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Portfolio risk management with CVaR-like constraints. (English) Zbl 1219.91132

Summary: A current research stream in the portfolio allocation literature develops models that take into account the asymmetric nature of asset return distributions. Our paper contributes to this research stream by extending the Krokhmal, Palmquist, and Uryasev approach. We add CVaR-like constraints in the traditional portfolio optimization problem to reshape the tails of the portfolio return distribution while not significantly affecting its mean and variance. We illustrate how to apply this approach, called the “MV + CVaR approach,” to manage tail risk of an insurer’s asset-liability portfolio. Finally, we compare the MV + CVaR approach with the traditional Markowitz method and a method recently introduced by Boyle and Ding. Our numerical analysis provides empirical support for the effectiveness of the MV + CVaR approach in controlling downside risk. Moreover, we find that the MV + CVaR approach may improve skewness of mean-variance portfolios, especially for high-variance portfolios.

MSC:

91G10 Portfolio theory
91B30 Risk theory, insurance (MSC2010)
90C90 Applications of mathematical programming
91G50 Corporate finance (dividends, real options, etc.)
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References:

[1] Alexander G. J., Journal of Portfolio Management 29 (4) pp 93– (2003)
[2] Arditti F. D., Journal of Finance 30 pp 797– (1975)
[3] Artzner P., Mathematical Finance 9 pp 203– (1999) · Zbl 0980.91042
[4] Bertsimas D., Journal of Economic Dynamics and Control 28 pp 1353– (2004) · Zbl 1200.91133
[5] BorCh K., Review of Economics and Statistics 36 pp 1– (1969)
[6] Boyle P., Numerical Methods in Finance pp 227– (2006)
[7] Boyle P. P., Journal of Financial Economics 8 (3) pp 259– (1980)
[8] Chow G., Journal of Portfolio Management 28 (3) pp 73– (2002)
[9] Conine T. E., Journal of Finance 36 pp 1143– (1981)
[10] David A., Journal of Financial Quantitative Analysis 32 (4) pp 427– (1997)
[11] Dowd K., Beyond Value at Risk: The New Science of Risk Management (1998) · Zbl 0924.90013
[12] Feldstein M., Review of Economic Studies 36 pp 5– (1969)
[13] Hardy M. R., An Introduction to Risk Measures for Actuarial Applications. Study note C-25–07 (2006)
[14] Ingersoll J., Journal of Financial and Quantitative Analysis 10 pp 785– (1975)
[15] Jean W. H., Journal of Financial and Quantitative Analysis 6 pp 505– (1971)
[16] Jorion P., Value at Risk: The New Benchmark for Controlling Market Risk (2006)
[17] Jorion P., Journal of Portfolio Management 34 (1) pp 127– (2007)
[18] Kraus A., Journal of Finance 31 pp 1085– (1976)
[19] Krokhmal P., Journal of Risk 4 (2) pp 43– (2002)
[20] Markowitz H., Journal of Finance 7 (1) pp 77– (1952)
[21] Markowitz H., Journal of Finance 46 pp 469– (1991)
[22] Mitton T., Review of Financial Studies 20 (4) pp 1255– (2007)
[23] Rockafellar R. T., Journal of Risk 2 (3) pp 21– (2000)
[24] Saunders A., Financial Institutions Management: A Modern Perspective., 3. ed. (1999)
[25] Simkowitz M. A., Journal of Financial and Quantitative Analysis 13 pp 927– (1978)
[26] Uryasev S., Financial Engineering News 14 pp 1– (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.