Abstract
In this paper the concept of quantile-based optimal portfolio selection is introduced and a specific portfolio connected to it, the conditional value-of-return (CVoR) portfolio, is proposed. The CVoR is defined as the mean excess return or the conditional value-at-risk (CVaR) of the return distribution. The portfolio selection consists solely of quantile-based risk and return measures. Financial institutions that work in the context of Basel 4 use CVaR as a risk measure. In this regulatory framework sufficient and necessary conditions for optimality of the CVoR portfolio are provided under a general distributional assumption. Moreover, it is shown that the CVoR portfolio is mean-variance efficient when the returns are assumed to follow an elliptically contoured distribution. Under this assumption the closed-form expression for the weights and characteristics of the CVoR portfolio are obtained. Finally, the introduced methods are illustrated in an empirical study based on monthly data of returns on stocks included in the S&P index. It is shown that the new portfolio selection strategy outperforms several alternatives in terms of the final investor wealth.
Highlights
Since Markowitz (1952) posed the allocation problem of portfolio theory a large number of extensions have been introduced
The two most commonly used are value-at-risk (VaR) and conditional value-at-risk (CVaR) which is a consequence of the solvency 2 and basel 3 requirements
We introduce the conditional value of return (CVoR) portfolio which is solely constructed from quantile-based measures
Summary
Since Markowitz (1952) posed the allocation problem of portfolio theory a large number of extensions have been introduced (see, e.g., Fastrich et al 2015; Kawas and Thiele 2017; Bauder et al 2021). For the motivation of the applications of other measures of portfolio profit, an investor is considered who delivers a certain capital or portfolio benchmark, such as a monthly percentage return In this case, a large loss (though rare) will heavily distort the result. From this perspective it is more natural to communicate aims and targets in terms of probabilities to achieve a certain profit over some specified time horizon With this argument the portfolio mean is essentially replaced by a return measure that is based on quantiles, which is the primary motivation for the problem at hand. 3 a special case of the CVoR portfolio is presented when assuming that the asset returns follow an elliptically contoured distribution Under this assumption one can connect the CVoR portfolio to the efficient frontier in the mean-variance space and give a closed-form solution to the portfolio weights and its characteristics.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
