Where is the distribution tail threshold? A tale on tail and copulas in financial risk measurement

Estimating the market risk is conditioned by the fat tail of the distribution of returns. But the tail index depends on the threshold of this distribution fat tail. We propose a methodology based on the decomposition of the series into positive outliers, Gaussian central part and negative outliers and uses the latter to estimate this cutoff point. Additionally, from this decomposition, we estimate extreme dependence correlation matrix which is used in the measurement of portfolio risk. For a sample consisting of six assets (Bitcoin, Gold, Brent, Standard&Poor-500, Nasdaq and Real Estate index), we find that our methodology presents better results, in terms of normality and volatility of the tail index, than the Kolmogorov–Smirnov distance, and its unnecessary capital consumption is lower. Also, in the measurement of the risk of a portfolio, the results of our proposal improve those of a t-Student copula and allow us to estimate the extreme dependence and the corresponding indexes avoiding the implicit restrictions of the elliptic and Archimedean copulas.     

A note on the existence of the power investor’s optimizer

Karatzas et al. (SIAM J. Control Optim. 29:707–730, 1991) ensure the existence of the expected utility maximizer for investors with constant relative risk aversion coefficients less than one. In this note, we explain a simple trick that allows us to use this result to provide the existence of utility maximizers for arbitrary coefficients of relative risk aversion. The simplicity of our approach is to be contrasted with the general existence result provided in Kramkov and Schachermayer (Ann. Appl. Probab. 9:904–950, 1999).     

Remarks on “A note on compound generalized distributions”

Abstract

1. INTRODUCTION

In [1] the authors derive recursion formulae for computing total claim probabilities for a general class of modified power series distributions. Such formulae provide an important tool for computing total claim size probabilities in risk-theory. As it turns out, two of their recursions (Theorem 3.2 and Theorem 3.4) need modifications. Unfortunately, these modifications have the effect that the recursions break down. In the following, we will state the modified theorems and show how these obstacles can be overcome.     

A note on “Modelling exchange rate returns: which flexible distribution to use?”

Corlu and Corlu [Quant. Finance, 2014, doi: 10.1080/14697688.2014.942231] provided a novel modelling of exchange rate data for nine currencies using five flexible distributions. They stated that the generalized lambda, skew t and normal inverse Gaussian distributions ‘do a good job’. Here, we reanalyse the data and show that a distribution simpler than all of these fits at least as well as these distributions. We also find that the normal inverse Gaussian distribution provides good fits for only one of the data-sets.     

Comments on “The Effect of a Common Currency on the Volatility of the Extensive Margin of Trade”

In this note, we correct two typos contained in the published version of Auray et al. (2012), which affect the quantitative results, without modifying the qualitative results and then the message of the paper. In addition, we present a modified pricing rule for exported goods, and allow export prices to be sticky as well. This extension slightly improves the quantitative predictions of the model. Finally, predictions are made closer to the data when considering an alternative inflation target.     

Seasonality in outliers of daily stock returns: A tail that wags the dog?

We document significant intra-year seasonality in outliers of S&P500 daily rates of return. Controlling for outliers in dummy regressions reveals that both the January and Monday effects turn from insignificant to highly significant. Mean daily return on January doubles and becomes significantly higher than all other months of the year, and Monday's mean return turns significantly positive and higher than other days of the week. The recently documented Halloween effect turns significant only after controlling for outliers as June, August, and September turn out to be months with remarkably low rates of returns. Being random, outliers cannot serve as instrumental variables for designing trading rules, yet, their impact on options pricing through the increase in volatility, may be applied for profitable options strategies.     

A note on the time–series relationship between market industry concentration and market volatility

Using cross-sectional regression analysis, previous studies provide conflicting results regarding the relationship between market industry concentration and market volatility. This paper investigates this relationship in the time–series. Using data from twenty one developed markets and the world market, we find that this relationship is significant and positive in about 61% of the markets: the more concentrated the market, the more volatile the market. We also find that, in 70% of the markets, there exists a causal relationship between market industry concentration and market volatility and the direction of causality runs from the former to the latter. Our results suggest that market industrial structure is a significant factor in explaining market volatility.     

A risk-return explanation of the momentum-reversal “anomaly”

This study investigates the nature of the momentum-reversal phenomenon exhibited by U.S. stock returns from 1962 to 2013. We use cumulative future returns of long–short portfolios, which are formed using prior returns as benchmarks, after portfolio formation to analyze the well-documented momentum-reversal pattern. Contrary to many previous studies our results demonstrate that there is no momentum-reversal anomaly. We show that size (market capitalization), which is often considered a proxy for risk, eventually dominates momentum's initial effect, causing stock prices and, hence, returns to move in the opposite direction. We demonstrate that this latter price movement is likely to be related to institutional trading.     

