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Author(s): K. Boudt, B. G. Peterson & P. Carl
Abstract:
Modified Value-at-Risk (VaR) and Expected Shortfall (ES) are recently introduced
downside risk estimators based on the Cornish-Fisher expansion for assets such as
hedge funds whose returns are non-normally distributed.
Modified VaR has been
widely implemented as a portfolio selection criterion.We are the first to investigate
hedge fund portfolio selection using modified ES as optimality criterion.We show
that for the EDHEC hedge fund style indices, the optimal portfolios based on
modified ES outperform out-of-sample the EDHEC Fund of Funds index and have
better risk characteristics than the equal-weighted and Fund of Funds portfolios.
Keywords:
portfolio optimization, modified expected shortfall, non-normal
returns.
1 Introduction:
It is generally accepted that rational investors should allocate their portfolio
optimally according to a return/risk criterion.
The most widely studied criteria
(minimumvariance and maximumSharpe ratio) are based on the first two portfolio
moments.
A more general set of positive preferences for odd moments (mean,
skewness) and aversion to even moments (variance, kurtosis) is discussed by
Scott and Horvath [1].
For largely intuitive reasons, the relationships between the
moments themselves are often summarized into risk measures.
In the presence
of non-normal returns and when investors have a non-quadratic utility function,
two issues arise: (i) the choice of risk measure and (ii) the estimator for this risk
measure.
...
Pages: 9
Size: 247 kb
Paper DOI: 10.2495/CF080101
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