CVaR Models Research Articles

How do precious and industrial metals hedge oil in a multi-frequency semiparametric CVaR portfolio?

This paper tries to reduce extreme risk of Brent oil by constructing multivariate portfolios with precious and industrial metals in a multi-frequency framework. Extreme risk is measured by the parametric CVaR and more elaborate semiparametric CVaR measure, while the wavelet technique is used to build portfolios in different time-horizons. The results indicate that gold dominates in the precious metal portfolios, creating the lowest downside risk in most cases. The back-testing results reveal that the raw data CVaR portfolio with precious metals is the best, while the midterm mCVaR portfolio with industrial metals has upper hand. In terms of forecasting, CVaR portfolios with precious and industrial metals are the best in the short- and midterm horizons, respectively. In the long-term horizon, none of the portfolios is good in back-testing and forecasting, which means that CVaR and mCVaR models are not adequate risk functions for identifying realized risk in the long term. In the oil-dominated portfolios, the CVaR portfolios with gold are the best in terms of the lowest risk as well as back-testing and forecasting performances. When Brent is replaced by WTI oil, the share of WTI is somewhat smaller in the portfolios because WTI has higher risk. When the US 10Y bond is added to the portfolios, the portfolio risk is reduced because the bonds are very weakly correlated with the commodities.

Forecasting Startup Return using Artificial Intelligence Methods and Econometric Models and Portfolio Optimization Using VaR and C-VaR

In this paper, we have tried to study the main role of startups in economy, their characteristics, main goals and etc. The main goal of article is prediction of startup's return using artificial intelligence methods such as genetic algorithm (GA) and artificial neural network (ANN). Some global indices such as S&P500, DJAI, and economic indicators such as 10 years Treasury yield, Wilshire 5000 Total Market Full Cap Index along with some other special indicators in startups like team, idea, timing and etc. are used as input variables. GA is used as feature selection and finding the most important variables. ANN is used as an optimization model and prediction of startup's returns. We used econometric models such as regression analysis. We have estimated Value at risk (VaR) and Conditional Value at risk (C-VAR) for considered portfolios including three startups (public company) such as Dropbox, Inc. (DBX), Scout24 SE (G24.DE) and TIE.AS and optimal portfolio formation. The results show that AI based methods are more powerful in prediction of startup's return. On the other hand, VaR and C-VaR models are very beneficial approach in minimizing risk and maximizing return.

Cointegration and Adjustment in the CVAR(∞) Representation of Some Partially Observed CVAR(1) Models

A multivariate CVAR(1) model for some observed variables and some unobserved variables is analysed using its infinite order CVAR representation of the observations. Cointegration and adjustment coefficients in the infinite order CVAR are found as functions of the parameters in the CVAR(1) model. Conditions for weak exogeneity for the cointegrating vectors in the approximating finite order CVAR are derived. The results are illustrated by two simple examples of relevance for modelling causal graphs.

Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk

Mean–variance, mean–VaR, and mean–CVaR models for portfolio selection with background risk

Backtesting para o Expected Shortfall do Trading Book: Uma Avaliação das Metodologias

Devido à Crise de 2008 o Comitê de Basileia acelerou o processo para atualização do Acordo e identificou algumas falhas como, por exemplo, a incapacidade do VaR em captar o risco de cauda. Posteriormente, recomendou-se substituir o VaR, uma medida não coerente de risco devido à ausência de subaditividade, pelo CVaR. Esta medida, apesar de não ser elicitável nem testável, é pelo menos condicionalmente elicitável e, portanto, também condicionalmente testável. Para validar os modelos do CVaR, foram feitas simulações com os três métodos de Acerbi e outro sugerido neste trabalho que adaptou a Aproximação dos Níveis de VaR. Destes quatro, nenhum foi perfeito. Os três de Acerbi tiveram falhas em alguns testes e o sugerido neste trabalho apresentou resultados melhores que o Backtesting do VaR.

Cointegration and Adjustment in the Infinite Order CVAR Representation of Some Partially Observed CVAR(1) Models

A multivariate CVAR(1) model for some observed variables and some unobserved variables is analysed using its infinite order CVAR representation of the observations. Cointegration and adjustment coefficients in the infinite order CVAR are found as functions of the parameters in the CVAR(1) model. Conditions for weak exogeneity of the cointegrating vectors in the approximating finite order CVAR are derived. The results are illustrated by a few simple examples of relevance for modelling causal graphs.

Risk Averse Decision Models for Resilient Supplier Selection

Decision models provided by this study aim to help managers to find remedies to devastating supply chain disruptions that could be caused by a mismatch between volatile customer demand and unreliable supply. We considered the newsvendor problem where the firm has more than one suppliers who are not necessarily reliable. We have provided a range of decision models with risk neutral and risk averse objective functions. The model uses scenarios to represent uncertain events (specifying customer demand and supplier reliability). Linear Programming formulations are provided which can be easily solved using commercially available software. A sample numerical study is also carried out to provide valuable managerial insights for optimal sourcing behaviors of risk averse and risk neutral firms. In the numerical study, expected profit, CVaR and Mean Excess Regret models are selected for evaluation.