A note on perceptions of auditors’ internal control report mandated by the PCAOB: Can reformatting the report enhance perceived value added?

The auditor’s report is a critical link in communicating financial data to users. Because of substantial audit costs incurred in integrated audits, the perceived value added by the auditor’s report becomes even more important. The auditor’s report prescribed by Auditing Standard No. 2 (and the new Auditing Standard No. 5) issued by the Public Company Accounting Oversight Board (PCAOB) includes a limitations paragraph. The SAS 58 audit report format that has been in use over 15 years does not contain a limitations paragraph. The SAS 58 report likely serves as a mental frame of reference (a referent report) for users evaluating other independent auditor’s report formats relating to assurance services, including the AS2 and AS5 reports. Whether inclusion of a limitations paragraph could adversely affect the users’ evaluation of the AS2 report is the focus of this study. In light of the publicity given to fraudulent financial reporting and other prevailing economic/environmental conditions, it is reasonable for users to expect that the auditor’s report provide a high degree of assurance regarding material fraud.We extend the [Foster, B. P., McClain, G., Shastri, T. (2005). A note on Pre-Sarbanes-Oxley Act users’ and auditors’ perceptions of a limitations paragraph in the auditor’s internal control report. Research in Accounting Regulations, 18, 195-217] study, by focusing on the AS2 report using data obtained about user perceptions from a field experiment conducted with MBA students. Results suggest that users perceive that an internal control report format without the limitations paragraph will enhance the readability and reliability of the report, and reduce the level of accommodation (additional information) required for decision making. Users perceive that the auditors’ exposure/liability is likely to remain substantially the same whether or not the report format includes a limitations paragraph. Also, users perceive that incorporating fraud wording would further enhance the readability and reliability dimensions of the internal control report format without the limitations paragraph. Taken collectively, the auditor’s report format with fraud wording, but without the limitations paragraph likely maximizes economic benefit accruing to users by minimizing their information risk. Policy-making bodies may find the results and approach taken in this study useful to evaluate report formats for assurance services.     

A note on foreigners’ trading and price effects across firms

We study the investment behavior of foreign investors in association with an equity market liberalization, and find a strong link between foreigners’ trading and local market returns. In the period following the liberalization, net purchases by foreign investors induced a permanent increase in stock prices, suggesting that local firms reduced their cost of equity capital. We also find a strong link between a firm’s fraction of foreign ownership and the magnitude of the cost reduction. Foreign investors seem to prefer large and well-known firms, and these firms realize the largest reduction in capital cost. Furthermore, our analysis suggests that foreigners increase their net holding in firms that have recently performed well. Analyzing foreigners’ performance, we find very little evidence of informed trading, suggesting that risk sharing is the most plausible explanation for the reduction of the cost of equity capital.     

An elusive panacea? The impact of the regulatory valuation regime on insurers' investment behaviour

This paper develops a framework to examine how the interactions between the valuation regime and solvency requirements influence investment behaviour of long-term investors with stable liabilities, such as life insurers. The results contribute to the debate over market-based valuation regimes, and shed light on new hybrid regimes explored in policy circles. We show that solvency requirements based on fair value regime can induce procyclical asset sales, but those based on historical cost valuation encourage insurers to engage in risk-shifting to the detriment of policyholders. A hybrid valuation regime, intended to address these unfavourable outcomes, does not strictly dominate the other two regimes on its own. However, market-based regimes can be made effective, if regulators calibrate their responses to solvency breaches using supervisory information about insurers' asset quality.     

Conglomerates on the rise again? A cross-regional study on the impact of the 2008–2009 financial crisis on the diversification discount

This paper investigates how the 2008–2009 financial crisis affected the value of diversification in different regions of the world, thereby emphasizing the role of the institutional context. We show that the effect of the credit crunch upon the diversification discount varied with the regions' level of capital market maturity and legal environment. In developed Asia Pacific, the British Isles, and North America, we find that the discount on conglomerates fell significantly during the crisis years; however, in Continental Europe – the region possessing the least developed capital markets and lowest legal investor protection in our sample – the impact of the financial meltdown upon the relative value of diversified firms was insignificant. Our study provides additional evidence on factors influencing the relative costs and benefits of diversified firms and highlights in particular the importance of accounting for different institutional settings.     

