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Mean-Variance Optimal Portfolios in the Presence of a Benchmark with Applications to Fraud Detection

Forthcoming in European Journal of Operational Research

27 Pages Posted: 30 Sep 2012 Last revised: 23 Jun 2013

Carole Bernard

Grenoble Ecole de Management

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: June 23, 2013

Abstract

We first study mean-variance efficient portfolios when there are no trading constraints and show that optimal strategies perform poorly in bear markets. We then assume investors use a stochastic benchmark (linked to the market) as a reference portfolio. We derive mean-variance efficient portfolios when investors aim to achieve a given correlation (or a given dependence structure) with a stochastic benchmark. We also provide upper bounds on Sharpe ratios and show how these can be useful for fraud detection. For example it is shown that under some conditions it is not possible for investment funds to display negative correlation with the financial market and to have a positive Sharpe ratio. All results are illustrated in a Black-Scholes market.

Keywords: Mean-variance, Fraud detection, Optimal portfolio, Correlation constraints

JEL Classification: G11, D81

Suggested Citation

Bernard, Carole and Vanduffel, Steven, Mean-Variance Optimal Portfolios in the Presence of a Benchmark with Applications to Fraud Detection (June 23, 2013). Forthcoming in European Journal of Operational Research. Available at SSRN: https://ssrn.com/abstract=2154531 or http://dx.doi.org/10.2139/ssrn.2154531

Carole Bernard (Contact Author)

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

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