Goal achieving probabilities of cone‐constrained mean‐variance portfolios

Chantal Labbé and François Watier

Applied Stochastic Models in Business and Industry, 2014, vol. 30, issue 5, 544-572

Abstract: In this paper, we establish closed‐form formulas for key probabilistic properties of the cone‐constrained optimal mean‐variance strategy, in a continuous market model driven by a multidimensional Brownian motion and deterministic coefficients. In particular, we compute the probability to obtain to a point, during the investment horizon, where the accumulated wealth is large enough to be fully reinvested in the money market, and safely grow there to meet the investor's financial goal at terminal time. We conclude that the result of Li and Zhou [Ann. Appl. Prob., v.16, pp.1751–1763, (2006)] in the unconstrained case carries over when conic constraints are present: the former probability is lower bounded by 80% no matter the market coefficients, trading constraints, and investment goal. We also compute the expected terminal wealth given that the investor's goal is underachieved, for both the mean‐variance strategy and the aforementioned hybrid strategy where transfer to the money market occurs if it allows to safely achieve the goal. The former probabilities and expectations are also provided in the case where all risky assets held are liquidated if financial distress is encountered. These results provide investors with novel practical tools to support portfolio decision‐making and analysis. Copyright © 2013 John Wiley & Sons, Ltd.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/asmb.2002

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmbi:v:30:y:2014:i:5:p:544-572

Access Statistics for this article

More articles in Applied Stochastic Models in Business and Industry from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().