Properties, formulations, and algorithms for portfolio optimization using Mean-Gini criteria

We study an extended set of Mean-Gini portfolio optimization models that encompasses a general version of the mean-risk formulation, the Minimal Gini model (MinG) that minimizes Gini’s Mean Differences, and the new risk-adjusted Mean-Gini Ratio (MGR) model. We analyze the properties of the various models, prove that a performance measure based on a Risk Adjusted version of the Mean Gini Ratio (RAMGR) is coherent, and establish the equivalence between maximizing this performance measure and solving for the maximal Mean-Gini ratio. We propose a linearization approach for the fractional programming formulation of the MGR model. We also conduct a thorough evaluation of the various Mean-Gini models based on four data sets that represent combinations of bullish and bearish scenarios in the in-sample and out-of-sample phases. The performance is (i) analyzed with respect to eight return, risk, and risk-adjusted criteria, (ii) benchmarked with the S&P500 index, and (iii) compared with their Mean-Variance counterparts for varying risk aversion levels and with the Minimal CVaR and Minimal Semi-Deviation models. For the data sets used in our study, our results suggest that the various Mean-Gini models almost always result in solutions that outperform the S&P500 benchmark index with respect to the out-of-sample cumulative return. Further, particular instances of Mean-Gini models result in solutions that are as good or better (for example, MinG in bullish in-sample scenarios, and MGR in bearish out-of-sample scenarios) than the solutions obtained with their counterparts in Mean-Variance, Minimal CVaR and Minimal Semi-Deviation models.

Calculating the Funding Valuation Adjustment (FVA) of Value-at-Risk (VAR) Based Initial Margin

Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg, 2010, 2012a), under counterparty risk with unsecured funding costs (FVA) (Burgard and Kjaer, 2011a, 2011b, 2013) and in the presence of regulatory capital (KVA) (Green, Kenyon and Dennis, 2014) are established through valuation adjustments, hitherto initial margin has not been considered. This paper further extends the semi-replication framework of Burgard and Kjaer (2013), itself later extended by Green, Kenyon and Dennis (2014), to cover the cost of initial margin, leading to Margin Valuation Adjustment (MVA). Initial margin requirements are typically generated through the use of VAR or CVAR models. Given the form of MVA as an integral over the expected initial margin profile this would lead to excessive computational costs if a brute force calculation were to be used. Hence we also propose a computationally efficient approach to the calculation of MVA through the use of regression techniques, Longstaff-Schwartz Augmented Compression (LSAC).

Dynamic hedge fund portfolio construction: A semi-parametric approach

In this article, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. We compare the standard mean–variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semi-parametric methodology, which is based on extreme value theory, copula and Monte Carlo simulation. We compare the semi-parametric approach with the standard, non-parametric approach, used to compute CVaR, CDaR and Omega, and the benchmark parametric approach, based on both static and dynamic mean–variance optimization. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the parametric mean–variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.

Dynamic Hedge Fund Portfolio Construction: A Semi-Parametric Approach

In this paper, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. Using monthly hedge fund index returns for the period 1990 to 2011, we compare the standard mean-variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semi-parametric methodology, in which we first model the marginal density of each hedge fund index using extreme value theory and construct the joint density of hedge fund index returns using a copula-based approach. We then simulate hedge fund returns from this joint density in order to compute CVaR, CDaR and Omega, which are used in the optimization process. We compare the semi-parametric approach with the standard, non-parametric approach, in which the quantiles of the marginal density of portfolio returns are estimated empirically and used to compute CVaR, CDaR and Omega. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the mean-variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.

A comparison of MAD and CVaR models with real features

In this paper we consider two different mixed integer linear programming models for solving the single period portfolio selection problem when integer stock units, transaction costs and a cardinality constraint are taken into account. The first model has been formulated by using the maximization of the worst conditional expectation as objective function. The second model is based on the maximization of the safety measure corresponding to the mean absolute deviation. Extensive computational results are provided to compare the financial characteristics of the optimal portfolios selected by the two models on real data from European stock exchange markets. Some simple heuristics are also introduced that provide efficient and effective solutions when an optimal integer solution cannot be found in a reasonable amount of time.

Traditional beta, downside risk beta and market risk premiums

The article develops a downside risk asset-pricing model, which is based on Conditional-VaR (Mean-shortfall) risk measure. As in the traditional model the model leads to a monetary separation and yields a CVaR beta analogous to the traditional beta. An empirical study indicates that CVaR beta, which considers also downside risk, has greater explanatory power than the traditional beta. This is especially true in the case of a bearish market. Moreover, a combined model, which uses both betas, outperforms both the traditional and the CVaR models. The results indicate that in a bullish economy, risk premiums may be partially explained by the traditional beta. However, in a depressed economy investors are most likely more concerned about downside risk, which is poorly captured by the traditional beta. This downside risk can best be captured by CVaR beta, which is based on historical data and avoids assuming any prior distribution.