Body and tail: an automated tail-detecting procedure

Hoffmann, Ingo; Börner, Christoph J.

doi:10.21314/jor.2020.447

Cited by 3 publications

(12 citation statements)

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“…This article follows a novel approach described by Hoffmann and Börner (2020a, 2020b, 2021 to automatically determine the optimal threshold for the tail of an unknown parent distribution. We denote negative returns as positive values as this analysis aims to describe extreme negative events (returns).…”

Section: Methodsmentioning

confidence: 99%

“…As this article finds higher riskiness in the analysed cryptocurrencies, we extend our analysis and apply the Extreme Value Theory to investigate extreme tail risks. For that we rely on a novel procedure described by Hoffmann and Börner (2020a, 2020b, 2021. Our analysis indicates, that cryptocurrency return series are not independent and identically distributed.…”

Section: Introductionmentioning

confidence: 99%

“…By calculating the confidence levels (p-values) the quality of the model can be measured. The p-value measures the probability of being mistaken, if the estimated GPD as the tail model is rejected, and should be close to 100%(Hoffmann and Börner 2020a).…”

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confidence: 99%

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Assessing the Risk Characteristics of the Cryptocurrency Market: A GARCH-EVT-Copula Approach

Bruhn

Ernst

2022

JRFM

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The cryptocurrency market offers significant investment opportunities but also entails higher risks as compared to other asset classes. This article aims to analyse the financial risk characteristics of individual cryptocurrencies and of a broad cryptocurrency market portfolio. We construct a portfolio comprising the 20 largest cryptocurrencies, which cover 82.1% of the total cryptocurrency market. The returns are examined for extreme tail risks by the application of Extreme Value Theory. We utilise the GARCH-EVT approach in combination with a novel algorithm to automatically determine the optimal threshold to model the tail distribution. Furthermore, we aggregate the individual market risks with a t-Student Copula to investigate possible diversification effects on a portfolio level. The empirical analysis indicates that all examined cryptocurrencies show high volatility in their price movements, whereby Bitcoin acts as the most stable cryptocurrency. All return distributions are heavy-tailed and subject to extreme tail risks. We find strong, positive intra-market correlations, in particular with the two largest cryptocurrencies Bitcoin and Ethereum. No diversification effect can be achieved by aggregating market risks. On the contrary, a negligibly lower expected return and higher joint extreme returns can be observed. From this analysis, it can be concluded that investments in individual cryptocurrencies as well as in a portfolio show extreme risks of losses. From the investor’s point of view, a possible strategy of risk reduction through portfolio formation within cryptocurrencies is only promising to a limited extent and does not offer a satisfactory solution to significantly reduce the risk within this asset class.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Assessing the Risk Characteristics of the Cryptocurrency Market: A GARCH-EVT-Copula Approach

Bruhn

Ernst

2022

JRFM

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“…In this regard, this study examines the question which class of distribution functions models CC returns most accurately. We answer this question using a novel approach to separate a distribution's body from its tail proposed by Hoffmann and Börner (2021). By doing so we are able determine the risk and statistical properties associated with CCs and provide valuable implications for portfoliomanagement and regulators alike.…”

Section: Introductionmentioning

confidence: 99%

“…Given this background, the generalized Pareto distribution (GPD), a statistical distribution which appears to model heavy tail properties more accurately, is used in further studies Gkillas and Katsiampa, 2018). Following the approach presented in Hoffmann and Börner (2021), we therefore attempt to use a combination of both described distributions. Analytically discovering the beginning of the tail of the analyzed return distributions, enables us to split the given data into a body and a tail for each of which we implement a different distribution.…”

Section: Introductionmentioning

confidence: 99%

On the Return Distributions of a Basket of Cryptocurrencies and Subsequent Implications

Börner¹,

Hoffmann²,

Krettek³

et al. 2021

Preprint

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This paper evaluates and assesses the risk associated with capital allocation in cryptocurrencies (CCs). In this regard, we take a basket of 27 CCs and the CC index EWCI − into account. After considering a series of statistical tests we find the stable distribution (SDI) to be the most appropriate to model the body of CCs returns. However, as we find the SDI to possess less favorable properties in the tail area for high quantiles, the generalized Pareto distribution is adapted for a more precise risk assessment. We use a combination of both distributions to calculate the Value at Risk and the Conditional Value at Risk, indicating two subgroups of CCs with differing risk characteristics.

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Tail Risks in Corporate Finance: Simulation-Based Analyses of Extreme Values

Börner,

Ernst,

Hoffmann

2023

JRFM

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Recently, simulation-based methods for assessing company-specific risks have become increasingly popular in corporate finance. This is because modern capital market theory, with its assumptions of perfect and complete capital markets, cannot satisfactorily explain the risk situation in companies and its effects on entrepreneurial success. Through simulation, the individual risks of a company can be aggregated, and the risk effect on a target variable can be shown. The aim of this article is to investigate which statistical methods can best assess tail risks in the overall distribution of the target variables. By doing so, the article investigates whether extreme value theory is suitable to model tail risks in a business plan independent of company-specific data. For this purpose, the simulated cash flows of a medium-sized company are analyzed. Different statistical ratios, statistical tests, calibrations, and extreme value theory are applied. The findings indicate that the overall distribution of the simulated cash flows can be multimodal. In the example studied, the potential loss side of the cash flow exhibits a superimposed, well-delimitable second distribution. This tail distribution is extensively analyzed through calibration and the application of extreme value theory. Using the example studied, it is shown that similar tail risk distributions can be modeled both by calibrating the simulation data in the tail and by using extreme value theory to describe it. This creates the possibility of working with tail risks even if only a few planning data are available. Thus, this approach contributes to systematically combining risk management and corporate finance and significantly improving corporate risk management. Based on these findings, further analyses can be performed in terms of risk coverage potential and rating to improve the risk situation in a company.

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Body and tail: an automated tail-detecting procedure

Cited by 3 publications

References 0 publications

Assessing the Risk Characteristics of the Cryptocurrency Market: A GARCH-EVT-Copula Approach

Assessing the Risk Characteristics of the Cryptocurrency Market: A GARCH-EVT-Copula Approach

On the Return Distributions of a Basket of Cryptocurrencies and Subsequent Implications

Tail Risks in Corporate Finance: Simulation-Based Analyses of Extreme Values

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