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Report on Analysis of the 260-Day Value at Risk (VAR) of Portfolio of Shares

Report on Analysis of the 260-Day Value at Risk (VAR) of Portfolio of Shares
Author: Calvin Monroe
Publisher: GRIN Verlag
Total Pages: 19
Release: 2014-02-28
Genre: Business & Economics
ISBN: 365660536X

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Scientific Essay from the year 2012 in the subject Business economics - Investment and Finance, grade: B, King`s College London, language: English, abstract: For quite a long time now the main concern for investors as well as regulators of financial markets has been the risk of catastrophic market and the sufficiency of capital needed to counter such kind of risk when it occurs. Many institutions have undergone loses despite their gigantic nature and good forecasting and this has been associated with inappropriate forms of pricing and poor management together with the fraudulent cases, factors that have always brought the issue of managing risk and regulating these financial markets to the level of public policy as well as discussion. A basic tool that has been identified as being effective in the assessment of financial risk is the Value at Risk (VaR) process (Artzner, et al., 1997). The VaR has been figured out as being an amount that is lost on a given form of portfolio including a small probability in a certain fixed period of time counted in terms of days. VaR however poses a major challenge during its implementation and this has more to do with the specification of the kind of probability distribution having extreme returns that is made use of during the calculation of the estimates used in the VaR analysis (Mahoney, 1996; McNeil & Frey, 2000; Dowd, 2001). As has been noted, the nature of VaR estimation majorly does depend on the accurate predictions of some uncommon events or risks that are catastrophic. This is attributed to the fact that VaR is a calculation made from the lowest portfolio returns. For this reason, any form of calculation that is employed in the estimation of VaR must be able to encompass the tail events’ prediction and make this its primary goal (Chiang, et al., 2007; Engle, 2002; Engle & Kroner, 1995; Engle & Rothschild, 1990; Francis, et al., 2001). There have been statistical techniques as well as thumb rules that many researchers argue as having been very instrumental in the prediction and analysis of intra-day and in most cases day-to-day risk. These are however; not appropriate for the analysis of VaR. The predictions of VaR now fall under parametric predictions that encompass conditional volatilities and non-parametric prediction that incorporate the unconditional volatilities (Jorion, 2006; Jorion, 2007).


Comparative Analysis of Value at Risk (VAR) Methods for Portfolio with Non-Linear Return

Comparative Analysis of Value at Risk (VAR) Methods for Portfolio with Non-Linear Return
Author: Manohar Lal
Publisher:
Total Pages: 14
Release: 2013
Genre:
ISBN:

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In this study various value at risk methods such as Historical Simulation, Variance-Covariance Approach and Monte Carlo Simulation are calculated, compared and tested for accuracy. Backtesting for the VaR methods is applied to check the accuracy of the VaR methods. The portfolio includes equally weighted three banking stock and one at-the-money (ATM) call option for one of the banking stock in the portfolio. The log return for the portfolio and individual investments are calculated. Different VaR calculation methods are used to calculate the downside risk of the portfolio and individual investments. VaR is calculated at 95% and 99% confidence level for the portfolio and individual securities. The value at risk for the portfolio at 95% confidence level from all the three methods are within the defined level of downside risk, while at 99% confidence level only Mote Carlo Simulation method provides good approximation of downside risk for a portfolio with options. Thus from this study it is inferred that for instrument or portfolio with non-linear return structure Monte Carlo simulation method provide good approximation of the downside risk.


Market Risk Analysis, Value at Risk Models

Market Risk Analysis, Value at Risk Models
Author: Carol Alexander
Publisher: John Wiley & Sons
Total Pages: 503
Release: 2009-02-09
Genre: Business & Economics
ISBN: 0470997885

