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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 purpose of this paper is to examine the nature of the relationship between business risk and financial leverage. While past theoretical and empirical studies on this topic use similar variables, overall, their findings are inconclusive. In this paper, the author contends this is partially due to inappropriate proxies for business risk that are commonly used in these research papers. To correct for this misspecification, this paper proposes an alternative proxy for business risk that is isolated from the effects of financial leverage.

Past research on the relationship between business risk and financial leverage uses some variations in a firm’s operating cash flow as a proxy for business risk. This proxy cannot solely reflect business risk and may very well be affected by the level of financial leverage, especially for financially distressed firms. This paper proposes an alternative proxy for business risk that is isolated from the effects of financial leverage. This proxy is the cost of capital of an all-equity firm. The theoretical model developed in this paper is based on deriving the optimum level of debt as a function of business risk in the context of the Modigliani and Miller Proposition II model.

The findings show a positive linkage between business risk and financial leverage. This relationship is robust to the various forms the cost of financial distress function may take.

The mixed findings in past research papers regarding the relationship between business risk and financial leverage are mainly due to “inappropriate” measures of business risk that do not only reflect one firm attribute and are contaminated with other factors mainly financial leverage. As such, since the variable of interest is misspecified, the outcome of these studies cannot be credible. This paper attempts to correct for such misspecification by proposing a proxy that only reflects business risk. In addition, the proposed model is based on the widely acceptable Modigliani and Miller static theory of capital structure.

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.

The purpose of this study is to investigate the impact of disputed tax litigation risk on firm performance and stock return behavior using a sample of Indian listed firms.

The authors use disputed tax liability, reported as a contingent liability by the listed firms, as a proxy for the disputed tax litigation risk. To examine the impact of disputed tax litigation risk on firm performance (measured by accounting and market-based measures), the empirical approach used in this study focusses on the panel estimation technique. A portfolio-based approach using alternative asset pricing models examines the cross-sectional return variation because of the influence of disputed tax litigation risk.

The results of this study show a negative relationship between firm performance measures and disputed tax litigation risk. Cross-sectional test results reveal that higher disputed tax litigation risk is associated with higher expected returns.

This study focusses on disputed tax reported under the heading of contingent liability as a proxy for litigation risk. The study will help investors and portfolio managers to consider disputed tax litigation risk as an important parameter in the evaluation of firm performance. This study will also help regulators to get feedback on tax related policies and improve the dispute resolution process.

This study adds to the existing literature on the relationship between litigation risk and firm performance. In the context of emerging market, this study is the first-of-its-kind study, which focusses on disputed tax as a litigation risk proxy and examines its possible impact on firm performance and stock return behavior.

This study investigates the economic content of the two firm‐specific characteristics, size and book‐to‐market equity. Size is found to be significantly related to a combination of betas on all of the macro variables proposed in this research. Its significance persists through out the entire sample period. This provides further evidence that size is a proxy for pervasive risk factors in the stock market. The support for book‐to‐market equity’s role as a risk proxy is also evidenced, however to a lesser extent. Securities are then sorted into size and book‐to‐market equity portfolios and their effects on investment decisions are examined in the context of macro variables. Important investment implications are drawn based on the findings.

This paper aims to analyse the exposure at default (EAD) in the event of multiple banking relationships to understand the differences with respect to solo banking relationships and forecast the banks risk exposure.

The paper uses a unique database provided by the Italian public credit register representative of the full Italian market before the financial crisis. The analysis compares different EAD risk proxies for debtors with unique and multiple banking relationships to underline the main differences among the two groups.

Results show that EAD forecast could be improved considering the existence of exposures with other lenders and banks that consider such type of information can reduce the risk of underestimating the risk exposure of a debtor.

The paper is the first attempt to model the EAD on the basis of the existence of multiple lending exposures. Results demonstrate a different lender’s risk exposure for debtors with multiple credit risk exposure and show the usefulness of the information about the overall system exposure in evaluating the risk exposure related to this type of customers.

The purpose of this study is to examine whether lengthy audit delays lead to auditor changes in the subsequent year. The paper hypothesizes that a lengthy interaction between clients and their auditors reflects high audit risk factors relating to management integrity, internal controls, and the financial reporting process. It argues that auditors are more likely to drop clients with long audit delays because they would like to avoid these types of audit risks.

