Value at Risk (VaR) Measurement on a Diversified Portfolio: Decomposition of Idiosyncratic Risk in a Pharmaceutical Industry

Risk measurement is one of the most prominent tools of financial institutions and managers. Many investors try to know potential maximum loss of their financial assets as well as possible. There are many internal and publicly known risk measurement methods in the financial world.  In this study, maximum daily loss of diversified portfolio is calculated by using variance-covariance approach of the Value at Risk (VaR) Models.  Correlation and covariance matrices are used to estimate daily loss. VaR values are estimated both with and without portfolio effect.  Moreover, total risk of portfolio and individual shares are estimated by separating as idiosyncratic and systematic portions. 252 days of data belonging a year of 2015 are analyzed. Keywords: Risk Measurement, VaR, Variance-Covariance approach, Systematic Risk, Idiosyncratic Ris

Optimalisasi Portofolio Menggunakan Capital Asset Pricing Model (Capm) Dan Mean Variance Efficient Portfolio (Mvep) (Studi Kasus: Saham-saham Lq45)

Investment is planting some funds to get profit. However, there is a positive relationship between risk and return that is High Risk High Return. So, the investor seeks to maximize expected return using portfolio optimization. The nature of the stock fluctuates over time, often times it poses a risk to lose money. In the science of finance, the fluctuations of stock returns is known as volatility. Then the stock volatility measurement uses Exponentially Weighted Moving Average (EWMA). Methods of Capital Assets Pricing Model (CAPM) is used for the selection of the best stocks of the nine sectors LQ45. Portfolios are formed of nine sectors were weighted using the Mean-Variance optimal Efficient Portfolio (MVEP). The weight placed on the largest fund shares at IMAS 25.12%, amounting to 19.53% BDMN, BWPT by 6.40%, 9.75% for INCO, SMCB by 7.72%, amounting to 9.37% INDF, BKSL for 2.27%, 16.87% and TLKM of MAPI by 2.98%. Based on analysis, volatility measurement of IMAS, TLKM and BDMN especially using EWMA. Risk measurement tool used for stock portfolio is Value at Risk (VaR) and Risk measurement tool used for stocks is Component Value at Risk (CVaR). With a confidence level of 95% and an investment of IDR 100.000.000 the loss investment using VaR for one day in the future is IDR 1.799.824. Meanwhile, if using CVaR then the maximum loss investment for the day ahead is IDR 1.523.000,73

Variance–Covariance (Delta Normal) Approach of VaR Models: An Example From Istanbul Stock Exchange

Many investors desire to know how much money they can lose for example in a day or in a ten days. In this study, variance-covariance approach of the VaR models is introduced to the reader. It estimates maximum potential loss for a given probability and time horizon. It shows money type one loss value. In a calculation process, firstly, portfolios are created. Then, returns distribution is identified. And lastly, VaR values of portfolios are measured. Daily loss is calculated with using 252 days historical data belonging to the year 2015. Stocks are chosen from Istanbul Stock Exchange (BIST 100 Index).  Calculation is made for both 95 % and 99 % confidence level and one day and ten days holding periods. Keywords: Risk Measurement, VaR, Variance-Covariance approach, correlation, portfolio ris

Problems of Monotonicity of Some Popular Risk Measures

In the article the author checked the properties of coherent measures of risk for Expected Value, Expected Shortfall, Maximum Loss (for losses weighted with probability), Median, Median Absolute Deviation, “Arithmetic Mean of Absolute Deviations from Median”, Quantiles, Cumulative Distribution Function and Mid-Range in connection with the last financial crisis. Methodology of the research – mathematical proving and theoretical analysis. Results. The survey shows that the above functions are not coherent measures of risk with some definition of stochastic order and in many cases not measures of risk in terms of the axiomatic definition. The paper shows also that the lemma used in the literature to prove monotonicity of Expected Shortfall is not truth and we will prove the lemma with the opposite relation. Value of the paper – Mathematical proofs in the field of risk measurement. Showing some problems with monotonicity of risk measures. Contradicting the lemma of monotonicity of Expected Shortfall. Own definition of first degree stochastic order

Perhitungan Risiko Nilai Tukar Atas Posisi Devisa Netto Bank X melalui Pendekatan Value At Risk (VaR)

