• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.389-407
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• 2006

Extreme value theory has been used widely in many areas of science and engineering to deal with the assessment of extreme events which are rare but have catastrophic consequences. The potential of extreme value theory has only been recognized recently in finance area. In this paper, we provide an overview of extreme value theory for estimating and assessing value at risk and expected shortfall which are the methods for modelling and measuring the extreme financial risks. We illustrate that the approach based on extreme value theory is very useful for estimating tail related risk measures through backtesting of an empirical data.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.29-43
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• 2012

Financial data such as stock index returns and exchange rates have the properties of heavy tail and asymmetry compared to normal distribution. When we estimate VaR using the GARCH model (with the conditional return distribution of normal) it shows the tendency of the lower estimation and clustering in the losses over the estimated VaR. In this paper, we argue that this problem can be resolved through the adaptation of the unbounded Johnson distribution as that of the condition return. We also compare this model with the GARCH with the conditional return distribution of normal and student-t. Using the losses exceed the ex-ante VaR, estimates, we check the validity of the GARCH models through the failure proportion test and the clustering test. We nd that the GARCH model with conditional return distribution of unbounded Johnson provides an appropriate estimation of the VaR and does not occur the clustering of violations.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.825-835
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• 2008

Multivariate GARCH(MGARCH) has been useful in financial studies and econometrics for modeling volatilities and correlations between components of multivariate time series. An obvious drawback lies in that the number of parameters increases rapidly with the number of variables involved. This thesis tries to resolve the problem by using dimension reduction technique. We briefly review both factor models for dimension reduction and the MGARCH models including EWMA (Exponentially weighted moving-average model), DVEC(Diagonal VEC model), BEKK and CCC(Constant conditional correlation model). We create meaningful portfolios obtained after reducing dimension through statistical factor models and fundamental factor models and in turn these portfolios are applied to MGARCH. In addition, we compare portfolios by assessing MSE, MAD(Mean absolute deviation) and VaR(Value at Risk). Various financial time series are analyzed for illustration.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1333-1343
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• 2014

Hansen and Lund (2005) documented that a univariate GARCH(1,1) model is no worse than other sophisticated GARCH models in terms of prediction errors such as MSPE and MAE. Here, we extend Hansen and Lund (2005) by considering multivariate GARCH models and incorporating risk management measures such as VaR and fail percentage. Our Monte Carlo simulations study shows that multivariate GARCH(1,1) model also performs well compared to asymmetric GARCH models. However, we suggest that actual model selection should be done with care in light of risk management. It is applied to the realized volatilities of KOSPI, NASDAQ and HANG SENG index for recent 10 years.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.169-180
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• 2017

Multivariate GARCH models are interested in conditional variances (volatilities) as well as conditional correlations between return time series. This paper is concerned with high-frequency multivariate financial time series from which realized volatilities and realized conditional correlations of intra-day returns are calculated. Existing multivariate GARCH models are reviewed comparatively with the realized volatility via canonical correlations and value at risk (VaR). Korean stock prices are analysed for illustration.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1479-1494
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• 2015

Since the Markowitz's mean-variance framework for portfolio analysis, the topic of portfolio optimization has been an important topic in finance. Traditional approaches focus on maximizing the expected return of the portfolio while minimizing its variance, assuming that risky asset returns are normally distributed. The normality assumption however has widely been criticized as actual stock price distributions exhibit much heavier tails as well as asymmetry. To this extent, in this paper we employ the genetic algorithm to find the optimal portfolio under the Value-at-Risk (VaR) constraint, where the tail of risky assets are modeled with the generalized Pareto distribution (GPD), the standard distribution for exceedances in extreme value theory. An empirical study using Korean stock prices shows that the performance of the proposed method is efficient and better than alternative methods.

• The Korean Journal of Applied Statistics
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• v.22 no.2
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• pp.261-270
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• 2009

Current financial crisis triggered by shaky U.S. banking system adds to the emphasis on the importance of the volatility in controlling and understanding financial time series data. The ARCH and GARCH models have been useful in analyzing economic time series volatilities. In particular, multivariate GARCH(MGARCH, for short) provides both volatilities and conditional correlations between several time series and these are in turn applied to computations of hedge-ratio and VaR. In this short article, we try to assess various MGARCH models with respect to the back-testing performances in VaR study. To this end, 14 korean stock prices are analyzed and it is found that MGARCH outperforms rolling window, and BEKK and CCC are relatively conservative in back-testing performance.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.741-752
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• 2016

Numerous studies have shown that normal inverse Gaussian (NIG) distribution adequately fits the empirical return distribution of financial securities. The estimation of parameters can also be done relatively easily, which makes the NIG distribution more useful in financial markets. The maximum likelihood estimation and the method of moments estimation are easy to implement; however, we may encounter a problem in practice when a relationship among the moments is violated. In this paper, we investigate this problem in the parameter estimation and try to find a simple solution through simulations. We examine the effect of our adjusted estimation method with real data: daily log returns of KOSPI, S&P500, FTSE and HANG SENG. We also checked the performance of our method by computing the value at risk of daily log return data. The results show that our method improves the stability of parameter estimation, while it retains a comparable performance in goodness-of-fit.

• The Journal of the Korea Contents Association
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• v.21 no.11
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• pp.320-332
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• 2021

This paper investigates the influence of stock-level left-tail risk, which is defined using Value-at-Risk(VaR) estimates of past one-year daily stock returns, in the expected stock returns in the Korean stock market. Our results are summarized as follows: First, monthly-constructed zero-cost portfolios that buy (shortsell) the highest (lowest) left-tail risk decile in the previous month exhibit an average monthly return (called left-tail risk premium) of -2.29%. Second, Fama-MacBeth cross-sectional regressions suggest that left-tail risk in the previous month shows significant and negative explanatory power over return in this month, after controlling for various firm characteristics such as firm size, B/M, market beta, liquidity, maximum daily return, idiosyncratic volatility, and skewness. Third, the stocks with larger recent month loss have lower returns in the next month. Fourth, the magnitude of left-tail risk premium is negatively related with lagged market-level volatility. These results support the hypothesis from a perspective of behavioral finance that the overpricing of stocks with left-tail risk is attributed to the investors' underreaction to it.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.5
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• pp.839-850
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• 2021

Risk-adjusted return is believed to be one of the optimal parameters to determine an optimum portfolio. A risk-adjusted return is a calculation of the profit or potential profit from an investment that takes into account the degree of risk that must be accepted to achieve it. This paper presents a new procedure in portfolio selection and utilizes these results to optimize the risk level of risk-adjusted Islamic stock portfolios. It deals with the weekly close price of active issuers listed on Jakarta Islamic Index Indonesia for a certain time interval. Overall, this paper highlights portfolio selection, which includes determining the number of stocks, grouping the issuers via technical analysis, and selecting the best risk-adjusted return of portfolios. The nominated portfolio is modeled using Quadratic Programming (QP). The result of this study shows that the portfolio built using the lowest Value at Risk (VaR) outperforms the market proxy on a risk-adjusted basis of M-squared and was chosen as the best portfolio that can be optimized using QP with a minimum risk of 2.86%. The portfolio with the lowest beta, on the other hand, will produce a minimum risk that is nearly 60% lower than the optimal risk-adjusted return portfolio. The results of QP are well verified by a heuristic optimizer of fmincon.