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The use of risk proxies in internal models remains a popular modelling solution. However, there is some risk that a proxy may not constitute an adequate representation of the underlying asset in terms of capturing tail risk. Therefore, using empirical examples for the financial collateral haircut model, this paper aims to critically review available statistical tools for measuring the adequacy of capturing tail risk by proxies used in the internal risk models of banks. In doing so, this paper advises on the most appropriate solutions for validating risk proxies.

This paper reviews statistical tools used to validate if the equity index/fund benchmark are proxies that adequately represent tail risk in the returns on an individual asset (equity/fund). The following statistical tools for comparing return distributions of the proxies and the portfolio items are discussed: the two-sample Kolmogorov–Smirnov test, the spillover test and the Harrell’s C test.

Upon the empirical review of the available statistical tools, this paper suggests using the two-sample Kolmogorov–Smirnov test to validate the adequacy of capturing tail risk by the assigned proxy and the Harrell’s C test to capture the discriminatory power of the proxy-based collateral haircuts models. This paper also suggests a tool that compares the reactions of risk proxies to tail events to verify possible underestimation of risk in times of significant stress.

The current regulations require banks to prove that the modelled proxies are representative of the real price observations without underestimation of tail risk and asset price volatility. This paper shows how to validate proxy-based financial collateral haircuts models.

The authors examined whether stocks with higher left-tail risk measures earn higher or lower futures returns. Specifically, the authors estimate the cross-sectional principal component of a battery of left-tail risk measures and analyze future returns on stocks with high principal component values. In contrast to finance theories on the risk–return trade-off relationship, the study results show that high left-tail risk stocks have lower future returns. This finding is robust to various left-tail risk measures and controls for other risk factors. Moreover, the negative relationship between the left-tail risk and returns is more pronounced for stocks that are actively traded by retail investors. This empirical result is consistent with behavioral theory that when investors make decisions based on experience, they tend to underweight the likelihood of rare events.

Value at risk (VaR) and expected shortfall (ES) are popular market risk measurements. The former is not coherent but robust, whereas the latter is coherent but less interpretable, only conditionally backtestable and less robust. In this chapter, we compare an innovative artificial neural network (ANN) model with a time series model in the context of forecasting VaR and ES of the univariate time series of four asset classes: US large capitalization equity index, European large cap equity index, US bond index, and US dollar versus euro exchange rate price index for the period of January 4, 1999, to December 31, 2018. In general, the ANN model has more favorable backtesting results as compared to the autoregressive moving average, generalized autoregressive conditional heteroscedasticity (ARMA-GARCH) time series model. In terms of forecasting accuracy, the ANN model has much fewer in-sample and out-of-sample exceptions than those of the ARMA-GARCH model.

This study aims to investigate the risk-return trade-off in the Indian equity market at both the aggregate equity market level and in the cross-sections of stock return using alternative risk measures.

The study uses weekly and monthly data of 3,085 Bombay Stock Exchange-listed stocks spanning over 20 years from January 2000 to December 2019. The study evaluates the risk-return trade-off at the aggregate equity market level using the value-weighted and the equal-weighted broader portfolios. Eight different risk proxies belonging to the conventional, downside and extreme risk categories are considered to analyse the cross-sectional risk-return relationship.

The results show a positive equity premium on the value-weighted portfolio; however, the equal-weighted portfolio of these stocks shows an average return lower than the return on the 91-day Treasury Bills. The inverted size premium mainly causes this anomaly in the Indian equity market as the small stocks have lower returns than big stocks. The study presents a strong negative risk-return relationship across different risk proxies. However, under the subsample of more liquid stocks, the low-risk anomaly regarding other risk proxies becomes moderate except the beta-anomaly. This anomalous relationship seems to be caused by small and less liquid stocks having low institutional ownership and higher short-selling constraints.

The findings have important implications for investors, managers and practitioners. Investors can incorporate the effects of different highlighted anomalies in their investment strategies to fetch higher returns. Managers can also use these findings in their capital budgeting decisions, resource allocations and other diverse range of direct and indirect decisions, particularly in emerging markets such as India. The findings provide insights to practitioners while valuing the firms.

The study is among the earlier attempts to examine the risk-return trade-off in an emerging equity market at both the aggregate equity market level and in the cross-sections of stock returns using alternative measures of risk and expected returns.

What causes the downward trend of real interest rates in major developed economies since the 1980s? What are the challenges of the near-zero interest and inflation rates for monetary policy? What can the policymakers learn from the latest developments in the monetary and interest rate theory? This paper aims to answer these questions by reviewing both basic principles of interest rate determination and recent academic and policy debates.

The paper critically reviews the explanations for the downward trend of real interest rates in recent decades and monetary policy options in a near-zero interest rate environment.

The decline of real interest rates is likely an outcome of multiple technological, social and economic factors including diminished productivity growth, changing demographics, elevated tail-risk concerns, time-varying convenience yields of safe assets, increased global demand for safe assets, rising wealth and income inequality, falling relative price of capital, accommodative monetary policies, and changes in industry structure that alter the investment and saving behaviors of the corporate sector. The near-zero interest rate limits the space of central banks' response to economic crises. It also challenges some conventional wisdoms of monetary theory and sparks radically new ideas about monetary policy.