This study was conducted at the Bank X Jakarta, while the samples from this study are on the Net Open Position. The model used in this study is a descriptive study of quantitative models. The study was conducted to measure the risks that may arise from changes in exchange rates based on net open position of 31 December 2007 and calculate Capital Charge based on Net Open Position as of December 31, 2007. Effective risk management requires measurement attempts to determine the amount of capital that must be prepared to cover the risk and be used for strategic planning activities of foreign exchange by the Bank. Selection of study topics is based on the need for measurement methods that banks will be able to measure the potential risk in a comprehensive manner that is able to measure the sensitivity of the potential risk of product or activity of factors - factors that influence it. The maximum loss on risks resulting from changes in exchange rates are calculated through the approach of Value at Risk (VaR) using Historical Simulation method for each foreign currency and in the form of portfolio under the provisions of the Bank for International Settlements (BIS) as outlined in the provisions of Basel II, which then adopted by Bank Indonesia in PBI. 5/8/PBI/2003 dated May 19, 2003 and the rules of Bank Indonesia Regulation. 9/13/PBI/2007 about the use of internal methods for measuring market risk. The result of exchange rate risk measurement approach to Value at Risk (VaR) with Historical Simulation method ruing a time horizon of 1 day and performed at the 99% confidence level, the losses that may be suffered by Bank X Jakarta on January 1, 2007 is at a maximum of Rp. 507 322 635 762. And based on the calculation of the percentage of capital charge against capital is known that at 116.92% of the total capital charge compared with the total capital. This amount is still above the limit set by Bank Indonesia, which are as high as 30% of the capital

Analysis of operational risk in the South African banking sector using the standardised measurement approach

Abstract : Over the last decade, financial markets across the world have been devastated by operational risk-related incidents. These incidents were caused by a number of aspects, such as, inter alia, fraud, improper business practices, natural disasters, and technology failures. As new losses are incurred, they become part of each financial institution’s internal loss database. The inclusion of these losses has caused notable upward spikes in the operational risk Pillar I regulatory capital charge for financial institutions across the board. The inherent imperfections in people, processes, and systems–be it by intention or oversight–are exposures that cannot be entirely eliminated from bank operations. Thus, the South African Reserve Bank mandates South African financial institutions to reserve capital to cover their idiosyncratic operational risk exposures. Investors fund capital reserves that are held by financial institutions, and these stakeholders demand a viable return on their investment. Consequently, the risk exposure and capital held relationship should be fully understood, managed, and optimised. This thesis extends Sundmacher (2007)’s work through the use of one instance of the Standardised Measurement Approach data against that of the Advanced Measurement Approach, the Standardised Approach, and the Basic Indicator Approach to estimate the potential financial benefit that financial institutions in South Africa could attain or lose, should they move from a Basic Indicator Approach to a Standardised Approach, or from a Standardised Approach to an Advanced Measurement Approach, or from an Advanced Measurement Approach to a Standardised Measurement Approach. The Advanced Measurement Approach, a Loss Distribution Approach coupled with a Monte Carlo simulation was used. Parametric models were imposed to generate the annual loss distribution through the convolution of the annual loss severity and frequency distribution. To fit the internal loss data for each class, the mean annual number of losses was calculated and was assumed to follow a Poisson distribution. The Maximum Likelihood Estimator was used to fit four severity distributions: Lognormal;Weibull; Generalized Pareto; and Burr distributions. To determine the goodness of fit, the Kolmogorov-Smirnov Test at a 5% level of significance was used. To select the best fitting distribution, the Akaike Information Criterion was used. Robustness and stability tests where then performed, using bootstrapping and stress-testing respectively. Overall, we find that the Basel Committee on Banking Supervision’s primary consideration that postulates that there is value in a financial institution moving from the Basic Indicator Approach to the Standardised Approach, or from the Standardised Approach to the Advanced Measurement Approach is indeed valid, but fails in the movement from an Advanced Measurement Approach to a Standardised Measurement Approach. The best Pillar I Capital reprieve is offered by the Diversified Advanced Measurement Approach, whilst the second best is the Standardised Measurement Approach based on an average total loss threshold of €100k (0.87% higher than the Diversified Advanced Measurement Approach), closely followed by the default Standardised Measurement Approach based on average total loss threshold of €20k (5.63% higher than the Diversified Advanced Measurement Approach). To the best of our abilities, we could not find any work that is comprehensive enough to include all four available operational risk quantification approaches (Basic Indicator Approach, Standardised Approach, Advanced Measurement Approach, and Standardised Measurement Approach), for the South African market in particular. This work foresees South African financial institutions pushing back on the implementation of SMA, and potentially lobbying the regulator to remain in AMA – as the alternative might mean increased capital requirements leading to reduced Economic Value Added to shareholders (as more capital is required at the same level of profitability or business activity). The financial institutions are anticipated to sight advanced modelling techniques as helping management have a deeper understanding of their exposures – whilst the Scenario Analysis process allows them a method of identifying their key risks and quantifying them (adding to management’s tools set). However, if South African financial institutions want to compete at a global stage and wanted to be accepted among ‘internationally active’ institutions – their adoption of SMA may not be a choice but an obligation and an entry ticket to the game (global trade).M.Com. (Financial Economics

