Conditional Value-at-risk Model Research Articles

On solving the dual for portfolio selection by optimizing Conditional Value at Risk

This note is focused on computational efficiency of the portfolio selection models based on the Conditional Value at Risk (CVaR) risk measure. The CVaR measure represents the mean shortfall at a specified confidence level and its optimization may be expressed with a Linear Programming (LP) model. The corresponding portfolio selection models can be solved with general purpose LP solvers. However, in the case of more advanced simulation models employed for scenario generation one may get several thousands of scenarios. This may lead to the LP model with huge number of variables and constraints thus decreasing the computational efficiency of the model. To overcome this difficulty some alternative solution approaches are explored employing cutting planes or nondifferential optimization techniques among others. Without questioning importance and quality of the introduced methods we demonstrate much better performances of the simplex method when applied to appropriately rebuilt CVaR models taking advantages of the LP duality.

A multiobjective conditional Value-at-Risk model in time interval for loan portfolios

Within the past several years, important advances have been made in conditional value-at-risk (CVaR) model in finance engineering. CVaR has superior properties in many respects. But, some practical risk problems, such as lending plan of bank, are multiobjective decision making. So, it is key question to study multiobjective CVaR model. This paper proposes a general multiobjective CVaR model in time interval for loan portfolios. First, we introduce the concept of α-VaR and α-CVaR for the case of multiple losses with random variable under the multiple confidence level vector α in time interval. Then, we propose a multiobjective CVaR model in time interval and prove two equality theorems. The solution of solving multiobjective CVaR model can be obtained by finding out solution to another nonlinear optimal problem. Next, we build multiobjective CVaR model to find out the best period and proportion for lending plan. Finally, the numerical results of the best period and proportion for lending plan are given in time interval.

CVaR Model for Optimizing Crop Insurance under Climate Variability

This paper studies the application of the Conditional Value-at-Risk (CVaR) in the crop insurance industry under climate variability. We designed a model to help farmers decide about buying crop insurance products to reduce climate and price risks. The objective is to minimize farmers’ return losses, while using CVaR to control the risk aversion level. We illustrate the application of the model by studying a farm with two crops (cotton and peanut) in Jackson Co., Fl. Crop insurance contracts with the greatest expected return were: for peanut, 75% actual production history (APH) during El Nino and Neutral years, and 65% APH during La Nina years; and for cotton, 75% APH in all El Nino Southern Oscillation phases. Risk averse farmers could select 75% APH for peanut during La Nina years.

Stability analysis of portfolio management with conditional value-at-risk

We examine the stability of a portfolio management model based on the conditional value-at-risk (CVaR) measure; the model controls risk exposure of international investment portfolios. We use a moment-matching method to generate discrete distributions (scenario sets) of asset returns and exchange rates so that their statistical properties match corresponding values estimated from historical data. First, we establish that the scenario generation procedure does not bias the results of the optimization program, and we determine the required number of scenarios to attain stable solutions. We then investigate the sensitivity of the CVaR model to mis-specifications in the statistics of stochastic parameters: mean, standard deviation, skewness, kurtosis, as well as correlations. The results are most sensitive to estimation errors in the means of the stochastic parameters (asset returns and currency exchange rates). Mis-specifications in the standard deviation, skewness and correlations of the random parameters also have considerable impact on the solutions. The effect of mis-specifications in the values of kurtosis, although less than that of the other statistics, is still not negligible.

CVaR models with selective hedging for international asset allocation

We develop an integrated simulation and optimization framework for multicurrency asset allocation problems. The simulation applies principal component analysis to generate scenarios depicting the discrete joint distributions of uncertain asset returns and exchange rates. We then develop and implement models that optimize the conditional-value-at-risk (CVaR) metric. The scenario-based optimization models encompass alternative hedging strategies, including selective hedging that incorporates currency hedging decisions within the portfolio selection problem. Thus, the selective hedging model determines jointly the portfolio composition and the level of currency hedging for each market via forward exchanges. We examine empirically the benefits of international diversification and the impact of hedging policies on risk–return profiles of portfolios. We assess the effectiveness of the scenario generation procedure and the stability of the model's results by means of out-of-sample simulations. We also compare the performance of the CVaR model against that of a model that employs the mean absolute deviation (MAD) risk measure. We investigate empirically the ex post performance of the models on international portfolios of stock and bond indices using historical market data. Selective hedging proves to be the superior hedging strategy that improves the risk–return profile of portfolios regardless of the risk measurement metric. Although in static tests the MAD and CVaR models often select portfolios that trace practically indistinguishable ex ante risk–return efficient frontiers, in successive applications over several consecutive time periods the CVaR model attains superior ex post results in terms of both higher returns and lower volatility.