This survey differs from the existing work by taking a broader view of both economics and finance literature. It critically assesses the economic forces driving the global decline of real interest rates through the lens of basic principles and empirical evidence and discusses the merits and limitations of each proposed explanation. The study emphasizes the importance of a better understanding of economic forces driving diverging trends of corporate investment and saving behaviors. It also discusses the implications of the neo-Fisherism and the fiscal theory of price level for monetary policy in a low interest rate environment.

The purpose of this paper is to measure a single financial institution's contribution to systemic risk by using extremal quantile regression and analyzing the influential factors of systemic risk.

Extreme value theory is applied when measuring the systemic risk of financial institutions. Extremal quantile regression, where extreme value distribution is assumed for the tail, is used to measure the extreme risk and analyze the changes in and dependencies of risk. Furthermore, influential factors of systemic risk are analyzed using panel regression.

The key findings of the paper are that value at risk and contribution to systemic risk are very different when measuring the risk of a financial institution; banks’ contributions to systemic risk are much higher; and size and leverage ratio are two significant and important factors influencing an institution's systemic risk.

Characterizing variables of financial institutions such as size, leverage ratio and market beta should be considered together when regulating and constraining financial institutions.

To take extreme risk into account, this paper measures systemic financial risk using extremal quantile regression for the first time.

Given the continuing growth in both the complexity and severity of cyber risk, a fundamental rethink of cyber risk management has become an issue of paramount importance, particularly as insurance firms are now providing both cyber risk management services and cyber risk insurance coverage. In this study, we set out to provide analyses of the prevailing cyber risk levels in various industries using the “Chronology of Data Breaches” database and then go on to assess the overall benefits of cyber risk insurance coverage. Our results reveal that compared to other industries, insurance firms exhibit superior cyber risk management. Regardless of internal and external cyber risk, insurance companies retain the lowest cyber losses. We further provide evidence to show that cyber risk insurance policies alone cannot effectively cover the potentially extreme cyber risk losses for most industries. However, the situation can be improved by implementing cyber risk management services provided by insurance firms. Insurance firms may need to provide an efficient cyber risk management system to lower the frequency and severity of extreme events.

It has been demonstrated in the US market that expected market excess returns can be predicted using the average higher-order moments of all firms. This study aims to empirically test this theory in emerging markets.

Two measures of average higher moments have been used (equal-weighted and value-weighted) along with the market moments to predict subsequent aggregate excess returns using the linear as well as the quantile regression model.

The authors report that both equal-weighted skewness and kurtosis significantly predict subsequent market returns in two countries, while value-weighted average skewness and kurtosis are significant in predicting returns in four out of nine sample markets. The results for quantile regression show that the relationship between the risk variable and aggregate returns varies along the spectrum of conditional quantiles.

This is the first study that investigates the impact of third and fourth higher-order average realized moments on the predictability of subsequent aggregate excess returns in the MSCI Asian emerging stock markets. This study is also the first to analyze the sensitivity of future market returns over various quantiles.

The purpose of this paper is to examine the relationship between accounting conservatism and pledging of shares by controlling shareholders of a firm to obtain a loan. The pledging of shares by the controlling shareholders of a firm results in alterations to the payoff and risk structure for these shareholders. Since accounting numbers have valuation implications, pledging of shares by a controlling shareholder has an impact on accounting policy choices made by the firm. The purpose of this paper is to examine the impact of controlling shareholder share pledging to obtain a loan on a specific accounting policy choice, namely, conservatism.

The paper uses a large data set from India comprising 14,786 firm years consisting of 1,570 firms belonging to 58 industries for a period of 11 years (2009–2019). The authors use ordinary least square regression with robust standard errors. The authors conduct robustness checks and the results are consistent across alternative statistical methodologies and alternative measures of the primary dependent and independent variables.

The primary results show that pledging of shares by the controlling shareholders results in higher conditional conservatism and lower unconditional conservatism. Further analysis reveals that the relationship is stronger when the controlling shareholder holds a majority ownership in the firm. Additionally, the results show that for business group affiliated firms, which are unique to developing countries, both the conditional and the unconditional conservatism are incrementally lower when the controlling shareholder pledges the shares. For family firms with a family member as CEO, the conditional conservatism is incrementally higher and the unconditional conservatism is incrementally lower. Finally, the authors show that the results hold when the pledge intensity variable is measured with a one-year lag and finally, the authors show that conditional conservatism is incrementally higher in the year of the increase in the pledge and the year after, but there is no such incremental impact on unconditional conservatism.

The research is limited to the listed firms in India. Since majority of the listed firms are controlled by families and the family firms around the world are heterogeneous the findings of the research may not be applicable to other countries.

The study has implications for policy-making and monitoring of the pledging by the controlling shareholders. It also helps the investors in making investment decisions with respect to family firms in India.

The study is unique as it focuses on the relationship between pledging of shares by the controlling shareholders and its impact on accounting conservatism. To the best of the authors’ knowledge, this is the first research integrating these two aspects.

Tails probabilities are of paramount importance in shaping the risk profile of portfolios with credit risk sensitive securities. In this context, risk management tools require simulations that accurately capture the tails, and optimization models that limit tail effects. Ignoring tail events in the simulation or using inadequate optimization metrics can have significant effects and reduce portfolio efficiency. The resulting portfolio risk profile can be grossly misrepresented when long‐run performance is optimized without accounting for short‐term tail effects. This article illustrates pitfalls and suggests models to avoid them.