The chicken or the egg? A note on the dynamic interrelation between government bond spreads and credit default swaps

This note provides the first empirical assessment of the dynamic interrelation between government bond spreads and their associated credit default swaps (CDS). We use data for the Southern European countries (Greece, Italy, Portugal and Spain) that found themselves with a problematic public sector in the dawn of the recent financial distress. We find that CDS prices Granger-cause government bond spreads after the eruption of the 2007 sub-prime crisis. Feedback causality is detected during periods of financial and economic turmoil, thereby indicating that high risk aversion tends to perplex the transmission mechanism between CDS prices and government bond spreads.     

Summary of “evaluating your curriculum”: A report by the Federation of Shools of Accountancy Committee on Assessment of Curriculum Changes

The Accounting Education Change Commission (AECC) has called for change in the accounting curriculum “so that entrants to the accounting profession possess the skills, knowledge, and attitudes required for success in accounting career paths (AAA, 1986). Concluding that “change just for the sake of change may not bring any improvement,” the Federation of Schools of Accountancy (FSA) charged its Committee on Assessment of Curriculum Changes in January, 1991 “ to identify the theories and suggest methods to allow Departments and Schools of Accounting to measure the results of curriculum changes (FSA, 1991).” ¹ This paper summarizes the committee's findings and its recommendations regarding issues that should be addressed by accounting programs undertaking the development of an assessment program.²     

A note on trading mechanism and securities’ value: The analysis of rejects from continuous trade

We examine 97 stocks that moved from continuous trade back to single daily auctions. The response to exit from continuous trade is almost a mirror image of the entry response documented in Amihud et al., 1997 (Amihud, Y., Mendelson, H., Lauterbach, B., 1997. Journal of Financial Economics 45, 365–390). Upon exiting continuous trade, stock liquidity, price accuracy, and value drop. An exception is, however, identified. Ten stocks that were omitted from continuous trade within three months of their addition have negative excess returns upon entry into continuous trade and positive excess returns upon exit. These immediate rejects had relatively low volumes before entering continuous trade, which suggests that for thinly traded stocks simple unassisted continuous trade may not be optimal.     

The influence of cultural tightness–looseness,religiosity, and the institutional environment on tax evasion behaviour: A cross-country study

We examine whether the strength of norms and tolerance for deviations play a role in explaining cross-country differences in tax evasion (TEVA). We also investigate the effects of religiosity, legal enforcement, voice and accountability, and the stability of political systems on TEVA across 48 countries over the period 1997–2018. Results show that the higher the voice and accountability and the lower the degree of cultural tightness–looseness, the rule of law, and political stability, the higher the degree of TEVA across nations. The results are important for policymakers to assess the likelihood of TEVA from a holistic perspective.     

Bayesian estimators of the lognormal–Pareto composite distribution

In this paper, Bayesian methods with both Jeffreys and conjugate priors for estimating parameters of the lognormal–Pareto composite (LPC) distribution are considered. With Jeffreys prior, the posterior distributions for parameters of interest are derived and their properties are described. The conjugate priors are proposed and the conditional posterior distributions are provided. In addition, simulation studies are performed to obtain the upper percentage points of Kolmogorov–Smirnov and Anderson–Darling test statistics. Furthermore, these statistics are used to compare Bayesian and likelihood estimators. In order to clarify and advance the validity of Bayesian and likelihood estimators of the LPC distribution, well-known Danish fire insurance data-set is reanalyzed.     

An extension of the validity of »Student»-Fisher's law of distribution

Abstract

One of the fundamental laws of the distribution of errors within modern theoretical statistics is the »Student»-Fisher law of distribution, which answers the question:     

Discussion of: “Flattening the organization: the effect of organizational reporting structure on budgeting effectiveness”

This paper is a discussion of Hannan et al. (Rev Account Stud, 2010), wherein subordinate-participants are endowed with private information, and superior-participants can potentially affect budget requests through their ability to reject them. Their findings are of interest to research on both the design of budgeting systems and span of control. I discuss the relevance of HRT to these literatures and comment on their implementation and experimental design. Also, I offer suggestions for future research, one of which is to explicitly introduce monitoring into experiments on span of control.     

Discussion of “on the relation between expected returns and implied cost of capital”

This paper discusses the paper “On the relationship between expected returns and implied cost of capital” by Hughes, Liu, and Liu. The discussion focuses on developing the intuition behind the mathematical results and on extensions of the analysis that future research could address.