극단적 투자성과에 대한 회피 성향과 주식 수익률의 횡단면

장지원(Jeewon Jang) 한국증권학회 2016 한국증권학회지 Vol.45 No.5

한국 주식시장에서 과거 일정기간의 일별 실현 수익률을 바탕으로 개별 주식의 역사적 왜도 및 첨도를 추정할 때, 고유첨도에 따라 정렬된 포트폴리오 수익률은 유의한 횡단면 차이를 나타내는 반면 고유왜도, 체계적 왜도 및 체계적 첨도는 수익률의 횡단면과 뚜렷한 관계를 보이지 않는다. 고유변동성과 고유첨도를 기준으로 구성한 이중정렬 포트폴리오 수익률을 관찰한 결과 고유변동성이 높은 주식이 과대평가되며 고유첨도가 높은 주식은 과소평가되는 것을 발견하며, 이와 같은 가격오류를 이용한 매수-매도 전략은 월평균 1.70%의 높은 수익률을 나타낸다. 또한 고유첨도에 따른 포트폴리오 수익률의 차이는 고유변동성 상위 표본에서 더욱 강하게 드러난다. 고유첨도와 주식 수익률의 양의 횡단면 관계는 개별 주식 수익률의 횡단면 회귀분석을 통해 다양한 특성변수들의 영향력을 통제한 후에도 여전히 유의하다. 본 연구의 결과는 주식시장의 일부 투자자들이 극단적 투자성과에 대한 회피 성향을 가져 고유첨도가 높은 주식에 대한 투자를 줄이고자 하기 때문에 발생하는 현상으로 해석된다. Using historical estimates of skewness and kurtosis based on daily realized stock returns, we find that stocks with high idiosyncratic kurtosis earn higher returns subsequently on average, while none of idiosyncratic skewness, systematic skewness, and systematic kurtosis is significantly related to the cross-section of stock returns in the Korean stock market. By constructing double-sorted portfolios based on idiosyncratic volatility and idiosyncratic kurtosis, we find that the trading strategy buying stocks with high kurtosis and low volatility that are relatively underpriced and selling stocks with low kurtosis and high volatility that are relatively overpriced yields a monthly return of 1.70% on average. The positive cross-sectional relation between idiosyncratic kurtosis and subsequent returns is much stronger for stocks with high idiosyncratic volatility. The cross-sectional relation is not accounted for by various firm characteristics, nor risk factors. Our findings suggest that stocks with high idiosyncratic kurtosis can be underpriced and earn relatively high returns subsequently, since a group of investors is averse to high kurtosis and thus they are not willing to pay for stocks with high kurtosis.

Skewness vs. Kurtosis for Pricing and Hedging S&P 500 Options

Sol Kim 한국재무학회 2015 한국재무학회 학술대회 Vol.2015 No.05

For S&P 500 options, we examine the relative influence of the skewness and kurtosis of the riskneutral distribution on pricing and hedging performances. Both the nonparametric method suggested by Bakshi, Kapadia and Madan (2003) and the parametric method suggested by Corrado and Su (1996) are used to estimate the risk-neutral skewness and kurtosis. We find that skewness exerts a greater impact on pricing and hedging errors than kurtosis does. The option pricing model that considers skewness shows better performance for pricing and hedging the options than does the model that considers kurtosis. All the results are statistically significant and robust to all sub-periods, which confirms that the risk-neutral skewness is a more important factor than the risk- neutral kurtosis for pricing and hedging stock index options.

첨도가 피로 수명에 미치는 영향

홍창섭,오재윤 한국기계기술학회 2015 한국기계기술학회지 Vol.17 No.4

This paper studies on the effect of kurtosis on fatigue life. A typical vibration test machine uses a normal distribution signal. However, the vibration signal generated in the actual operating environment is a non-normal distribution signal with kurtosis. In this paper, a signal which has the same power spectral density, but has different kurtosis is generated using the Zero Memory Non-Linear(ZMNL) method. The power spectral densities of these two signal will coincide within ±3dB. Fatigue damage spectrum(FDS) computed with a normal distribution signal and FDS computed with a non-normal distribution signal generated using the ZMNL method are compared. FDS computed using the normal distribution signal of kurtosis 3 will show a big difference over the 100Hz with FDS computed using the signal of kurtosis 6. This paper shows through such FDS comparison that a difference in fatigue life prediction may result in if a vibration profile which does not consider kurtosis occurring in the operating environment of a product is used in a vibration test.

