Advances in Analysis

Download PDF (532.3 KB) PP. 1 - 15 Pub. Date: October 6, 2020

DOI: 10.22606/aan.2020.51001

• Ngongo Isidore Séraphin
  Department of Mathematics, ENS, University of Yaoundé I, Cameroon
• Jimbo Henri Claver^*
  Department of Mathematics, ENS, University of Yaoundé I, Cameroon; Department of Applied Mathematics and Statistics, AUAF & Waseda University, Tokyo, Japan
• Dongfack Saufack Arnaud
  Department of Mathematics, University of Yaoundé 1, Cameroon
• Dongmo Tsamo Arthur
  Department of Mathematics, University of Yaoundé 1, Cameroon
• Nkague Nkamba Léontine
  Department of Mathematics, ENS, University of Yaoundé I, Cameroon
• Andjiga Gabriel Nicolas
  Department of Mathematics, University of Yaoundé 1, Cameroon
• Etoua Rémy Magloire
  Department of Mathematics, Higher National Polytechnic School. Yaoundé 1, Cameroon

Measuring risks in a portfolio of financial assets is a very high profile issue in financial mathematics research. In this article, we focus on the search for an efficient portfolio and a smooth efficient frontier using the Downside Risk method measured by the Semi-Variance to have a portfolio with minimal variance. More specifically, and considering a set of financial securities, we compare the Markowitz Mean-Variance method and the Downside Risk method. We find that Downside Risk is a better measure of risk than Mean-Variance and is therefore more suitable for building a portfolio of minimum variance.

downside risk, average variance, efficient portfolio, efficient frontier, risk

[1] 1. H. C. Jimbo, I. S. Ngongo, N. G. Andjiga, and T. Suzuki, "Portfolio Optimization Under Cardinality Constraints: A comparative Study," Open Journal of Statistics, vol.7, pp.731-742, 2017.

[2] 2. H. C. Jimbo, and M. J. Craven, "Optimizing Stock Investment Portfolio with Stochastic Constraints," Journal of Nonlinear and Convex Analysis, vol.1, pp.127-141, 2011.

[3] 3. H. Markowitz, "portfolio selection," The Journal of finance, vol.7, N1, pp.77-79, 1952.

[4] 4. H. Markowitz, "Mean-variance analysis in portfolio choice and capital markets," Basil Blackwell, Oxford, 1987.

[5] 5. E. Ballestro, "Stochastic goal programming: A Mean-variance appreach," European Journal of Operational Research, pp.479-581, 2001.

[6] 6. E. Ballestro, "Mean-Semivariance Effecient Frontier: A Downside Risk Model for Portfolio Selection," Applied Mathemetical Finance Volume, pp.1-15, 2005.

[7] 7. J. Estarda, "Mean-Semivariance Behavior: An Alternative Behavioral Model," Journal of Emerging Market Finance, pp.231-248, 2004.

[8] 8. J. Estarda, "Semivariance Optimisation: A Heuristic Approach," Journal of Applied Finance, pp.57-72, 2008.

[9] 9. P. Athayde, F. Delbaen, J. Eber, and D. Heath, "Coherent Measures of Risk," Mathemetical Finance, pp.203-228, 1999.

[10] 10. G. Athayde, "Building a Mean-Downside Risk Portfolio Frontier", Developments in Forescast Combinaison and Portfolio Choice, 2001.

[11] 11. G. Athayde, "The mean-downside risk portfolio frontier: A Non-Parametric approch," Advances in portfolio construction and implementation, 2003.

[12] 12. A. Bergonzat A, and F. Cavals, "Garanties en cas de vie sur contrats multisupports," Mémoire d’actuariat, ENSAE, 2006.

[13] 13. P. Bougerol, "Modèles stochastiques et Applications à la finance", 2011.

[14] 14. P. Briand, "Le modèle de Black Scholes", 2003.

[15] 15. C. Acerbi, "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking and Finance, vol.2, N1, pp.1505-1518, 2002.

[16] 16. M. Denuit, and A. Charpentier, "Mathématiques de l’assurance non vie: Principes fondamentaux de la théorie du risque," Economica, 2004.

[17] 17. C. Partrat C, J. Besson, "Assurance non-vie: Modélisation,simulation," Economica, 2005.