Exposure-Based Cash-Flow-at-Risk: An Alternative to VaR for Industrial Companies

Cash-Flow-at-Risk (CFaR) is the cash flow equivalent of Value-at-Risk (VaR), a measure widely used as the basis for risk management in financial institutions. Whereas VaR-based systems specify the maximum amount of total value a firm is expected to lose under most foreseeable conditions (for example, with a 99% confidence level), CFaR-based systems determine the maximum shortfall of cash the firm is willing to tolerate. CFaR is gaining in popularity among industrial companies for much the same reasons VaR has succeeded with financial firms: it sums up all the company's risk exposures in a single number that can be used to guide corporate risk management decisions.
The authors describe a six-step process for calculating a measure they call "exposure-based CFaR" and then demonstrate its application to Norsk Hydro, the Norwegian industrial conglomerate. Exposure-based CFaR involves the estimation of a set of exposure coefficients that provide information about how various macroeconomic and market variables are expected to affect the company's cash flow, while also accounting for interdependencies among such effects. The resulting model enables management to estimate the variability in corporate cash flow as a function of various risks, and to predict how a hedging contract or a change in financial structure will alter the company's risk profile.     

A Bayesian encompassing test using combined value-at-risk estimates

The Value at Risk (VaR) is a risk measure that is widely used by financial institutions in allocating risk. VaR forecast estimation involves the conditional evaluation of quantiles based on the currently available information. Recent advances in VaR evaluation incorporate conditional variance into the quantile estimation, yielding the Conditional Autoregressive VaR (CAViaR) models. However, the large number of alternative CAViaR models raises the issue of identifying the optimal quantile predictor. To resolve this uncertainty, we propose a Bayesian encompassing test that evaluates various CAViaR models predictions against a combined CAViaR model based on the encompassing principle. This test provides a basis for forecasting combined conditional VaR estimates when there are evidences against the encompassing principle. We illustrate this test using simulated and financial daily return data series. The results demonstrate that there are evidences for using combined conditional VaR estimates when forecasting quantile risk.     

Optimal Insurance Under the Insurer's VaR Constraint

In this paper, we impose the insurer's Value at Risk (VaR) constraint on Arrow's optimal insurance model. The insured aims to maximize his expected utility of terminal wealth, under the constraint that the insurer wishes to control the VaR of his terminal wealth to be maintained below a prespecified level. It is shown that when the insurer's VaR constraint is binding, the solution to the problem is not linear, but piecewise linear deductible, and the insured's optimal expected utility will increase as the insurer becomes more risk-tolerant. Basak and Shapiro (2001) showed that VaR risk managers often choose larger risk exposures to risky assets. We draw a similar conclusion in this paper. It is shown that when the insured has an exponential utility function, optimal insurance based on VaR constraint causes the insurer to suffer larger losses than optimal insurance without insurer's risk constraint.     

基于VaR模型的最优套期保值比例探析——以美元远期套保为例

VaR模型被认为是兼顾投机套利与套期保值两大动机的衍生工具决策模型。国内文献对此讨论较少。基于其理论推导,可以归纳地认为VaR模型具有兼容性、一般性、"期权"特征和可操作性。以美元远期套保为例,研究发现,基于VaR模型的最优套保比较之传统最优套保比、最小方差最优套保比更有优势,能够解释中国企业运用衍生工具失败的原因。但据此推论,基于VaR模型确定最优套保比在实践中仍然存在一些问题,如非正态分布、现货头寸不确定、损益报告困难等。     

基于VaR的开放式股票型基金市场风险的测量与评价

通过采用半参数法计算投资组合VaR,得到相应VaR的近似置信区间,并结合成分VaR、边际VaR对投资组合vaR进行分解,结果发现,VaR作为风险管理工具同样可以有效应用于开放式股票型基金市场风险的测量与评价.     

