larger index includes all the assets from the benchmark index. The resulting MVaR index includes exactly the same number of assets as the benchmark index. An empirical study with S&P BSE 100 as the benchmark index, with the MVaR index being derived from S&P BSE 200, with five different optimization problems shows outperformance by the MVaR portfolio over the benchmark portfolio. This highlights the advantage of the inclusion of MVaR resulting in improved performance of the managed portfolio.

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References

  • Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203–228.

    Article  Google Scholar 

  • Birge, J. R., & Louveaux, F. (1997). Introduction to stochastic programming. New York: Springer.

    Google Scholar 

  • Black, F., & Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48(5), 28–43.

    Article  Google Scholar 

  • Cai, X., Teo, K. L., Yang, X., & Zhou, X. Y. (2000). Portfolio optimization under a minimax rule. Management Science, 46(7), 957–972.

    Article  Google Scholar 

  • Cheung, Y. H., & Powell, R. J. (2012). Anybody can do value at risk: A nonparametric teaching study. Australasian Accounting, Business and Finance Journal, 6(1), 111–123.

    Google Scholar 

  • Dentcheva, D., & Ruszczynski, A. (2006). Portfolio optimization with stochastic dominance constraints. Journal of Banking and Finance, 30(2), 433–451.

    Article  Google Scholar 

  • Fabozzi, F. J., Kolm, P. N., Pachamanova, D. A., & Focardi, S. M. (2007). Robust portfolio optimization and management. Hoboken: Wiley.

    Google Scholar 

  • Francis, J. C., & Kim, D. (2013). Modern portfolio theory: Foundations, analysis, and new developments (Vol. 795). New York: Wiley.

    Google Scholar 

  • Gaivoronski, A. A., & Pflug, G. (2005). Value-at-risk in portfolio optimization: Properties and computational approach. The Journal of Risk, 7(2), 1–31.

    Article  Google Scholar 

  • Gotoh, J. Y., & Takano, Y. (2007). Newsvendor solutions via conditional value-at-risk minimization. European Journal of Operational Research, 179(1), 80–96.

    Article  Google Scholar 

  • Hallerbach, W. G. (1999). Decomposing portfolio Value-at-Risk: A general analysis (No. 99-034/2). Tinbergen Institute Discussion Paper.

  • Investopedia. (2019). Retrieved August 1, 2019 from https://www.investopedia.com/terms/m/marginal-var.asp.

  • Kapsos, M., Zymler, S., Christofides, N., & Rustem, B. (2014). Optimizing the Omega ratio using linear programming. Journal of Computational Finance, 17(4), 49–57.

    Article  Google Scholar 

  • Keating, C., & Shadwick, W. F. (2002). A universal performance measure. Journal of Performance Measurement, 6(3), 59–84.

    Google Scholar 

  • Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2014). Recent developments in robust portfolios with a worst—Case approach. Journal of Optimization Theory and Applications, 161(1), 103–121.

    Article  Google Scholar 

  • Konno, H., & Shirakawa, H. (1994). Equilibrium relations in a capital asset market: A mean absolute deviation approach. Financial Engineering and the Japanese Markets, 1(1), 21–35.

    Article  Google Scholar 

  • Konno, H., Shirakawa, H., & Yamazaki, H. (1993). A mean-absolute deviation-skewness portfolio optimization model. Annals of Operations Research, 45(1), 205–220.

    Article  Google Scholar 

  • Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science, 37(5), 519–531.

    Article  Google Scholar 

  • Kopa, M., & Chovanec, P. (2008). A second-order stochastic dominance portfolio efficiency measure. Kybernetika, 44(2), 243–258.

    Google Scholar 

  • Krokhmal, P., Palmquist, J., & Uryasev, S. (2002). Portfolio optimization with conditional value-at-risk objective and constraints. The Journal of Risk, 4, 43–68.

    Article  Google Scholar 

  • Leitner, J. (2005). A short note on second-order stochastic dominance preserving coherent risk measures. Mathematical Finance, 15(4), 649–651.

    Article  Google Scholar 

  • Linsmeier, T. J., & Pearson, N. D. (1996). Risk measurement: An introduction to value-at-risk. Technical report 96-04, OFOR, University of Illinois at Urbana-Champaign.

  • Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91.

    Google Scholar 

  • Marshell, A. W., & Olkin, I. (1979). Inequalities: Theory of majorization and its applications. San Diego: Academic Press.

    Google Scholar 

  • Mausser, H., Saunders, D., & Seco, L. (2006). Optimizing Omega. Risk, 19(11), 88–92.

    Google Scholar 

  • Mavrotas, G. (2009). Effective implementation of the \(\epsilon\)-constraint method in multi-objective mathematical programming problems. Applied Mathematics and Computation, 213(2), 455–465.

    Article  Google Scholar 

  • Michalowski, W., & Ogryczak, W. (2001). Extending the MAD portfolio optimization model to incorporate downside risk aversion. Naval Research Logistics, 48(3), 185–200.

    Article  Google Scholar 

  • Michaud, R. O. (1989). The Markowitz optimization enigma: Is “optimized” optimal? Financial Analysts Journal, 45(1), 31–42.

    Article  Google Scholar 

  • Ogryczak, W., & Ruszczynski, A. (1999). From stochastic dominance to mean-risk models: Semideviations as risk measures. European Journal of Operational Research, 116(1), 33–50.

    Article  Google Scholar 

  • Polak, G. G., Rogers, D. F., & Sweeney, D. J. (2010). Risk management strategies via minimax portfolio optimization. European Journal of Operational Research, 207(1), 409–419.

    Article  Google Scholar 

  • Rau-Bredow, H. (2004). Value at risk, expected shortfall, and marginal risk contribution. In G. Szego (Ed.), Risk measures for the 21st century (pp. 61–68).

  • Rockafeller, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. The Journal of Risk, 2, 21–42.

    Article  Google Scholar 

  • Sharma, A., & Mehra, A. (2013). Portfolio selection with a minimax measure in safety constraint. Optimization, 62(11), 1473–1500.

    Article  Google Scholar 

  • Sharma, A., & Mehra, A. (2017). Extended omega ratio optimization for risk-averse investors. International Transactions in Operational Research, 24(3), 485–506.

    Article  Google Scholar 

  • Speranza, M. G. (1994). Linear models for portfolio selection and their application to the Milano stock market. In: Financial modelling (pp. 320–333). Physica-Verlag HD.

  • Teo, K. L., & Yan, X. Q. (2001). Portfolio selection problem with minimax type risk function. Annals of Operations Research, 101(1–4), 333–349.

    Article  Google Scholar 

  • Von Neumann, J., & Morgenstern, O. (1947). Theory of games and economic behaviour. Princeton: Princeton University Press.

    Google Scholar 

  • Young, M. R. (1998). A minimax portfolio selection rule with linear programming solution. Management Science, 44(5), 673–683.

    Article  Google Scholar 

Download references

Acknowledgements

The authors express their gratitude to both the reviewers for their detailed comments which resulted in an improved manuscript.

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Correspondence to Siddhartha P. Chakrabarty.

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Jain, S., Chakrabarty, S.P. Does Marginal VaR Lead to Improved Performance of Managed Portfolios: A Study of S&P BSE 100 and S&P BSE 200. Asia-Pac Financ Markets 27, 291–323 (2020). https://doi.org/10.1007/s10690-019-09294-0

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