Capital requirements: Are they the best solution?
General risk functions are becoming very important in finance and insurance. Many risk functions are interpreted as initial capital requirements that a manager must add and invest in a risk-free security in order to protect his clients wealth. Nevertheless, until now it has not been proved that an alternative investment will be outperformed by the riskless asset. This paper deals with a complete arbitrage free market and a general expectation bounded risk measure and analyzes whether the investment in the riskless asset of the capital requirements is optimal. It is shown that it is not optimal in many important cases. For instance, if the risk measure is the CVaR and we consider the assumptions of the CAPM or the Black and Scholes model. Furthermore, the Black and Scholes model the explicit expression of the optimal strategy is provided, and it is composed of several put options. If the confidence level of the CVaR is close to 100% then the optimal strategy becomes a classical portfolio insurance strategy. This may be a surprising and important finding for both researchers and practitioners. In particular, managers can discover how to reduce the level of initial capital requirements by trading options.
|Date of creation:||Dec 2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +34 91 624-9630
Fax: +34 91 624-9608
Web page: http://portal.uc3m.es/portal/page/portal/dpto_economia_empresa
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, 01.
- René Garcia & Éric Renault & Georges Tsafack, 2007. "Proper Conditioning for Coherent VaR in Portfolio Management," Management Science, INFORMS, vol. 53(3), pages 483-494, March.
- Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
- Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2009. "Optimal reinsurance with general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 374-384, June.
- Jeremy Staum, 2004. "Fundamental Theorems of Asset Pricing for Good Deal Bounds," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 141-161.
- Annaert, Jan & Osselaer, Sofieke Van & Verstraete, Bert, 2009. "Performance evaluation of portfolio insurance strategies using stochastic dominance criteria," Journal of Banking & Finance, Elsevier, vol. 33(2), pages 272-280, February.
- Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, EconWPA, revised 08 Oct 2005.
- Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999.
"From stochastic dominance to mean-risk models: Semideviations as risk measures,"
European Journal of Operational Research,
Elsevier, vol. 116(1), pages 33-50, July.
- W. Ogryczak & A. Ruszczynski, 1997. "From Stochastic Dominance to Mean-Risk Models: Semideviations as Risk Measures," Working Papers ir97027, International Institute for Applied Systems Analysis.
- Barbarin, Jerome & Devolder, Pierre, 2005. "Risk measure and fair valuation of an investment guarantee in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 297-323, October.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.
- Goovaerts, Marc J. & Kaas, Rob & Dhaene, Jan & Tang, Qihe, 2004. "Some new classes of consistent risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 505-516, June.
- Alexander, S. & Coleman, T.F. & Li, Y., 2006. "Minimizing CVaR and VaR for a portfolio of derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 583-605, February.
- Balbas, Alejandro & Ibanez, Alfredo, 1998. "When can you immunize a bond portfolio?," Journal of Banking & Finance, Elsevier, vol. 22(12), pages 1571-1595, December.
When requesting a correction, please mention this item's handle: RePEc:cte:wbrepe:wb087114. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.