Value-at-risk-based risk management: optimal policies and asset prices

This article analyzes optimal, dynamic portfolio and wealth/consumptionpolicies of utility maximizing investors who must also managemarket-risk exposure using Value-at-Risk (VaR). We find thatVaR risk managers often optimally choose a larger exposure torisky assets than non-risk managers and consequently incur largerlosses when losses occur. We suggest an alternative risk-managementmodel, based on the expectation of a loss, to remedy the shortcomingsof VaR. A general-equilibrium analysis reveals that the presenceof VaR risk managers amplifies the stock-market volatility attimes of down markets and attenuates the volatility at timesof up markets.     

Risk measure pricing and hedging in incomplete markets

This article attempts to extend the complete market option pricing theory to incomplete markets. Instead of eliminating the risk by a perfect hedging portfolio, partial hedging will be adopted and some residual risk at expiration will be tolerated. The risk measure (or risk indifference) prices charged for buying or selling an option are associated to the capital required for dynamic hedging so that the risk exposure will not increase. The associated optimal hedging portfolio is decided by minimizing a convex measure of risk. I will give the definition of risk-efficient options and confirm that options evaluated by risk measure pricing rules are indeed risk-efficient. Relationships to utility indifference pricing and pricing by valuation and stress measures will be discussed. Examples using the shortfall risk measure and average VaR will be shown. The work of Mingxin Xu is supported by the National Science Foundation under grant SES-0518869. I would like to thank Steven Shreve for insightful comments, especially his suggestions to extend the pricing idea from using shortfall risk measure to coherent ones, and to study its relationship to utility based derivative pricing. The comments from the associate editor and the anonymous referee have reshaped the paper into its current version. The paper has benefited from discussions with Freddy Delbaen, Jan Večeř, David Heath, Dmitry Kramkov, Peter Carr, and Joel Avrin.     

Pricing and hedging guaranteed minimum withdrawal benefits under a general Lévy framework using the COS method

This paper extends the Fourier-cosine (COS) method to the pricing and hedging of variable annuities embedded with guaranteed minimum withdrawal benefit (GMWB) riders. The COS method facilitates efficient computation of prices and hedge ratios of the GMWB riders when the underlying fund dynamics evolve under the influence of the general class of Lévy processes. Formulae are derived to value the contract at each withdrawal date using a backward recursive dynamic programming algorithm. Numerical comparisons are performed with results presented in Bacinello et al. [Scand. Actuar. J., 2014, 1–20], and Luo and Shevchenko [Int. J. Financ. Eng., 2014, 2, 1–24], to confirm the accuracy of the method. The efficiency of the proposed method is assessed by making comparisons with the approach presented in Bacinello et al. [op. cit.]. We find that the COS method presents highly accurate results with notably fast computational times. The valuation framework forms the basis for GMWB hedging. A local risk minimisation approach to hedging intra-withdrawal date risks is developed. A variety of risk measures are considered for minimisation in the general Lévy framework. While the second moment and variance have been considered in existing literature, we show that the Value-at-Risk (VaR) may also be of interest as a risk measure to minimise risk in variable annuities portfolios.     

Tail risk of coal futures in China's market

This study evaluates the downside tail risk of coal futures contracts (coke, coking coal and thermal coal) traded in the Chinese market between 2011 and 2021, measured by value at risk (VaR). We examine the one-day-ahead VaR forecasting performance with a hybrid econometric and deep learning model (GARCH-LSTM), GARCH family models, extreme value theory models, quantile regression models and two naïve models (historical simulation and exponentially weighted moving average). We use four backtesting techniques and the model confidence set to identify the optimal models. The results suggest that the models focusing on tail risk or utilising long short-term memory generate more effective risk management.     

Retracted: Risk Management in Financial Institutions

We study risk management in financial institutions using data on hedging of interest rate and foreign exchange risk. We find strong evidence that institutions with higher net worth hedge more, controlling for risk exposures, across institutions and within institutions over time. For identification, we exploit net worth shocks resulting from loan losses due to declines in house prices. Institutions that sustain such shocks reduce hedging significantly relative to otherwise-similar institutions. The reduction in hedging is differentially larger among institutions with high real estate exposure. The evidence is consistent with the theory that financial constraints impede both financing and hedging.     

