Value at Risk, Capital Management, and Capital Allocation

2007 ◽  
pp. 1-5 ◽  
Author(s):  
Francesco Saita
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Capital Allocation ◽  
Capital Management ◽  
Risk Capital

Modelling random vectors of dependent risks with different elliptical components

2021 ◽  
pp. 1-19
Author(s):  
Zinoviy Landsman ◽  
Tomer Shushi
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Degrees Of Freedom ◽  
Risk Measures ◽  
Capital Allocation ◽  
Risk Capital ◽  
Dependent Risks ◽  
Risk Capital Allocation ◽  
Elliptical Copula ◽  
T Distribution

Abstract In Finance and Actuarial Science, the multivariate elliptical family of distributions is a famous and well-used model for continuous risks. However, it has an essential shortcoming: all its univariate marginal distributions are the same, up to location and scale transformations. For example, all marginals of the multivariate Student’s t-distribution, an important member of the elliptical family, have the same number of degrees of freedom. We introduce a new approach to generate a multivariate distribution whose marginals are elliptical random variables, while in general, each of the risks has different elliptical distribution, which is important when dealing with insurance and financial data. The proposal is an alternative to the elliptical copula distribution where, in many cases, it is very difficult to calculate its risk measures and risk capital allocation. We study the main characteristics of the proposed model: characteristic and density functions, expectations, covariance matrices and expectation of the linear regression vector. We calculate important risk measures for the introduced distributions, such as the value at risk and tail value at risk, and the risk capital allocation of the aggregated risks.

scholarly journals Sharing Risk – An Economic Perspective

2009 ◽  
Vol 39 (2) ◽  
pp. 591-613 ◽  
Author(s):  
Andreas Kull
Keyword(s):  
Value At Risk ◽  
Risk Sharing ◽  
Risk Measures ◽  
Insurance Industry ◽  
Risk Measure ◽  
Capital Allocation ◽  
Risk Capital ◽  
Risk Class ◽  
Capital Costs ◽  
Risk Transfer

AbstractWe revisit the relative retention problem originally introduced by de Finetti using concepts recently developed in risk theory and quantitative risk management. Instead of using the Variance as a risk measure we consider the Expected Shortfall (Tail-Value-at-Risk) and include capital costs and take constraints on risk capital into account. Starting from a risk-based capital allocation, the paper presents an optimization scheme for sharing risk in a multi-risk class environment. Risk sharing takes place between two portfolios and the pricing of risktransfer reflects both portfolio structures. This allows us to shed more light on the question of how optimal risk sharing is characterized in a situation where risk transfer takes place between parties employing similar risk and performance measures. Recent developments in the regulatory domain (‘risk-based supervision’) pushing for common, insurance industry-wide risk measures underline the importance of this question. The paper includes a simple non-life insurance example illustrating optimal risk transfer in terms of retentions of common reinsurance structures.

Boom and Bust Driven by Value-at-Risk

2019 ◽  
pp. 28-55
Author(s):  
Hyun Song Shin
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Hedge Fund ◽  
Balance Sheet ◽  
Asset Returns ◽  
Expected Returns ◽  
Capital Management ◽  
A Value ◽  
Boom And Bust

An example of a hedge fund illustrates a long-short strategy that maximises expected returns subject to a Value-at-Risk strategy. Balance sheet capacity depends on the measured volatility of asset returns and the book equity of the long-short hedge fund. The principles are illustrated by the case of Long Term Capital Management (LTCM).

scholarly journals The Value-At-Risk Estimate of Stock and Currency-Stock Portfolios’ Returns

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 133 ◽  
Author(s):  
Jung-Bin Su ◽  
Jui-Cheng Hung
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Suitable Model ◽  
Conditional Correlation ◽  
Risk Capital ◽  
Forecast Performance ◽  
Stock Portfolios ◽  
Out Of Sample ◽  
Efficiency Test ◽  
Risk Managers

This study utilizes the seven bivariate generalized autoregressive conditional heteroskedasticity (GARCH) models to forecast the out-of-sample value-at-risk (VaR) of 21 stock portfolios and seven currency-stock portfolios with three weight combinations, and then employs three accuracy tests and one efficiency test to evaluate the VaR forecast performance for the above models. The seven models are constructed by four types of bivariate variance-covariance specifications and two approaches of parameters estimates. The four types of bivariate variance-covariance specifications are the constant conditional correlation (CCC), asymmetric and symmetric dynamic conditional correlation (ADCC and DCC), and the BEKK, whereas the two types of approach include the standard and non-standard approaches. Empirical results show that, regarding the accuracy tests, the VaR forecast performance of stock portfolios varies with the variance-covariance specifications and the approaches of parameters estimate, whereas it does not vary with the weight combinations of portfolios. Conversely, the VaR forecast performance of currency-stock portfolios is almost the same for all models and still does not vary with the weight combinations of portfolios. Regarding the efficiency test via market risk capital, the NS-BEKK model is the most suitable model to be used in the stock and currency-stock portfolios for bank risk managers irrespective of the weight combination of portfolios.