VALUE AT RISK ANALYSIS ON BLUE CHIP STOCKS PORTFOLIO WITH GAUSSIAN COPULA

Value at Risk (VaR) is a risk measurement tool to calculate the estimated maximum investment loss with a certain confidence level and period. VaR calculations using financial data are often not normally distributed, so the copula method is used, which is flexible on the assumption of normality on stock return data. Previous research discussed Gaussian copula using stocks from the telecommunications sector. In this research, using Gaussian copula on Blue Chip stocks. Blue Chip stocks have a good reputation and have a stable growth rate so they have a lower risk. Therefore, the research objective is to analyze the VaR portfolio of Blue Chip stock with Gaussian copula. This research uses the daily stock closing prices of BBNI and BBTN from November 2, 2020 to October 27, 2022. The analysis results suggested that a VaR portfolio using Gaussian copula with a confidence level of 90%, 95%, and 99%, respectively are 2.24%, 2.88%, and 4.02%. The value shows the percentage of investment risk that may be obtained in the next one-day period. This result also indicates that the higher the confidence level, the greater the VaR

Risk Management in the Financial Services Sector—Applicability and Performance of VaR Models in Pakistan

Financial services sector has become a major driver of economic growth in the developing countries through innovation in response to the forces of globalisation and technology. Sound risk management practices by financial institution are critical to the stability of the institutions and to the sustainability of economic growth. Therefore, measurement of market risk is important to all market participants for devising risk management strategies. Value-at-Risk (VaR) is the most widely used measure of market risk, which is defined as the maximum possible loss to the value of financial assets with a given probability over a certain time horizon. However, the task of implementing the VaR approach still remains a challenge as the empirical return distributions are found to be fat tailed and skewed in contrast to the normal distribution as assumed in the theoretical models. An extensive literature in finance (e.g., Nassim Taleb’s The Black Swan) underscores the importance of rare events in asset pricing and portfolio choice. These rare events may materialise in the shape of a large positive or negative investment returns, a stock market crash, major defaults, or the collapse of risky asset prices

THE APPLICATION OF GUMBEL COPULA TO ESTIMATE VALUE AT RISK WITH BACKTESTING IN TELECOMMUNICATION STOCK

The Value at Risk (VaR) method refers to a statistical risk measurement tool used to determine the maximum loss of an investment, while the distribution that must be met is the normal distribution. This is not in line with the actual situation, because the distribution of the return value is found to be not normally distributed but depends on market conditions that occurred at that time, thus invalidating the VaR estimate and resulting in greater portfolio risk. Therefore, in this study, the estimation of risk value will be carried out using the Gumbel Copula method which can model the dependency structure between stocks and is flexible enough to model financial return data from https://finance.yahoo.com/. The parameter estimates produced by the Gumbel Copula method are then used to calculate the VaR at 90%, and 99% confidence levels. The resulting VaR values ​​are 0,076 and 0.231. To test the feasibility of the VaR model, backtesting was carried out and concluded that the VaR value obtained was valid and suitable for use in the risk assessment of PT. XL Axiata Tbk and PT. Telkomunikasi Indonesia Tbk

PERBANDINGAN METODE VARIANCE COVARIANCE DAN HISTORICAL SIMULATION UNTUK MENGUKUR RISIKO INVESTASI REKSA DANA

One of the instruments of financial assets are investments in mutual funds. Every day of the total fair value of the assets in the mutual fund is always changing because the market value of each type of asset that is changing. Thus causing mutual fund has a risk. It is necessary for the measurement of risk in mutual funds using the Value at Risk (VaR). There are three methods of calculating the VaR Variance-covariance method, Monte Carlo simulation methods and methods Historical Simulation. In this study, the variance-covariance method used and the Historical Simulation method to measure potential losses on investments largest mutual fund shares at 95% confidence level. The test used is the Kolmogorov-Smirnov normality test and Kupiec test return data to test the accuracy of the calculation of VaR. Because the data are not normally distributed returns, the adjustment is then performed using the Cornish-Fisher Expansion. By using the t test results show that the calculation of VaR with variance-covariance and Historical Simulation did not differ significantly. The test results show that the accuracy of the VaR VaR accurately all used to measure the magnitude of the maximum potential loss on investments in mutual fund shares. Keywords : Value at Risk (VaR), Variance-covariance, Historical Simulation, Mutual Fund, Risk