A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model

In this paper we provide a survey of recent contributions to robust portfolio strategies from operations research and finance to the theory of portfolio selection. Our survey covers results derived not only in terms of the standard mean-variance objective, but also in terms of two of the most popular risk measures, mean-VaR and mean-CVaR developed recently. In addition, we review optimal estimation methods and Bayesian robust approaches.

show abstract

“…Finally, we are in a position to present an interesting conclusion found by Alexander and Baptista (2004) …”

Section: Mean-cvar Modelmentioning

confidence: 66%

Robust portfolios: contributions from operations research and finance

2009

View full text Add to dashboard Cite

show abstract

“…5 See Jorion, 2001. 6 See Basak andShapiro, 2001;Krokhmal et al, 2002;Rockafellar and Uryasev, 2002;Alexander and Baptista, 2004; and Gaivoronski and Pflug, 2005. 7 Gaivoronski and Pflug (2005 Cai and Tan (2007).…”

mentioning

confidence: 99%

Enhancing Insurer Value Using Reinsurance and Value-at-Risk Criterion

Tan

Weng

2011

Geneva Risk Insur Rev

View full text Add to dashboard Cite

The quest for optimal reinsurance design has remained an interesting problem among insurers, reinsurers, and academicians. An appropriate use of reinsurance could reduce the underwriting risk of an insurer and thereby enhance its value. This paper complements the existing research on optimal reinsurance by proposing another model for the determination of the optimal reinsurance design. The problem is formulated as a constrained optimization problem with the objective of minimizing the value-at-risk of the net risk of the insurer while subjecting to a profitability constraint. The proposed optimal reinsurance model, therefore, has the advantage of exploiting the classical tradeoff between risk and reward. Under the additional assumptions that the reinsurance premium is determined by the expectation premium principle and the ceded loss function is confined to a class of increasing and convex functions, explicit solutions are derived. Depending on the risk measure's level of confidence, the safety loading for the reinsurance premium, and the expected profit guaranteed for the insurer, we establish conditions for the existence of reinsurance. When it is optimal to cede the insurer's risk, the optimal reinsurance design could be in the form of pure stop-loss reinsurance, quota-share reinsurance, or a combination of stop-loss and quota-share reinsurance. The Geneva Risk and Insurance Review (2012) 37, 109-140. doi:10.1057/grir.2011; published online 23 August 2011Keywords: value-at-risk (VaR); optimal reinsurance; expectation premium principle; linear programming in infinite dimensional spaces IntroductionThe importance of sound risk management for financial institutions and insurance enterprises has been dramatically highlighted by the subprime crisis. Risk professionals are constantly seeking better risk measures to quantify risks associated with market, credit, operational, catastrophic, and many others. Risk measures such as value-at-risk (VaR) and conditional VaR or conditional tail expectation (CTE) have been proposed. Among these risk The Geneva Risk and Insurance Review, 2012, 37, (109-140) 9 and Zhou and Wu 10 demonstrated that employing VaR as a constraint could assist an insured in determining his or her optimal insurance policy. By minimizing VaR or CTE of the total risk exposure of an insurer, Cai and Tan 11 and Cai et al. 12 derived explicitly the optimal reinsurance treaties for the insurer. 13 While analytic solutions have been derived in the above reinsurance models, these results can be criticized on the ground that the optimality is based exclusively on minimizing an insurer's risk exposure. In practice, an insurer is concerned not only with its exposure to risk but also its profitability of insuring the underlying risks. To elaborate this point, let us first note that when an insurer uses reinsurance to cede (or transfer) part of its loss to a reinsurer, the insurer is liable to pay reinsurance 1 Artzner et al. (1999). 2 Basak and Shapiro (2001). 3 Yamai and Yoshiba (2005). 4 See Basle Commi...

show abstract

“…For this purpose, we considered a number of optimization models: a) the classical mean-variance approach (Markowitz, 1952(Markowitz, , 1959 and the minimum variance approach (Jagannathan and Ma, 2003); b) robust optimization techniques, as the most diversified portfolio, (see Choueifaty and Coignard, 2008;and Choueifaty et al, 2013) and the equally-weighted risk contributions portfolios (see Qian, 2005Qian, , 2006Qian, , 2011; c) portfolio optimization based on Conditional Value at Risk, "CVaR" Uryasev, 2000, 2002;Alexander and Baptista, 2004;Quaranta and Zaffaroni, 2008); d) functional approach based on risk measures such as the "Maximum draw-down" (MaxDD), the "Average draw-down" (AvDD), and the "Conditional draw-down at risk" (CDAR), all proposed by Chekhlov et al (2000Chekhlov et al ( , 2005. As well as the Conditional draw-down at risk "MinCDaR" (see Cheklov et al, 2005;and Kuutan, 2007); e) Young (1998)'s minimax optimization model, based on minimizing risk and optimizing the risk/return ratio; f) application of Copula theory to build the minimum tail-dependent portfolio, where the variance-covariance matrix is replaced by lower tail dependence coefficient (see Frahma et al, 2005;Fischer andDörflinger, 2006, andStadtmüller, 2006); g) a defensive approach to systemic risk by beta strategy ("Low Beta").…”

Section: Compared the Cvar And Conditionalmentioning

confidence: 99%

Portfolios in the Ibex 35 Index: Alternative Methods to the Traditional Framework, a Comparative with the Naive Diversification in a Pre- and Post- Crisis Context

2015

View full text Add to dashboard Cite

In this paper, we present an analysis of the effectiveness of various portfolio optimization strategies Simón Sosvilla-RiveroComplutense University of Madrid sosvilla@ccee.ucm.es Abstract:In this paper, we present an analysis of the effectiveness of various portfolio optimization strategies applied to the stocks included in the Spanish Ibex 35 index, for a period of 14 years, from 2001 until 2014. The period under study includes episodes of volatility and instability in financial markets, incorporating the Global Financial Crisis and the European Sovereign Debt Crisis. This implies a challenge in portfolio optimization strategies since the methodologies are restricted to the assignment of positive weights. We have taken for asset allocation the daily returns with an estimation window equal to 1 year and we hold portfolio assets for another year. This paper attempts to influence the discussion over whether the naive diversification proves to be an effective strategy as opposed to portfolio optimization models. For that, we evaluate the out-of-sample performance of 15 strategies for asset allocation in the Ibex 35 index, before and after of the Global Financial Crisis. Our results suggest that a large number of strategies outperform to the 1/N rule and to the Ibex 35 index in terms of return, Sharpe ratio and lower VaR and CVaR. The mean-variance portfolio of Markowitz with shortsale constraints, it is the only strategy that renders a Sharpe ratio statistically different to Ibex 35 index in the

show abstract

A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model

Cited by 292 publications

References 13 publications

Robust portfolios: contributions from operations research and finance

Robust portfolios: contributions from operations research and finance

Enhancing Insurer Value Using Reinsurance and Value-at-Risk Criterion

Portfolios in the Ibex 35 Index: Alternative Methods to the Traditional Framework, a Comparative with the Naive Diversification in a Pre- and Post- Crisis Context

Contact Info

Product

Resources

About