• Journal of the Korea Society for Simulation
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• v.33 no.1
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• pp.27-34
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• 2024

This study aims to propose an optimal asset allocation that minimizes the risk of insufficient realized replacement rates compared to the OECD average replacement rate. To do this, we set the shortfall risk of replacement rates and calculates an asset allocation plan to minimize this risk based on the period of enrollment, the income level and additional contribution. We consider stocks and deposits as investment assets, using Monte Carlo simulation with a GBM model to generate return distributions for stocks. Our result show that, for individuals with a enrollment period of less than 30 years, participants should invest a minimum of 70-80% of their funds in risky assets to minimize the shortfall risk. However, the proportion of funds that need to be invested in risky assets declines significantly when participants contribute an additional premiums. This effect is particularly pronounced among low-income individuals. Therefore, to achieve OECD average replacement rates, the government needs to incentivize participants to invest more in risky assets, while also providing policies to encourage additional contributions, especially for the low-income population.

• Journal of the Korean Data and Information Science Society
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• v.24 no.3
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• pp.625-636
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• 2013

In this paper we study four kernel machines for estimating expected shortfall, which are constructed through combinations of support vector quantile regression (SVQR), restricted SVQR (RSVQR), least squares support vector machine (LS-SVM) and support vector expectile regression (SVER). These kernel machines have obvious advantages such that they achieve nonlinear model but they do not require the explicit form of nonlinear mapping function. Moreover they need no assumption about the underlying probability distribution of errors. Through numerical studies on two artificial an two real data sets we show their effectiveness on the estimation performance at various confidence levels.

• The Korean Journal of Applied Statistics
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• v.37 no.3
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• pp.265-282
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• 2024

Research in the area of financial portfolio optimization, with the dual goals of increasing expected returns and reducing financial risk, has actively explored various risk measurement indicators. At the same time, the incorporation of various penalty terms to construct efficient portfolios with limited assets has been investigated. In this study, we present a novel portfolio optimization formula that combines the mean-shortfall portfolio and the SLOPE penalty term. Specifically, we formulate this optimization expression, which differs from linear programming, by introducing new variables and using the alternating direction method of multipliers (ADMM) algorithms. Through simulations, we validate the automatic grouping property of the SLOPE penalty term within the proposed mean-shortfall portfolio. Furthermore, using the model introduced in this paper, we propose and evaluate four different types of portfolio compositions relevant to real-world investment scenarios through empirical data analysis.

• The Korean Journal of Financial Management
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• v.24 no.3
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• pp.153-186
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• 2007

It is well known that the distributional properties of financial asset returns exhibit fatter-tails and skewer-mean than the assumption of normal distribution. The correct assumption of return distribution might improve the estimated performance of the Value-at-Risk(VaR) models in financial markets. In this paper, we estimate and compare the VaR performance using the RiskMetrics, GARCH and FIGARCH models based on the normal and skewed-Student-t distributions in two daily returns of the Korean Composite Stock Index(KOSPI) and Korean Won-US Dollar(KRW-USD) exchange rate. We also perform the expected shortfall to assess the size of expected loss in terms of the estimation of the empirical failure rate. From the results of empirical VaR analysis, it is found that the presence of long memory in the volatility of sample returns is not an important in estimating an accurate VaR performance. However, it is more important to consider a model with skewed-Student-t distribution innovation in determining better VaR. In short, the appropriate assumption of return distribution provides more accurate VaR models for the portfolio managers and investors.

• The Korean Journal of Applied Statistics
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• v.23 no.4
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• pp.651-668
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• 2010

Various estimators of two risk measures of a specific financial portfolio, Value-at-Risk and Expected Shortfall, are compared for each case of 1-day and 10-day horizons. We use the Korea Composite Stock Price Index data of 20-year period including the year 2008 of the global financial crisis. Indexes of five foreign stock markets are also used for the empirical comparison study. The estimator considering both the heavy tail of loss distribution and the conditional heteroscedasticity of time series is of main concern, while other standard and new estimators are considered too. We investigate which estimator is best for the Korean stock market and which one shows the best overall performance.

• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.327-347
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• 2020

We consider a credit portfolio with highly skewed exposures. In the portfolio, small number of obligors have very high exposures compared to the others. For the Bernoulli mixture model with highly skewed exposures, we propose a new importance sampling scheme to estimate the tail loss probability over a threshold and the corresponding expected shortfall. We stratify the sample space of the default events into two subsets. One consists of the events that the obligors with heavy exposures default simultaneously. We expect that typical tail loss events belong to the set. In our proposed scheme, the tail loss probability and the expected shortfall corresponding to this type of events are estimated by a conditional Monte Carlo, which results in variance reduction. We analyze the properties of the proposed scheme mathematically. In numerical study, the performance of the proposed scheme is compared with an existing importance sampling method.

• Journal of the Korea Society for Simulation
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• v.28 no.3
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• pp.57-63
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• 2019

This study suggests the level of guaranteed reserves that should be accumulated in order to provide guaranteed interest contracts to pension members. To calculate the guaranteed reserve, this study employs the method using variable insurance contracts with guaranteed interest options. The average return of three major pensions (national pension, private teacher's pension, civil servants pension) funds, from 2010 to 2018, is set as the target rate of return and then we establish 0%, 1.0%, 1.5% and 2.0% each as our minimum guaranteed returns for their respective guaranteed reserves. Our results firstly show that gaps between each guaranteed reserves are increasing as times goes on. Second, the probability of shortfall reserve is on the decrease as the pension fund is mature. Conclusively, a long-term conservative balance between risk and return is one of the best investing strategies in pension funds providing the guaranteed interest.

• The Korean Journal of Financial Management
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• v.23 no.2
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• pp.189-208
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• 2006

In this paper we are concerned with estimation of tail related risk measures for heteroscedastic financial time series and VaR limits that VaR tells us nothing about the potential size of the loss given. So we use GARCH-EVT model describing the tail of the conditional distribution for heteroscedastic financial series and adopt Expected Shortfall to overcome VaR limits. The main results can be summarized as follows. First, the distribution of stock return series is not normal but fat tail and heteroscedastic. When we calculate VaR under normal distribution we can ignore the heavy tails of the innovations or the stochastic nature of the volatility. Second, GARCH-EVT model is vindicated by the very satisfying overall performance in various backtesting experiments. Third, we founded the expected shortfall as an alternative risk measures.

• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.481-504
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• 2006

VaR, a tail-related risk measure is now widely used as a tool for a measurement and a management of financial risks. For more accurate measurement of VaR, recently we are particularly concerned about the approach based on extreme value theory rather than the traditional method based on the assumption of normal distribution. However, many studies about the approaches using extreme value theory was done only for the univariate case. In this paper, we discuss portfolio risk measurements with modelling multivariate extreme value distributions by combining copulas and extreme value theory. We also discuss the estimation of ES together with VaR as portfolio risk measures. Finally, we investigate the relative superiority of EVT-copula approach than variance-covariance method through the back-testing of an empirical data.

• Communications for Statistical Applications and Methods
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• v.17 no.5
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• pp.653-666
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• 2010

Under the retirement pension plan enforced since December 2005, retirees can just choose the payout strategy either of a lump sum allowance or of an annuity in receiving the retirement benefit. Therefore, it is imperative to review and introduce the program withdrawal system enforced by countries with mature pension plan, and complement the limitations of the current payout strategy in the future. In this study, the appropriateness of each of the payout strategies related to the program withdrawal system is examined in terms of shortfall risk and bequest fund per each risk propensity through the expected utility model that reflects the age of the retiree.