첨도가 피로 수명에 미치는 영향

홍창섭,오재윤 한국기계기술학회 2015 한국기계기술학회지 Vol.17 No.4

This paper studies on the effect of kurtosis on fatigue life. A typical vibration test machine uses a normal distribution signal. However, the vibration signal generated in the actual operating environment is a non-normal distribution signal with kurtosis. In this paper, a signal which has the same power spectral density, but has different kurtosis is generated using the Zero Memory Non-Linear (ZMNL) method. The power spectral densities of these two signal will coincide within ±3dB. Fatigue damage spectrum(FDS) computed with a normal distribution signal and FDS computed with a non-normal distribution signal generated using the ZMNL method are compared. FDS computed using the normal distribution signal of kurtosis 3 will show a big difference over the 100Hz with FDS computed using the signal of kurtosis 6. This paper shows through such FDS comparison that a difference in fatigue life prediction may result in if a vibration profile which does not consider kurtosis occurring in the operating environment of a product is used in a vibration test.

Omnibus tests for multivariate normality based on Mardia's skewness and kurtosis using normalizing transformation

Kim, Namhyun The Korean Statistical Society 2020 Communications for statistical applications and me Vol.27 No.5

Mardia (Biometrika, 57, 519-530, 1970) defined measures of multivariate skewness and kurtosis. Based on these measures, omnibus test statistics of multivariate normality are proposed using normalizing transformations. The transformations we consider are normal approximation and a Wilson-Hilferty transformation. The normalizing transformation proposed by Enomoto et al. (Communications in Statistics-Simulation and Computation, 49, 684-698, 2019) for the Mardia's kurtosis is also considered. A comparison of power is conducted by a simulation study. As a result, sum of squares of the normal approximation to the Mardia's skewness and the Enomoto's normalizing transformation to the Mardia's kurtosis seems to have relatively good power over the alternatives that are considered.

Pricing and Headging with a Skewness and Kurtosis Adjusted Option Model in the Presence of Stochastic Volatility

정도섭,이상휘 한국기업경영학회 2013 기업경영연구 Vol.20 No.1

It is well known that the volatility of asset returns is not constant, which has put forth the development of many option models incorporating a stochastic or GARCH process of volatility. Although these option models successfully reduce pricing and hedging errors of the Black-Scholes model, the complexity of the models often discourages market participants to utilize these models in pricing and hedging options. An alternative approach to adjust Black-Scholes model misspecification is to extend Black-Scholes model’s strict distributional assumption by adjusting non-lognormal skewness and kurtosis. This paper examines pricing and hedging performances of a skewness and kurtosis adjusted option model proposed by Jarrow and Rudd when volatility follows a stochastic process. Consistent with the previous research, the results of this study show that the skewness and kurtosis adjusted Jarrow-Rudd model reduces Black-Scholes pricing errors substantially especially for long-term, deep-in-the-money options. For hedging, however, improvements for the Jarrow-Rudd model over the Black-Scholes model are not virtually found. Overall, the study shows Jarrow-Rudd model could be a better alternative for the Black-Scholes model for option pricing but not necessarily for hedging. But considering the fact that Monte Carlo simulations employed in this study may subject to a model risk, the results of this simulation should be taken with caution.

