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.     

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.     

Innovation and Information Acquisition under Time Inconsistency and Uncertainty

When an agent invests in new industrial activities, he has a limited initial knowledge of his project's returns. Acquiring information allows him both to reduce the uncertainty on the dangerousness of this project and to limit potential damages that it might cause on people's health and on the environment. In this paper, we study whether there exist situations in which the agent does not acquire information. We find that an agent with time-consistent preferences, as well as an agent with hyperbolic ones, will acquire information unless its cost exceeds the direct benefit they could get with this information. Nevertheless, a hyperbolic agent may remain strategically ignorant and, when he does acquire information, he will acquire less information than a time-consistent type. Moreover, a hyperbolic-discounting type who behaves as a time-consistent agent in the future is more inclined to stay ignorant. We then emphasize that this strategic ignorance depends on the degree of precision of the information. Finally, we analyse the role that existing liability rules could play as an incentive to acquire information under uncertainty and with regard to the form of the agent's preferences.     

Portfolio selection based on the mean–VaR efficient frontier

Value-at-Risk (VaR) has become one of the standard measures for assessing risk not only in the financial industry but also for asset allocations of individual investors. The traditional mean–variance framework for portfolio selection should, however, be revised when the investor's concern is the VaR instead of the standard deviation. This is especially true when asset returns are not normal. In this paper, we incorporate VaR in portfolio selection, and we propose a mean–VaR efficient frontier. Due to the two-objective optimization problem that is associated with the mean–VaR framework, an evolutionary multi-objective approach is required to construct the mean–VaR efficient frontier. Specifically, we consider the elitist non-dominated sorting Genetic Algorithm (NSGA-II). From our empirical analysis, we conclude that the risk-averse investor might inefficiently allocate his/her wealth if his/her decision is based on the mean–variance framework.     

基于VaR模型的商业银行体系系统性风险研究

本文以中国2016年之前上市商业银行作为中国银行业的代表,测算银行业系统性 风险VaR。整体来讲,我国银行业系统性风险较低,但VaR在2015年较高。虽如此,我国银行业资本持有量能够抵御银行体系的系统性风险。在系统性风险VaR贡献度方面,本文实证分析表明,在样本期间内,浦发银行、中国银行、农业银行、交通银行贡献度较高。银行体系系统 性风险VaR受GDP增长率和沪深300指数收益率的显著影响。     

On the coherence of expected shortfall

Expected shortfall (ES) in several variants has been proposed as remedy for the deficiencies of value-at-risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss distributions have discontinuities. In this case even the coherence property of ES can get lost unless one took care of the details in its definition. We compare some of the definitions of ES, pointing out that there is one which is robust in the sense of yielding a coherent risk measure regardless of the underlying distributions. Moreover, this ES can be estimated effectively even in cases where the usual estimators for VaR fail.     

Improving expected tail loss estimates with neural networks

Expected tail loss (ETL) and other ‘coherent’ risk measures are rapidly gaining acceptance amongst risk managers due to the limitations of value‐at‐risk (VaR) as a risk measure. In this article we explore the use of multilayer perceptron supervised neural networks to improve our estimates of ETL numbers using information from both tails of the distribution. We compare the results with the historical simulation approach to the estimation of VaR and ETL. The evaluation results indicate that the ETL estimates using neural networks are superior to historical simulation ETL estimates in all periods except for one, and in that case the historical ETL is slightly superior. Overall, therefore, when the whole period is considered, our results indicate that the network estimates of ETL are superior to the historical ones. Finally, one of the most interesting results of the study is the fact that the neural networks seem to indicate that VaR and ETL (as a function of VaR itself) are dependent not only on the negative returns observed, but also on large positive returns, which indicates that too much emphasis on losses could lead us to overlook important risk information arising from large positive returns. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Coherent risk measures under filtered historical simulation

Recent studies have strongly criticised conventional VaR models for not providing a coherent risk measure. Acerbi provides the intuition for an entire family of coherent measures of risk known as “spectral risk measures” [Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking and Finance 26 (7) (2002) 1505–1518]. In this study we illustrate how the Filtered Historical Simulation [Barone-Adesi, G., Bourgoin, F., Giannopoulos, K., 1998. Don’t look back. Risk 11, 100–104; Barone-Adesi, Giannopoulos, K., Vosper, L., 1999. VaR without correlations for non-linear portfolios. Journal of Futures Markets 19, 583–602], can provide an improved methodology for calculating the Expected Shortfall. Thereafter, we prove that these new risk measures are spectral and are coherent as well, following Acerbi. Furthermore, we provide the statistical error formula that allows to calculate the error for our model.     

