Translation-invariant and positive-homogeneous risk measures and optimal portfolio management

Z. Landsman and U. Makov

The European Journal of Finance, 2011, vol. 17, issue 4, 307-320

Abstract: The problem of risk portfolio optimization with translation-invariant and positive-homogeneous risk measures, which includes value-at-risk (VaR) and tail conditional expectation (TCE), leads to the problem of minimizing a combination of a linear functional and a square root of a quadratic functional for the case of elliptical multivariate underlying distributions. In this paper, we provide an explicit closed-form solution of this minimization problem, and the condition under which this solution exists. The results are illustrated using the data of 10 stocks from NASDAQ/Computers. The distance between the VaR and TCE optimal portfolios has been investigated.

Keywords: translation-invariant and positive-homogeneous risk measure; value-at-risk; tail condition expectation; minimization of root of quadratic functional; elliptical family (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1080/1351847X.2010.481467

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