Dynamic mean–VaR portfolio selection in continuous time

The value-at-risk (VaR) is one of the most well-known downside risk measures due to its intuitive meaning and wide spectra of applications in practice. In this paper, we investigate the dynamic mean–VaR portfolio selection formulation in continuous time, while the majority of the current literature on mean–VaR portfolio selection mainly focuses on its static versions. Our contributions are twofold, in both building up a tractable formulation and deriving the corresponding optimal portfolio policy. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the original dynamic mean–VaR portfolio formulation. To overcome the difficulties arising from the VaR constraint and no bankruptcy constraint, we have combined the martingale approach with the quantile optimization technique in our solution framework to derive the optimal portfolio policy. In particular, we have characterized the condition for the existence of the Lagrange multiplier. When the opportunity set of the market setting is deterministic, the portfolio policy becomes analytical. Furthermore, the limit funding level not only enables us to solve the dynamic mean–VaR portfolio selection problem, but also offers a flexibility to tame the aggressiveness of the portfolio policy.     

Minimizing CVaR and VaR for a portfolio of derivatives

Value at risk (VaR) and conditional value at risk (CVaR) are frequently used as risk measures in risk management. Compared to VaR, CVaR is attractive since it is a coherent risk measure. We analyze the problem of computing the optimal VaR and CVaR portfolios. We illustrate that VaR and CVaR minimization problems for derivatives portfolios are typically ill-posed. We propose to include cost as an additional preference criterion for the CVaR optimization problem. We demonstrate that, with the addition of a proportional cost, it is possible to compute an optimal CVaR derivative investment portfolio with significantly fewer instruments and comparable CVaR and VaR. A computational method based on a smoothing technique is proposed to solve a simulation based CVaR optimization problem efficiently. Comparison is made with the linear programming approach for solving the simulation based CVaR optimization problem.     

Applying VaR to REITs: A comparison of alternative methods

This study employs five methods to calculate the VaR of twelve REITs portfolios and evaluates the accuracy of these methods. Firstly, we find that the VaR varies among individual portfolios. The Hotel REITs has consistently the largest VaR. The low-leveraging portfolio tends to have the largest VaR measured by the parametric methods, while the high leveraging portfolio has the largest VaR calculated by the non-parametric methods. Secondly, each method performs differently at different confidence levels, and no method dominates the others. At the 95% confidence level, the EWMA method performs relatively well. The EQWMA and the two non-parametric methods perform equivalently and slightly overestimate VaRs. The EQWMA_T method ranks the bottom and significantly overestimates VaRs for all portfolios. At the 99% confidence level, the EQWMA method performs the best. The EQWMA_T and the two non-parametric methods perform equivalently and may overestimate VaR for all portfolios. The EWMA method turns out to be the worst and tends to underestimate the VaR. These findings may provide more insights for institutional real estate investors.     

Hedging and speculative pressures and the transition of the spot-futures relationship in energy and metal markets

This paper examines the impact of hedging and speculative pressures on the transition of the spot-futures relationship in metal and energy markets. We build a Markov regime switching (MRS) model where hedging and speculative pressures affect the transition probabilities between a stronger and weaker spot-futures relationship. It is found that hedging pressure increases the likelihood of transition, i.e. destabilises the existing spot-futures relationship, while speculative pressure reduces it, i.e. stabilises the relationship, in the copper, crude oil and natural gas markets, but this effect is relatively weak in the silver and heating oil markets. We also examine whether these findings generate practical benefits by testing the hedging effectiveness of the minimum variance hedge ratios (MVH) derived from the MRS models with hedging and speculative pressures. A relatively strong reduction of the portfolio variance, hedger's utility and value at risk (VaR) is observed in the energy markets.     