Extreme spectral risk measures: An application to futures clearinghouse margin requirements

This paper applies the extreme-value (EV) generalised pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user’s risk-aversion function. It compares these to VaR and expected shortfall (ES) risk measures, and compares the precision of their estimators. It also discusses the usefulness of these risk measures in the context of clearinghouses setting initial margin requirements, and compares these to the SPAN measures typically used.     

Conditional value-at-risk for general loss distributions

Fundamental properties of conditional value-at-risk (CVaR), as a measure of risk with significant advantages over value-at-risk (VaR), are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. CVaR is able to quantify dangers beyond VaR and moreover it is coherent. It provides optimization short-cuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach. The numerical efficiency and stability of such calculations, shown in several case studies, are illustrated further with an example of index tracking.     

Valuing Companies with Cash‐Flow@Risk

The classic DCF approach to capital budgeting—the one that MBA students in the world's top business schools have been taught for the last 30 years—begins with the assumption that the corporate investment decision is “independent of” the financing decision. That is, the value of a given investment opportunity should not be affected by how a company is financed, whether mainly with debt or with equity. A corollary of this capital structure “irrelevance” proposition says that a company's investment decision should also not be influenced by its risk management policy—by whether a company hedges its various price exposures or chooses to leave them unhedged. In this article, the authors—one of whom is the CFO of the French high‐tech firm Gemalto—propose a practical alternative to DCF that is based on a concept they call “cash‐flow@risk.” Implementation of the concept involves dividing expected future cash flow into two components: a low‐risk part, or “certainty equivalent,” and a high‐risk part. The two cash flow streams are discounted at different rates (corresponding to debt and equity) when estimating their value. The concept of cash‐flow@risk derives directly from, and is fully consistent with, the concept of economic capital that was developed by Robert Merton and Andre Perold in the early 1990s and that has become the basis of Value at Risk (or VaR) capital allocation systems now used at most financial institutions. But because the approach in this article focuses on the volatility of operating cash flows instead of asset values, the authors argue that an internal capital allocation system based on cash‐flow@risk is likely to be much more suitable than VaR for industrial companies.     

A note on the importance of overnight information in risk management models

This paper examines the economic value of overnight information to users of risk management models. In addition to the information revealed by overseas markets that trade during the (domestic) overnight period, this paper exploits information generated via recent innovations in the structure of financial markets. In particular, certain securities (and associated derivative products) can now be traded at any time over a 24-h period. As such, it is now possible to make use of information generated by trading, in (almost) identical securities, during the overnight period. Of the securities that are available over such time periods, S&P 500 related products are by far the most actively traded and are, therefore, the subject of this paper. Using a variety of conditional volatility models that allow time-dependent information flow within (and across) three different S&P 500 markets, the results show that overnight information flow has a significant impact on the conditional volatility of daytime traded S&P 500 securities. Moreover (time-consistent) forecasts from models that incorporate overnight information are shown to have economic value to risk managers. In particular, Value-at-Risk (VaR) models based on these conditional volatility models are shown to be more accurate than VaR models that ignore overnight information.     

Raising Value at Risk

In this paper I consider the properties for a coherent risk measure, outlined by Artzner et al. (1996), and relate these requirements to a well-known measure, value at risk (VaR), which attempts to evaluate economic risk. I show how the usual method of calculating VaR does not adhere to the coherency requirements and discuss the implications of such a result. As well, I discuss the use of the mean excess loss function to help solve this problem.     

Value-at-risk capital requirement regulation,risk taking and asset allocation: a mean–variance analysis

In this study, the mean–variance framework is employed to analyze the impact of the Basel value-at-risk (VaR) market risk regulation on the institution's optimal investment policy, the stockholders’ welfare, as well as the tendency of the institution to change the risk profile of the held portfolio. It is shown that with the VaR regulation, the institution faces a new regulated capital market line, which induces resource allocation distortion in the economy. Surprisingly, only when a riskless asset is available does VaR regulation induce the institution to reduce risk. Otherwise, the regulation may induce higher risk, accompanied by asset allocation distortion. On the positive side, the regulation implies an upper bound on the risk the institution takes and it never induces the firm to select an inefficient portfolio. Moreover, when the riskless asset is available, tightening the regulation always increases the amount of maintained eligible capital and decreases risk.     

Minimizing CVaR in global dynamic hedging with transaction costs

This study develops a global derivatives hedging methodology which takes into account the presence of transaction costs. It extends the Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239] framework in two ways. First, to reduce the occurrence of extreme losses, the expected utility is replaced by the conditional Value-at-Risk (CVaR) coherent risk measure as the objective function. Second, the normality assumption for the underlying asset returns is relaxed: general distributions are considered to improve the realism of the model and to be consistent with fat tails observed empirically. Dynamic programming is used to solve the hedging problem. The CVaR minimization objective is shown to be part of a time-consistent framework. Simulations with parameters estimated from the S&P 500 financial time series show the superiority of the proposed hedging method over multiple benchmarks from the literature in terms of tail risk reduction.     

