How does the underlying affect the risk-return profiles of structured products?

Regulators of some of the major markets have adopted value at risk (VaR) as the risk measure for structured products. Under the mean-VaR framework, this paper discusses the impact of the underlying’s distribution on structured products. We expand the expected return and the VaR of a structured product with its underlying’s moments (mean, variance, skewness, and kurtosis), so that the impact of the moments can be investigated simultaneously. Results are tested by Monte Carlo and historical simulations. The findings show that for the majority of structured products, underlyings with large positive skewness are preferred. The preferences for the variance and the kurtosis of the underlying are both ambiguous.     

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.

     

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.     

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.     

Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach

We propose a method for estimating Value at Risk (VaR) and related risk measures describing the tail of the conditional distribution of a heteroscedastic financial return series. Our approach combines pseudo-maximum-likelihood fitting of GARCH models to estimate the current volatility and extreme value theory (EVT) for estimating the tail of the innovation distribution of the GARCH model. We use our method to estimate conditional quantiles (VaR) and conditional expected shortfalls (the expected size of a return exceeding VaR), this being an alternative measure of tail risk with better theoretical properties than the quantile. Using backtesting of historical daily return series we show that our procedure gives better 1-day estimates than methods which ignore the heavy tails of the innovations or the stochastic nature of the volatility. With the help of our fitted models we adopt a Monte Carlo approach to estimating the conditional quantiles of returns over multiple-day horizons and find that this outperforms the simple square-root-of-time scaling method.     

Value at risk,cross-sectional returns and the role of investor sentiment

In this paper, we find that the relationship between the value-at-risk (VaR) and expected returns is negative and this negative relationship between the VaR and expected returns can be explained by volatility in the U.S. market. However, for different levels of investor sentiment, this relationship changes. For a high sentiment period, VaR is negatively related with the expected return and cannot be explained by momentum, short-term reversal, volatility, and financial distress. In comparison, the relation between the VaR and expected returns during a low sentiment period is mixed.     

Capital adequacy rules, catastrophic firm failure, and systemic risk

This paper studies capital adequacy rules based on Value-at-Risk (VaR), leverage ratios, and stress testing. VaR is the basis of Basel II, and all three approaches are proposed in Basel III. This paper makes three contributions to the literature. First, we prove that these three rules provide an incentive to increase the probability of catastrophic financial institution failure. Collectively, these rules provide an incentive to increase (not decrease) systemic risk. Second, we argue that an unintended consequence of the Basel II VaR capital adequacy rules was the 2007 credit crisis. Third, we argue that to reduce systemic risk, a new capital adequacy rule is needed. One that is based on a risk measure related to the conditional expected loss given insolvency.     

A Generalized Extreme Value Approach to Financial Risk Measurement

This paper develops an unconditional and conditional extreme value approach to calculating value at risk (VaR), and shows that the maximum likely loss of financial institutions can be more accurately estimated using the statistical theory of extremes. The new approach is based on the distribution of extreme returns instead of the distribution of all returns and provides good predictions of catastrophic market risks. Both the in-sample and out-of-sample performance results indicate that the Box–Cox generalized extreme value distribution introduced in the paper performs surprisingly well in capturing both the rate of occurrence and the extent of extreme events in financial markets. The new approach yields more precise VaR estimates than the normal and skewed t distributions.     

Value at risk and the cross-section of hedge fund returns

Using two large hedge fund databases, this paper empirically tests the presence and significance of a cross-sectional relation between hedge fund returns and value at risk (VaR). The univariate and bivariate portfolio-level analyses as well as the fund-level regression results indicate a significantly positive relation between VaR and the cross-section of expected returns on live funds. During the period of January 1995 to December 2003, the live funds with high VaR outperform those with low VaR by an annual return difference of 9%. This risk-return tradeoff holds even after controlling for age, size, and liquidity factors. Furthermore, the risk profile of defunct funds is found to be different from that of live funds. The relation between downside risk and expected return is found to be negative for defunct funds because taking high risk by these funds can wipe out fund capital, and hence they become defunct. Meanwhile, voluntary closure makes some well performed funds with large assets and low risk fall into the defunct category. Hence, the risk-return relation for defunct funds is more complicated than what implies by survival. We demonstrate how to distinguish live funds from defunct funds on an ex ante basis. A trading rule based on buying the expected to live funds and selling the expected to disappear funds provides an annual profit of 8–10% depending on the investment horizons.     