Optimal regulation,executive compensation and risk taking by financial institutions

We present an equilibrium model of financial institutions to examine the optimal regulation of risk taking. Shareholders provide incentives for management to increase risk to excessive levels. Regulators use caps on asset risk and compensation to achieve the socially optimal risk level. This level trades off costs of risk shifting and costs of bank default. Without regulation, equilibrium risk lies above the optimal level. If information and enforcement are perfect, either policy tool (caps on asset risk or compensation) achieves the optimal risk level. If there are frictions – if enforcement is limited, if there is uncertainty about the incentives facing management and costs of risk shifting, or if regulation cannot be bank specific – welfare can be improved by employing both policy tools.     

Optimal hedge ratios and alternative hedging strategies in the presence of cointegrated time-varying risks

This paper utilizes the inter-temporal relationship between the FTSE-100 stock index and its futures price level between 1992 and 1999 to examine the characteristics of several minimum variance hedge ratios and the performances of several alternative hedging strategies for dynamic portfolio management in the presence of cointegrated time-varying risks. Earlier studies neglected the importance of cointegration between the two variables which resulted in biased estimates. These studies, in general, also assume that the hedging period is the same as the estimation time interval. This paper also looks at several key issues when the holding period is longer than the estimation period, such as the construction of optimal minimum variance hedge ratios, and the trade-off between transaction costs and risk reduction.     

An analysis of VaR-based capital requirements

We study the behavior of a financial institution subject to capital requirements based on self-reported VaR measures, as in the Basel Committee's Internal Models Approach. We view these capital requirements and the associated backtesting procedure as a mechanism designed to induce financial institutions to reveal the risk of their investments and to support this risk with adequate levels of capital. Accordingly, we consider the simultaneous choice of an optimal dynamic reporting and investment strategy. Overall, we find that VaR-based capital requirements can be very effective not only in curbing portfolio risk but also in inducing revelation of this risk.     

Optimal insurance contract under a value-at-risk constraint

This study develops an optimal insurance contract endogenously under a value-at-risk (VaR) constraint. Although Wang et al. [2005] had examined this problem, their assumption implied that the insured is risk neutral. Consequently, this study extends Wang et al. [2005] and further considers a more realistic situation where the insured is risk averse. The study derives the optimal insurance contract as a single deductible insurance when the VaR constraint is redundant or as a double deductible insurance when the VaR constraint is binding. Finally, this study discusses the optimal coverage level from common forms of insurances, including deductible insurance, upper-limit insurance, and proportional coinsurance. JEL Classification G22     

Hedging and liquidity

This article develops a model for evaluating alternative hedgingstrategies for financially constrained firms. A key advantageof the model is the ability to capture the intertemporal effectsof hedging on the firm's financial situation. We characterizethe optimal hedge. A wide range of alternative hedging strategiescan be specified and the model allows us to determine in eachcase if the hedging strategy raises or lowers firms value andby how much. We show that hedging firm value, hedging cash flowfrom operations and hedging sales revenue are not optimal. Thearticle highlights the fact that every hedging strategy comespackaged with a borrowing strategy which requires careful consideration.     

Analysing Perceived Downside Risk: the Component Value‐at‐Risk Framework

Multinational companies face increasing risks arising from external risk factors, e.g. exchange rates, interest rates and commodity prices, which they have learned to hedge using derivatives. However, despite increasing disclosure requirements, a firm's net risk profile may not be transparent to shareholders. We develop the ‘Component Value‐at‐Risk (VaR)’ framework for companies to identify the multi‐dimensional downside risk profile as perceived by shareholders. This framework allows for decomposing downside risk into components that are attributable to each of the underlying risk factors. The firm can compare this perceived VaR, including its composition and dynamics, to an internal VaR based on net exposures as it is known to the company. Any differences may lead to surprises at times of earnings announcements and thus constitute a litigation threat to the firm. It may reduce this information asymmetry through targeted communication efforts.