Finance and Stochastics

, Volume 10, Issue 4, pp 529–551 | Cite as

Asymptotic behaviour of mean-quantile efficient portfolios

Article

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 risk 

Mathematics Subject Classification

91B28 93E20 

JEL Classification

G11 C61 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.The Mathematical and Computational Finance Laboratory, Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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