Using logistic regressions, the paper first tests whether a lengthy audit delay leads to an auditor change. It then examines whether as audit delays increase, auditor changes are more likely to be downward than lateral.

The results support the hypothesis that Big N auditor‐client realignments occur following long audit delays. Further, as the length of the delay increases, the paper finds that there are more downward changes.

An implication of our study is that a long audit delay represents a publicly observed proxy for the presence of audit risk factors that lead to an auditor change.

This study suggests that all else constant, investors should consider a lengthy audit delay as indicating that there has been deterioration in the quality of the client‐auditor interaction. An audit delay also presents an observable proxy for successor auditors to consider while evaluating risks associated with a new client.

The results of our study increase our understanding of how Big N auditors manage their client portfolios to mitigate their exposure to risk factors.

The purpose of this research is to provide further evidence on the association between the IPO signaling mechanisms (i.e. retained ownership, auditor choice, and earnings forecast) by using a less restrictive sample and by performing additional empirical tests.

Single equations are used as the baseline approach to estimate the three models. In addition, Copley and Douthett's 2002 simultaneous equation systems are applied to examine whether the results remain the same. Moreover, ranked values of the risk proxies of IPOs are derived and general least squares are run on these ranked variables.

Findings indicate that auditor reputation and retained ownership are not substitute signals. It is observed that as firm risk increases, entrepreneurs are more likely to retain higher ownership to signal firm value. In addition, contended that positive earnings disclosure before IPO is not associated with retained ownership in a significant manner. An analysis of the economic implication of the results suggests that findings are more representative.

In this study the risk measures used (as well as those used in other studies) may not adequately proxy for offering firm risk. Additionally, the sample is restricted by missing values of the retained ownership variable. Further study can expand the sample using retained ownership obtained from other data sources. A study employing alternative approaches to control for the supply‐side effect of firm risk could be also productive.

Findings are of particular interest to firms that are planning to go to the public. They need to evaluate the benefit and cost of selecting a particular information system in signaling firm value to the market.

Using a larger sample, comprehensive testing periods, and ranked risk proxies contribute to the literature on evaluating singling mechanisms of IPOs.

Recent studies have shown that low-volatility shares outperform high-volatility shares. Given the conventional finance theory that risk drives return, this study aims to investigate and attempt to explain the presence of the low-risk anomaly (LRA) in South Africa.

Using share prices from 1990 to 2016, various buy-and-hold strategies are constructed to determine the return to an investor attempting to capitalise on such an anomaly. These strategies involve combinations relating to a price filter, the calculation of risk and volatility, value-weighting or equal-weighting of portfolios and the window period to construct said portfolios.

It was found that the LRA exists on the Johannesburg Stock Exchange (JSE_=) when using univariate sorts, without controlling for the size or value effect. When using multivariate portfolio sorts (size and volatility or value and volatility), it was found that the LRA does not exist on the JSE under the majority of risk proxies, but particularly prevalent when downside risk is used. This loosely points towards a potential “inverse momentum” effect where low-return portfolios outperform their counterparts.

In general, it is established that the risk–return relationship is non-linear and deterministic under traditional proxies, but improves to being somewhat, but not completely, linear under a Kalman filter. The Kalman filter, which can be considered a proxy for learning, does not remove the anomaly in its entirety, indicating that behavioural approaches are needed to explain such phenomena.

This paper aims to investigate the attributes and information content of risk reporting in two different institutional and regulatory, namely, Canadian and German, settings during the period surrounding the financial crisis of 2008.

For a matched sample of manufacturing firms in the period 2006–2010, this study conducts a detailed content analysis of annual reports to assess and compare the volume and patterns of risk disclosures. Panel regressions are used to explore how risk disclosures related to corporate risk proxies and performance indicators.

Over the sample period, Canadian and German firms increase the volume but largely maintain the patterns of risk disclosures. Risk disclosures relate to corporate risk proxies but are not incrementally informative to assess firm performance.

The paper contributes to research on risk reporting by providing detailed cross-country evidence for a period particularly shaped by significant risk. The findings have implications for the regulation and usefulness of risk reporting.