Asymptotic behaviour of mean-quantile efficient portfolios
Article
First Online:
Received:
Accepted:
- 100 Downloads
- 5 Citations
Abstract
In this paper we investigate portfolio optimization in the Black–Scholes continuous-time setting under quantile based risk measures: value at risk, capital at risk and relative value at risk. We show that the optimization results are consistent with Merton’s two-fund separation theorem, i.e., that every optimal strategy is a weighted average of the bond and Merton’s portfolio. We present optimization results for constrained portfolios with respect to these risk measures, showing for instance that under value at risk, in better markets and during longer time horizons, it is optimal to invest less into the risky assets.
Keywords
Portfolio optimization Merton’s portfolio Quantile Value at risk Capital at riskMathematics Subject Classification
91B28 93E20JEL Classification
G11 C61Preview
Unable to display preview. Download preview PDF.
References
- 1.Dmitrašinović-Vidović, G.: Portfolio selection under downside risk measures. Ph.D. Thesis. University of Calgary (2004)Google Scholar
- 2.Dmitrašinović-Vidović, G., Lari-Lavassani, A., Li, X., Ware, A.: Dynamic portfolio selection under Capital at Risk. University of Calgary Yellow Series, Report 833 (2003)Google Scholar
- 3.Dmitrašinović-Vidović, G., Lari-Lavassani, A., Li, X.: Continuous time portfolio selection under conditional Capital at Risk. University of Calgary Yellow Series, Report 837 (2004)Google Scholar
- 4.Emmer S., Klüppelberg C., Korn R. (2001) Optimal portfolios with bounded Capital at Risk. Math. Financ. 11, 365–384MATHCrossRefGoogle Scholar
- 5.Jorion P. (1997) All about Value at Risk. McGraw-Hill, New YorkGoogle Scholar
- 6.Lari-Lavassani, A., Sadeghi, A., Ware, A.: Modeling and implementing mean reverting price processes in energy markets. In: Electronic Publications of the International Energy Credit Association, pp. 30., (www.ieca.net) (2001)Google Scholar
Copyright information
© Springer-Verlag 2006