GENERAL ARTICLES

 

Development of a more applied version of coherency called 'sensible coherency' for assessment of financial risk measures

 

 

M. Jasemi^I; A.M. Kimiagari^II; A. Memariani^III

^IDepartment of Industrial Engineering, Amirkabir University of Technology, Iran Miladj@aut.ac.ir
^IIDepartment of Industrial Engineering, Amirkabir University of Technology, Iran kimiagar@aut.ac.ir
^IIIDepartment of Industrial Engineering, Bu-Ali Sina University, Iran

 

 

---

ABSTRACT

Coherency is becoming a necessary feature for any risk measure, and now is an acceptable tool in risk management to assess the risk measures. For example, recent studies have strongly criticised VaR-based models for not providing a coherent risk measure. Because of such acceptance, it is important to improve the efficiency of the touchstone for evaluating risk measures in order to achieve a fairer assessment. This is just the challenge that this paper seeks to address. This goal is achieved on the one hand by doing some simplifications in axioms of coherency without losing their major financial points, and on the other hand by removing the paradox between two of the axioms. The new concept is called 'sensible coherency', and the risk measure that satisfies the four new simplified and corrected axioms will be 'sensibly coherent'. Finally, the new axioms are applied to a particular type of lower partial moments as a case study.

---

OPSOMMING

Koherensie word 'n noodsaaklike kenmerk van enige risikomaatstaf en is nou 'n aanvaarbare gereedskapstuk in die beoordeling van risikomaatstawwe. Die doel van hierdie artikel word bereik deur enersyds die aksiomas van koherensie te vereenvoudig en andersyds die paradoks tussen die aksiomas te verwyder. Die resultaat word "sinvolle koherensie" genoem.

---

 

 

“Full text available only in PDF format”

 

REFERENCES

[1] Markowitz, H.M. 1952. Portfolio selection. Journal of Finance, 25, 71 - 79.         [ Links ]

[2] Konno, H. & Suzuki, K. 1992. A fast algorithm for solving large scale mean - variance models by compact factorization of covariance matrices. Journal of the Operations Research Society of Japan, 35, 93 - 104.         [ Links ]

[3] Perold, A.F. 1984. Large-scale portfolio optimization. Journal of Management Science, 30, 1143 - 1160.         [ Links ]

[4] Artzner, P., Delbaen,F., Eber, J.M. & Heath, D. 1997. Thinking coherently. Journal of Risk, 10, 68 - 71.         [ Links ]

[5] Artzner, P., Delbaen,F., Eber, J.M. & Heath, D. 19971999. Coherent measures of risk. Journal of Mathematical Finance, 9, 203 - 228.         [ Links ]

[6] Bertsimas, D., Lauprete, G.J. & Samarov, A. 2000. Shortfall as a risk measure: Properties, optimization and applications. Working paper, Sloan School of Management, MIT, Cambridge.         [ Links ]

[7] Delbaen, F. 2000. Coherent risk measures on general probability spaces. In: Sandmann, K. and Schonbucher, P.J. (eds), Advances in finance and stochastics. Essays in honour of Dieter Sondermann. Springer-Verlag, Berlin, pp. 1 - 37.         [ Links ]

[8] Kusuoka, S. 2001. On law invariant coherent risk measures. Journal of Advances in Mathematical Economics, 3, 83-95.         [ Links ]

[9] Acerbi, C. 2002. Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking and Finance, 26, 1505-1518.         [ Links ]

[10] Fritelli, M. & Rosazza Gianin, E. 2002. Putting order in risk measures. Journal of Banking and Finance, 26, 1473-1486.         [ Links ]

[11] Acerbi, C. & Tasche, D. 2002. On the coherence of expected shortfall. Journal of Banking and Finance, 26, 1487-1503.         [ Links ]

[12] Szego, G. 2002. Measures of risk. Journal of Banking and Finance, 26, 1253-1272.         [ Links ]

[13] Inoue, A. 2003. On the worst conditional expectation. Journal of Mathematical Analysis and Applications, 286, 237-247.         [ Links ]

[14] Pelessoni, R. & Vicig, P. 2001. Coherent risk measures and upper previsions. In: Second International Symposium on Imprecise Probabilities and Their Applications, Ithaca, New York.         [ Links ]

[15] Giannopoulos, K. & Tunaru, R. 2005. Coherent risk measures under filtered historical simulation. Journal of Banking and Finance, 29, 979-996.         [ Links ]

[16] Embrechts, P., McNeil, A. & Straumann, D. 2002. Correlation and dependence in risk management: Properties and pitfalls. In: Dempster, M.A.H. (ed.), Risk management: Value at risk and beyond. Cambridge University Press, Cambridge, pp. 176-223.         [ Links ]

[17] Unser, M. 2000. Lower partial moments as measures of perceived risk: An experimental study. Journal of Economic Psychology, 21, 253-280.         [ Links ]

[18] Roy, A. 1952. Safety-first and the holding of assets. Journal of Econometrica, 20, 431-449.         [ Links ]

[19] Markowitz, H.M. 1959. Portfolio selection: Efficient diversification of investments. Wiley, New York.         [ Links ]

[20] Mao, J. 1970. Survey of capital budgeting theory and practice. Journal of Finance, 25, 349-360.         [ Links ]

[21] Harlow, W.V. & Rao, R.K.S. 1999. Asset pricing in a generalized mean-lower partial moment framework: Theory and evidence. The Journal of Financial and Quantitative Analysis, 24, 285-311.         [ Links ]

[22] Bawa, V.S. 1975. Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2, 95-121.         [ Links ]

[23] Bawa, V.S. 1978. Safety-first, stochastic dominance, and optimal portfolio choice. Journal of Financial and Quantitative Analysis, 13, 255-271.         [ Links ]

[24] Fishburn, P.C. 1977. Mean-risk analysis with risk associated with below-target returns. Journal of The American Economic Review, 116-126.         [ Links ]

[25] Bawa, V.S. & Lindenberg, E.B. 1977. Capital market equilibrium in a mean-lower partial moment framework. Journal of Financial Economics, 5, 189-200.         [ Links ]

[26] Grootveld, H. & Hallerbach, W. 1999. Variance vs. downside risk: Is there really that much difference? European Journal of Operations Research, 114, 304-319.         [ Links ]

[27] Boyd, S. & Vandenberghe, L. 2004. Convex optimization. Cambridge University Press, New York.         [ Links ]