Implied Equity Duration: A New Measure of Equity Risk

Duration is an important and well-established risk characteristic for fixed income securities. We use recent developments in financial statement analysis research to construct a measure of duration for equity securities. We find that the standard empirical predictions and results for fixed income securities extend to equity securities. We show that stock price volatility and stock beta are both positively correlated with equity duration. Moreover, estimates of common shocks to expected equity returns extracted using our measure of equity duration capture a strong common factor in stock returns. Additional analysis shows that the book-to-market ratio provides a crude measure of equity duration and that our more refined measure of equity duration subsumes the Fama and French (1993) book-to-market factor in stock returns. Our research shows how structured financial statement analysis can be used to construct superior measures of equity security risk.     

Value-at-risk versus expected shortfall: A practical perspective

Value-at-Risk (VaR) has become a standard risk measure for financial risk management. However, many authors claim that there are several conceptual problems with VaR. Among these problems, an important one is that VaR disregards any loss beyond the VaR level. We call this problem the “tail risk”. In this paper, we illustrate how the tail risk of VaR can cause serious problems in certain cases, cases in which expected shortfall can serve more aptly in its place. We discuss two cases: concentrated credit portfolio and foreign exchange rates under market stress. We show that expected shortfall requires a larger sample size than VaR to provide the same level of accuracy.     

Extreme downside risk and expected stock returns

We propose a measure for extreme downside risk (EDR) to investigate whether bearing such a risk is rewarded by higher expected stock returns. By constructing an EDR proxy with the left tail index in the classical generalized extreme value distribution, we document a significantly positive EDR premium in cross-section of stock returns even after controlling for market, size, value, momentum, and liquidity effects. The EDR premium is more prominent among glamor stocks and when high market returns are expected. High-EDR stocks are generally characterized by high idiosyncratic risk, large downside beta, lower coskewness and cokurtosis, and high bankruptcy risk. The EDR premium persists after these characteristics are controlled for. Although Value at Risk (VaR) plays a significant role in explaining the EDR premium, it cannot completely subsume the EDR effect.     

Extreme risk spillover network: application to financial institutions

Using the CAViaR tool to estimate the value-at-risk (VaR) and the Granger causality risk test to quantify extreme risk spillovers, we propose an extreme risk spillover network for analysing the interconnectedness across financial institutions. We construct extreme risk spillover networks at 1% and 5% risk levels (which we denote 1% and 5% VaR networks) based on the daily returns of 84 publicly listed financial institutions from four sectors—banks, diversified financials, insurance and real estate—during the period 2006–2015. We find that extreme risk spillover networks have a time-lag effect. Both the static and dynamic networks show that on average the real estate and bank sectors are net senders of extreme risk spillovers and the insurance and diversified financials sectors are net recipients, which coheres with the evidence from the recent global financial crisis. The networks during the 2008–2009 financial crisis and the European sovereign debt crisis exhibited distinctive topological features that differed from those in tranquil periods. Our approach supplies new information on the interconnectedness across financial agents that will prove valuable not only to investors and hedge fund managers, but also to regulators and policy-makers.     

Forecasting VaR using analytic higher moments for GARCH processes

It is widely accepted that some of the most accurate Value-at-Risk (VaR) estimates are based on an appropriately specified GARCH process. But when the forecast horizon is greater than the frequency of the GARCH model, such predictions have typically required time-consuming simulations of the aggregated returns distributions. This paper shows that fast, quasi-analytic GARCH VaR calculations can be based on new formulae for the first four moments of aggregated GARCH returns. Our extensive empirical study compares the Cornish–Fisher expansion with the Johnson SU distribution for fitting distributions to analytic moments of normal and Student t, symmetric and asymmetric (GJR) GARCH processes to returns data on different financial assets, for the purpose of deriving accurate GARCH VaR forecasts over multiple horizons and significance levels.     