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Written by leading market risk academic, Professor Carol Alexander, Value-at-Risk Models forms part four of the Market Risk Analysis four volume set. Building on the three previous volumes this book provides by far the most comprehensive, rigorous and detailed treatment of market VaR models. It rests on the basic knowledge of financial mathematics and statistics gained from Volume I, of factor models, principal component analysis, statistical models of volatility and correlation and copulas from Volume II and, from Volume III, knowledge of pricing and hedging financial instruments and of mapping portfolios of similar instruments to risk factors. A unifying characteristic of the series is the pedagogical approach to practical examples that are relevant to market risk analysis in practice. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Parametric linear value at risk (VaR)models: normal, Student t and normal mixture and their expected tail loss (ETL); New formulae for VaR based on autocorrelated returns; Historical simulation VaR models: how to scale historical VaR and volatility adjusted historical VaR; Monte Carlo simulation VaR models based on multivariate normal and Student t distributions, and based on copulas; Examples and case studies of numerous applications to interest rate sensitive, equity, commodity and international portfolios; Decomposition of systematic VaR of large portfolios into standard alone and marginal VaR components; Backtesting and the assessment of risk model risk; Hypothetical factor push and historical stress tests, and stress testing based on VaR and ETL.


Value at Risk and Expected Stock Returns

Value at Risk and Expected Stock Returns
Author: Turan G. Bali
Publisher:
Total Pages:
Release: 2012
Genre:
ISBN:

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Stock size, liquidity, and value at risk (VAR) can explain the cross-sectional variation in expected returns, but market beta and total volatility have almost no power to capture the cross-section of expected returns at the stock level. Furthermore, the strong positive relationship between average returns and VAR is robust for different investment horizons and loss-probability levels. In addition to the cross-sectional regressions at the stock level, this study used a time-series approach to test the empirical performance of VAR at the portfolio level. The results, based on 25 size/book-to-market portfolios, indicate that VAR has additional explanatory power after the characteristics of market return, size, book-to-market ratio, and liquidity are controlled for.


Value-at-Risk for Greek Stocks

Value-at-Risk for Greek Stocks
Author: Timotheos Angelidis
Publisher:
Total Pages: 28
Release: 2005
Genre:
ISBN:

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This paper analyses the application of several volatility models to forecast daily Value-at-Risk (VaR) both for single assets and portfolios. We calculate the VaR number for 4 Greek stocks, 2 portfolios based on these securities and for Athens Stock Exchange General Index (ASE). We model VaR for long and short trading positions by employing non-parametric methods, such as historical and filtered historical simulation, and parametric ones. Especially for the later techniques we use a collection of ARCH models (GARCH, EGARCH and TARCH) based on three distributional assumptions (Normal, Student-T and Skewed Student-T), while we combine the Extreme Value Theory with a volatility updating technique (via GARCH type-modeling). In order to choose one model among the various forecasting methods, we employ a two-stage backtesting procedure. In the first one, we implement two backtesting criteria (unconditional and conditional coverage) to test the statistical accuracy of the models. In the second stage, we employ standard forecast evaluation methods in order to examine whether the diferences between the models, which have converged suficiently, are statistically significant.


Estimating the Accuracy of Value-at-Risk (VAR) in Measuring Risk in Equity Investment in India

Estimating the Accuracy of Value-at-Risk (VAR) in Measuring Risk in Equity Investment in India
Author: Vanita Tripathi
Publisher:
Total Pages: 31
Release: 2008
Genre:
ISBN:

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Over the past few years, the Value-at-Risk (VaR) has become a standard measure of market risk embraced by banks, trading firms, mutual funds and others, including even the non financial firms. But any risk measure is useful and reliable only insofar as it can be verified for its accuracy. This paper attempts to evaluate the accuracy of VaR in estimating the risk in equity investment in India. For this purpose we have used daily data for 30 securities comprising BSE-Sensex and two major stock indices- BSE Sensex and NSE Nifty for the period January 2006 to February 2007 and portfolio-normal method (parametric approach to VaR calculation) for calculation of VaR. The hypothesis regarding accuracy of VaR estimates has been tested using Chi-square test. The results show that VaR estimate does not accurately measure the risk in equity investment in India as VaR overestimates the loss in 24 securities out of 30 securities. It is only in case of 4 securities that the observed number of violations is exactly equal to the expected number. These results may be attributed to non-normal distribution of equity returns in Indian securities market as against the normally distributed returns assumed under portfolio-normal method. All the securities are showing excess kurtosis estimate, exhibiting the leptokurtic returns' distribution and also, out of 30 securities, 20 are showing negatively skewed returns and 10 are showing positively skewed returns. Moreover the assumption of past representing the future is also not validated in the present case in the context of stock volatility observed during the period. We have also observed that portfolio- normal method of VaR computation is a better risk measure for estimating portfolio risk as compared to risk on individual securities.