scholarly journals Analytical Bounds for two Value-at-Risk Functionals

2002 ◽  
Vol 32 (2) ◽  
pp. 235-265 ◽  
Author(s):  
Werner Hürlimann
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Decision Makers ◽  
Conditional Value At Risk ◽  
General Interest ◽  
Dominance Order ◽  
Risk Capital ◽  
Time Period ◽  
Aggregate Loss ◽  
Stop Loss

AbstractBased on the notions of value-at-risk and conditional value-at-risk, we consider two functionals, abbreviated VaR and CVaR, which represent the economic risk capital required to operate a risky business over some time period when only a small probability of loss is tolerated. These functionals are consistent with the risk preferences of profit-seeking (and risk averse) decision makers and preserve the stochastic dominance order (and the stop-loss order). This result is used to bound the VaR and CVaR functionals by determining their maximal values over the set of all loss and profit functions with fixed first few moments. The evaluation of CVaR for the aggregate loss of portfolios is also discussed. The results of VaR and CVaR calculations are illustrated and compared at some typical situations of general interest.

MEASURING DEFAULT RISK FOR A PORTFOLIO OF EQUITIES

2019 ◽  
Vol 22 (01) ◽  
pp. 1950012
Author(s):  
MATHEUS PIMENTEL RODRIGUES ◽  
ANDRE CURY MAIALY
Keyword(s):  
At Risk ◽  
Default Risk ◽  
Value At Risk ◽  
Risk Measure ◽  
Capital Allocation ◽  
Banking Supervision ◽  
Merton Model ◽  
One Year ◽  
The One ◽  
A Company

This work evaluates some changes proposed by the Basel Committee on Banking Supervision in regulating capital allocation in the trading book for equities following a company default. In the last decade, the committee designed some measures to account for the risk of a company default that the ten-day value-at-risk measure does not capture. The first and more conservative measure designed to capture the effect of defaults was the incremental risk charge. With time, this measure evolved into the default risk charge. We use a Merton model to compute the probability of default and compare this probability to simulated asset returns in order to compute the one-year value-at-risk and capture the risk of a company default. The analysis compares portfolios of Ibovespa companies and S&P 500 companies. Additionally, we propose a method to account for the correlation in the companies and compare the effects of the standard method of capital allocation to those of our models.

Value-at-risk and related measures for the Bitcoin

2018 ◽  
Vol 19 (2) ◽  
pp. 127-136 ◽  
Author(s):  
Stavros Stavroyiannis
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Capital Allocation ◽  
Capital Requirements ◽  
Spot Price ◽  
Content Type ◽  
Type Iv ◽  
Pearson Type ◽  
Standard And Poor's

Purpose The purpose of this paper is to examine the value-at-risk and related measures for the Bitcoin and to compare the findings with Standard and Poor’s SP500 Index, and the gold spot price time series. Design/methodology/approach A GJR-GARCH model has been implemented, in which the residuals follow the standardized Pearson type-IV distribution. A large variety of value-at-risk measures and backtesting criteria are implemented. Findings Bitcoin is a highly volatile currency violating the value-at-risk measures more than the other assets. With respect to the Basel Committee on Banking Supervision Accords, a Bitcoin investor is subjected to higher capital requirements and capital allocation ratio. Practical implications The risk of an investor holding Bitcoins is measured and quantified via the regulatory framework practices. Originality/value This paper is the first comprehensive approach to the risk properties of Bitcoin.

scholarly journals Avaliação de Modelos de Cálculo de Exigência de Capital para Risco Cambial

2005 ◽  
Vol 3 (2) ◽  
pp. 223
Author(s):  
Claudio H. da S. Barbedo ◽  
Gustavo S. Araújo ◽  
João Maurício S. Moreira ◽  
Ricardo S. Maia Clemente
Keyword(s):  
At Risk ◽  
Financial Institutions ◽  
Value At Risk ◽  
Hybrid Approach ◽  
Capital Allocation ◽  
Capital Requirements ◽  
Internal Models ◽  
Capital Requirement ◽  
Brazilian Legislation ◽  
Historical Model

This paper examines capital requirement for financial institutions in order to cover market risk stemming from exposure to foreign currencies. The models examined belong to two groups according to the approach involved: standardized and internal models. In the first group, we study the Basel model and the model adopted by the Brazilian legislation. In the second group, we consider the models based on the concept of value at risk (VaR). We analyze the single and the double-window historical model, the exponential smoothing model (EWMA) and a hybrid approach that combines features of both models. The results suggest that the Basel model is inadequate to the Brazilian market, exhibiting a large number of exceptions. The model of the Brazilian legislation has no exceptions, though generating higher capital requirements than other internal models based on VaR. In general, VaR-based models perform better and result in less capital allocation than the standardized approach model applied in Brazil.

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