Financial crisis,Value-at-Risk forecasts and the puzzle of dependency modeling

Forecasting Value-at-Risk (VaR) for financial portfolios is a crucial task in applied financial risk management. In this paper, we compare VaR forecasts based on different models for return interdependencies: volatility spillover (Engle & Kroner, 1995), dynamic conditional correlations (Engle, 2002, 2009) and (elliptical) copulas (Embrechts et al., 2002). Moreover, competing models for marginal return distributions are applied. In particular, we apply extreme value theory (EVT) models to GARCH-filtered residuals to capture excess returns.Drawing on a sample of daily data covering both calm and turbulent market phases, we analyze portfolios consisting of German Stocks, national indices and FX-rates. VaR forecasts are evaluated using statistical backtesting and Basel II criteria. The extensive empirical application favors the elliptical copula approach combined with extreme value theory (EVT) models for individual returns. 99% VaR forecasts from the EVT-GARCH-copula model clearly outperform estimates from alternative models accounting for dynamic conditional correlations and volatility spillover for all asset classes in times of financial crisis.     

Bank Capital Regulation of Trading Portfolios: An Assessment of the Basel Framework

In setting minimum capital requirements for trading portfolios, the Basel Committee on Banking Supervision (1996, 2011a, 2013) initially used Value‐at‐Risk (VaR), then both VaR and stressed VaR (SVaR), and most recently, stressed Conditional VaR (SCVaR). Accordingly, we examine the use of SCVaR to measure risk and set these requirements. Assuming elliptically distributed asset returns, we show that portfolios on the mean‐SCVaR frontier generally lie away from the mean‐variance (M‐V) frontier. In a plausible numerical example, we find that such portfolios tend to have considerably higher ratios of risk (measured by, e.g., standard deviation) to minimum capital requirement than those of portfolios on the M‐V frontier. Also, we find that requirements based on SCVaR are smaller than those based on both VaR and SVaR but exceed those based on just VaR. Finally, we find that requirements based on SCVaR are less procyclical than those based on either VaR or both VaR and SVaR. Overall, our paper suggests that the use of SCVaR to measure risk and set requirements is not a panacea.     

Estimation of multiple period expected shortfall and median shortfall for risk management

With the regulatory requirements for risk management, Value at Risk (VaR) has become an essential tool in determining capital reserves to protect the risk induced by adverse market movements. The fact that VaR is not coherent has motivated the industry to explore alternative risk measures such as expected shortfall. The first objective of this paper is to propose statistical methods for estimating multiple-period expected shortfall under GARCH models. In addition to the expected shortfall, we investigate a new tool called median shortfall to measure risk. The second objective of this paper is to develop backtesting methods for assessing the performance of expected shortfall and median shortfall estimators from statistical and financial perspectives. By applying our expected shortfall estimators and other existing approaches to seven international markets, we demonstrate the superiority of our methods with respect to statistical and practical evaluations. Our expected shortfall estimators likely provide an unbiased reference for setting the minimum capital required for safeguarding against expected loss.     

Risk evaluations with robust approximate factor models

Approximate factor models and their extensions are widely used in economic analysis and forecasting due to their ability to extracting useful information from a large number of relevant variables. In these models, candidate predictors are typically subject to some common components. In this paper we propose a new method for robustly estimating the approximate factor models and use it in risk assessments. We consider a class of approximate factor models in which the candidate predictors are additionally subject to idiosyncratic large uncommon components such as jumps or outliers. By assuming that occurrences of the uncommon components are rare, we develop an estimation procedure to simultaneously disentangle and estimate the common and uncommon components. We then use the proposed method to investigate whether risks from the latent factors are priced for expected returns of Fama and French 100 size and book-to-market ratio portfolios. We find that while the risk from the common factor is priced for the 100 portfolios, the risks from the idiosyncratic factors are not. However, we find that model uncertainty risks of the idiosyncratic factors are priced, suggesting that with effective diversifications, only the predictable idiosyncratic risks can be reduced, but the unpredictable ones may still exist. We also illustrate how the proposed method can be adopted on evaluating value at risk (VaR) and find it can delivery comparable results as the conventional methods on VaR evaluations.     

Ethical and unethical investments under extreme market conditions

This study investigates the time-varying volatility and risk measures of ethical and unethical investments. We apply the Bayesian Markov-switching generalized autoregressive conditional heteroscedasticity (MS-GARCH) approach to compute the value-at-risk (VaR) and expected shortfall (ES) of ethical and unethical indices returns, which allows for detecting the differences between ethical and unethical investments. The innovative finding of our study is that ethical investments are less affected during global financial crises compared with unethical and conventional investments. The policy implication of this study is that investors should consider ethical investments as a hedging asset for their portfolios during extreme market conditions.