Spectral risk measures and portfolio selection

Abstract

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their nonGaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.JEL Classification: C61 ; D81 ; D84 ; G11

On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles

“…This finding extends a known trait of VaR (El Ghaoui et al 2003;Ye et al 2012) and expected shortfall (Chen et al 2011;Natarajan et al 2010). Adjusting portfolio weights enables spectral risk measures to accommodate subjective risk aversion (Acerbi 2002;Adam et al 2008;Cotter and Dowd 2006).…”

Comparing Return-Risk and Direct Utility Maximization Portfolio Optimization Methods by ‘Certainty Equivalence Curves’

“…There are many risk measures suggested as criteria for the optimization problem in this approach. Numerous papers such as Angelelli et al (2008) and Adam et al (2008) focus on comparing these risk measures…”

“…Plot Certainty Equivalance Graphs % Figure subplot (2,1,1) plot(beta,zeros(length(beta)),'k-') hold on plot(beta,CEeqwt,'k-') % plot CE with different level of risk averse xlabel('Beta (Risk aversion)') ylabel('Certainty Equivalence (CE)') title('CE Graphs') subplot(2,1,1) plot(beta,CEMV,'k.-') subplot(2,1,1) plot(beta,CECVaR,'k-x') subplot(2,1,1) plot(beta,CEUtil,'k-','linewidth',1.5) % plot CE with different subplot (2,1,2) plot(beta,zeros(length(beta)),'k-') hold on plot(beta,CEeqwtRf,'k-') % plot CE with different level of risk averse xlabel('Beta (Risk aversion)') ylabel('Certainty Equivalence (CE)') title('CE Graphs with Rf') subplot(2,1,2) plot(beta,CEMVRf,'k.-') subplot(2,1,2) plot(beta,CECVaRRf,'k-x') subplot(2,1,2) plot(beta,CEUtilRf,'k-','linewidth',1.5)% plot CE with different % %III.3. Plot Comparing Returns of Optimal portfolio obtained from three methods Figure …”

Portfolio Allocation of Hedge Funds

“…It is clear that the solution of this problem will maximize expected returns while minimizing portfolio variance. Each parameter λ > 0 involves an optimal portfolio corresponding to a given value of µ min in problem (2). Unfortunately, the correspondence between the risk aversion parameter λ and the resulting average return µ min can only be found by solving problem (3).…”

“…Bares et al (2002) and Cvitanic et al (2003) compute optimal portfolios in an expected utility framework. Amin and Kat (2003) Adam et al (2008) construct optimal portfolios using alternative risk measures. Given the increasing interest for risk management, there is indeed a multiplication of measures capturing different types of risks and several tentatives to unify these approaches.…”