Properties and Computation of Value at Risk Efficient Portfolios Based on Historical Data

Properties and Computation of Value at Risk Efficient Portfolios Based on Historical Data
Author: Alexei A. Gaivoronski
Publisher:
Total Pages: 31
Release: 2002
Genre:
ISBN:

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Value at risk (VaR) is an important and widely used measure of the extent to which a given portfolio is subject to risk present in financial markets. Considerable amount of research was dedicated during recent years to development of acceptable methods for evaluation of this risk measure.In this paper, we present a method of calculating the portfolio which gives the optimal VaR among those, which yield at least some specified expected return. This method allows to calculate the mean-VaR efficient frontier. The method is based on approximation of historic VaR by smoothed VaR (SVaR) which filters out local irregular behavior of historic VaR function.Moreover, we compare the VaR as a risk measure to other well known measures of risk such as the conditional value at risk (CVaR) and the standard deviation.It turns out, that the corresponding efficient frontiers are quite different. An investor, who wants to control his VaR should not look at portfolios lying on other than the VaR efficient frontier, although the calculation of this frontier is algorithmically more complex compared to other frontiers.


CFA Program Curriculum 2017 Level I, Volumes 1 - 6

CFA Program Curriculum 2017 Level I, Volumes 1 - 6
Author: CFA Institute
Publisher: John Wiley & Sons
Total Pages: 3708
Release: 2016-08-01
Genre: Business & Economics
ISBN: 1119316006

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Clear, concise instruction for all CFA Level I concepts and competencies for the 2017 exam The same official curricula that CFA Program candidates receive with program registration is now available publicly for purchase. CFA Program Curriculum 2017 Level I, Volumes 1-6 provides the complete Level I Curriculum for the 2017 exam, delivering the Candidate Body of Knowledge (CBOK) with expert instruction on all ten topic areas of the CFA Program. Fundamental concepts are explained with in-depth discussion and a heavily visual style, while cases and examples demonstrate how concepts apply in real-world scenarios. Coverage includes ethical and professional standards, quantitative analysis, economics, financial reporting and analysis, corporate finance, equities, fixed income, derivatives, alternative investments, and portfolio management, all organized into individual sessions with clearly defined Learning Outcome Statements. Charts, graphs, figures, diagrams, and financial statements illustrate concepts to facilitate retention, and practice questions provide the opportunity to gauge your understanding while reinforcing important concepts. The Level I Curriculum covers a large amount of information; this set breaks the CBOK down into discrete study sessions to help you stay organized and focused on learning-not just memorizing-important CFA concepts. Learning Outcome Statement checklists guide readers to important concepts to derive from the readings Embedded case studies and examples throughout demonstrate practical application of concepts Figures, diagrams, and additional commentary make difficult concepts accessible Practice problems support learning and retention CFA Institute promotes the highest standards of ethics, education, and professional excellence among investment professionals. The CFA Program Curriculum guides you through the breadth of knowledge required to uphold these standards. The three levels of the program build on each other. Level I provides foundational knowledge and teaches the use of investment tools; Level II focuses on application of concepts and analysis, particularly in the valuation of assets; and Level III builds toward synthesis across topics with an emphasis on portfolio management.


Value at Risk in Emerging Markets

Value at Risk in Emerging Markets
Author: Helder Centeno
Publisher:
Total Pages: 0
Release: 2006
Genre: Financial risk managment
ISBN:

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This study focuses on the relative performance of three Value-at-Risk (VaR) estimation methodologies. The daily stock market index returns of twelve different emerging markets are used for the empirical analysis. In addition to the well-known methodologies, such as the historical simulation and GARCH-based ones, the extreme value theory (EVT) is also used to estimate the daily VaR. In this paper, we focus on EVT because it studies the non-linear estimation of the tails and we expect to find many extreme events when analysing the return distributions in these twelve emerging markets. We focus on the negative extreme events rather than on the positive ones. The daily VaR is forecasted at three different quantile levels: 90%, 97.5%, 99.9%; and competing methodologies are back-tested accordingly. The results indicate that the historical simulation and GARCH-based methodologies work better at lower quantile levels than they do at higher quantile levels, while VaR estimated using EVT is more accurate at higher quantiles. EVT provides better information about extreme events, especially when financial distress occurs in these economies.