Intraday risk management in International stock markets: A conditional EVT approach

The study compares the predictive ability of various models in estimating intraday Value-at-Risk (VaR) and Expected Shortfall (ES) using high frequency share price index data from sixteen different countries across the world for a period of seven and half months from September 20, 2013 to May 07, 2014. The main emphasis of the study has been given to Extreme Value Theory (EVT) and to evaluate how well Conditional EVT model performs in modeling tails of distributions and in estimating and forecasting intraday VaR and ES measures. We have followed McNeil and Frey's (2000) two stage approach called Conditional EVT to estimate dynamic intraday VaR and ES. We have compared the accuracy of Conditional EVT approach to intraday VaR and ES estimation with other competing models. The best performing model is found to be the Conditional EVT in estimating both the quantiles for the entire sample. The study is useful for market participants (such as intraday traders and market makers) involved in frequent intraday trading in such equity markets.     

Time-consistent reinsurance and investment strategies for an AAI under smooth ambiguity utility

This paper investigates time-consistent reinsurance(excess-of-loss, proportional) and investment strategies for an ambiguity averse insurer(abbr. AAI). The AAI is ambiguous towards the insurance and financial markets. In the AAI's attitude, the intensity of the insurance claims' number and the market price of risk of a stock can not be estimated accurately. This formulation of ambiguity is similar to the uncertainty of different equivalent probability measures. The AAI can purchase excess-of-loss or proportional reinsurance to hedge the insurance risk and invest in a financial market with cash and an ambiguous stock. We investigate the optimization goal under smooth ambiguity given in Klibanoff, P., Marinacci, M., & Mukerji, S. [(2005). A smooth model of decision making under ambiguity. Econometrica 73, 1849–1892], which aims to search the optimal strategies under average case. The utility function does not satisfy the Bellman's principle and we employ the extended HJB equation proposed in Björk, T. & Murgoci, A. [(2014). A theory of Markovian time-inconsistent stochastic control in discrete time. Finance and Stochastics 18(3), 545–592] to solve this problem. In the end of this paper, we derive the equilibrium reinsurance and investment strategies under smooth ambiguity and present the sensitivity analysis to show the AAI's economic behaviors.     

Accrual mispricing,value-at-risk,and expected stock returns

We investigate the extent to which a parsimonious measure of maximum likely loss that captures the tail risk of returns—known as value-at-risk (VaR)—explains the relationship between accruals and the cross-sectional dispersion of expected stock returns. We construct portfolios based on Sloan’s (Account Rev 71(3):289–315, 1996) total accruals (TA) measure and individual asset-level VaR, which reflects the dynamic behavior of the asset distribution. We document that VaR is in congruence with portfolio-level accruals and that there is a significant positive relationship between VaR and the cross-section of portfolio returns. Allowing a double-sort involving VaR and TA further suggests that the spread between low- and high-TA portfolios is significantly attenuated after controlling for VaR. We also conduct a firm-level cross-sectional regression analysis and demonstrate that the TA- and VaR-based characteristics—but not the factor-mimicking portfolios—are compensated with higher expected returns, and that VaR neither subsumes nor is subsumed by TA. Finally, our cross-sectional decomposition analysis suggests that the firm-level VaR captures at least 7% of the accrual premium even in the presence of size and book-to-market. These findings lend support for the mispricing explanation of the accrual anomaly.

     

Forecasting value-at-risk and expected shortfall using fractionally integrated models of conditional volatility: International evidence

The present study compares the performance of the long memory FIGARCH model, with that of the short memory GARCH specification, in the forecasting of multi-period value-at-risk (VaR) and expected shortfall (ES) across 20 stock indices worldwide. The dataset is composed of daily data covering the period from 1989 to 2009. The research addresses the question of whether or not accounting for long memory in the conditional variance specification improves the accuracy of the VaR and ES forecasts produced, particularly for longer time horizons. Accounting for fractional integration in the conditional variance model does not appear to improve the accuracy of the VaR forecasts for the 1-day-ahead, 10-day-ahead and 20-day-ahead forecasting horizons relative to the short memory GARCH specification. Additionally, the results suggest that underestimation of the true VaR figure becomes less prevalent as the forecasting horizon increases. Furthermore, the GARCH model has a lower quadratic loss between actual returns and ES forecasts, for the majority of the indices considered for the 10-day and 20-day forecasting horizons. Therefore, a long memory volatility model compared to a short memory GARCH model does not appear to improve the VaR and ES forecasting accuracy, even for longer forecasting horizons. Finally, the rolling-sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models. Hence, the parameters' time-variant characteristic cannot be entirely due to the news information arrival process of the market; a portion must be due to the FIGARCH modelling process itself.