A VaR Black–Litterman model for the construction of absolute return fund-of-funds

Miguel Lejeune

Quantitative Finance, 2011, vol. 11, issue 10, 1489-1501

Abstract: The objective is to construct fund-of-funds (FoFs) that follow an absolute return strategy and meet the requirements imposed by the value-at-risk (VaR) market risk measure. We propose the VaR Black–Litterman model which accounts for the VaR and trading (diversification, buy-in threshold, liquidity, currency) requirements. The model takes the form of a probabilistic integer, non-convex optimization problem. We first derive a deterministic reformulation of the probabilistic problem, which, depending on the information on the probability distribution of the FoF return, is the equivalent, or a close approximation, of the original problem. We then show that the continuous relaxation of the reformulated problem is a second-order cone optimization problem for a wide range of probability distributions. Finally, we use a specialized nonlinear branch-and-bound algorithm which implements the portfolio risk branching rule to construct the optimal FoF. The practical relevance of the model and solution method is shown by their use by a financial institution for the construction of several FoFs that are now traded worldwide. The computational study attests that the proposed algorithmic technique is very efficient, outperforming, in terms of both speed and robustness, three state-of-the-art alternative solution methods and solvers.

Date: 2011
References: Add references at CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://hdl.handle.net/10.1080/14697680903121018 (text/html)
Access to full text is restricted to subscribers.

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:taf:quantf:v:11:y:2011:i:10:p:1489-1501

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RQUF20

DOI: 10.1080/14697680903121018

Access Statistics for this article

Quantitative Finance is currently edited by Michael Dempster and Jim Gatheral

More articles in Quantitative Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().