B-스플라인 능동적 윤곽 기반 얼굴 검출을 위한 차 에지 영상 획득

김가현(Gahyun Kim),정호기(Ho Gi Jung),서재규(Jae Kyu Suhr),김재희(Jaihie Kim) 大韓電子工學會 2010 電子工學會論文誌-SP (Signal processing) Vol.47 No.6

This paper proposes a method for enhancing detection performance and reducing computational cost when detecting a human face by applying B-spline active contour to the frame difference of consecutive images. Firstly, the method estimates amount of user's motion using kurtosis. If the kurtosis is smaller than a pre-defined threshold, it is considered that the amount of user's motion is insufficient and thus the contour fitting is not applied. Otherwise, the contour fitting is applied by exploiting the fact that the amount of motion is sufficient. Secondly, for the contour fitting, difference edges are detected by combining the distance transformation of the binarized frame difference and the edges of current frame. Lastly, the face is located by assigning the contour fitting process to the detected difference edges. Kurtosis-based motion amount estimation can reduce a computational cost and stabilize the results of the contour fitting. In addition, distance transformation-based difference edge detection can enhance the problems of contour lag and discontinuous difference edges. Experimental results confirm that the proposed method can reduce the face localization error caused by the contour lag and discontinuity of edges, and decrease the computational cost by omitting approximately 39% of the contour fitting. 본 논문은 B-스플라인 능동적 윤곽을 차 에지 영상에 적용하여 얼굴을 검출함에 있어, 검출 결과의 정확도를 제고하고 연산량을 감소시키는 방법을 제안한다. 제안 방법은 먼저, 차이 영상의 첨도(kurtosis)를 이용하여 사용자의 움직임량을 추정한다. 이때, 첨도 값에 따라 사용자의 움직임량이 작다고 판단된 경우에는 윤곽선 적합을 실시하지 않으며, 움직임량이 크다고 판단된 경우에만 윤곽선 적합을 실시한다. 그 후, 윤곽선 적합을 위하여 이진화된 차이 영상의 거리변환(distance transform)된 결과와 현재 영상의 에지(edge)를 사용하여 움직임과 관련된 차 에지 영상을 추출하고, 마지막으로 이렇게 추출된 차 에지 영상에 윤곽선 적합을 실시하여 얼굴의 위치를 검출하게 된다. 첨도를 이용하여 사용자의 움직임량을 추정하는 방법은 윤곽선 적합 결과를 안정화시켜주는 동시에 연산량을 절약시켜주며, 현재 영상의 에지와 이진화된 차이 영상의 거리변환을 사용한 움직임 에지 추정 방법은 윤곽선 처짐과 불연속적인 에지 추출의 문제점을 개선시켜준다. 실험을 통해, 제안한 방법이 기존의 윤곽선 처짐이나 에지 끊어짐에 의한 오류를 줄여 주는 동시에, 약 39%의 영상에 대한 윤곽선 적합을 생략시켜주어 연산량을 줄여 줄 수 있음을 확인하였다.

A novel fault diagnosis method based on EMD, cyclostationary, SK and TPTSR

Yijie Niu,Jiyou Fei,Yuanyuan Li,Deng Wu 대한기계학회 2020 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.34 No.5

A novel method based on empirical model decomposition (EMD), cyclostationary, spectral kurtosis (SK) and two-phase test sample sparse representation (TPTSR), called ECK-TPTSR is proposed for fault diagnosis in this paper. In the ECK-TPTSR method, the vibration signal is decomposed into several components by EMD. Then each component can be modelled as cyclostationary for noise reduction. Next, the proposed method computes the kurtosis of the unbiased autocorrelation on the squared envelope of each component, and extracts the component with the highest kurtosis. Finally, the extracted component is used to construct training samples and test samples, which are input into the TPTSR classifier to fulfill fault classification accurately. Moreover, the experimental results indicate that the ECK-TPTSR method can effectively achieve fault diagnosis of motor bearing and obtain higher classification accuracy.

첨도의 변화에 따른 Shewhart X-bar 관리도의 성능 연구

박잉근,이성임 한국자료분석학회 2013 Journal of the Korean Data Analysis Society Vol.15 No.5

These days statistical quality control chart for monitoring the process is widely used in various field. In particular, the Shewhart X-bar control chart is one of the most widely used tools for quality control, and also performs well under the assumption of normality of the quality characteristic. This assumption, however, is often violated as many quality characteristics follow non-normal distribution. To overcome this problem, Minitab, which is the leading statistical software for analyzing data in quality control, recommends normal transformation. Although this is one of well-known remedies, normal transformation is only aimed to make distribution symmetric. Non-normality problem caused by kurtosis would be unadjusted. In this paper, we explore performance of X-bar control according to the changes of kurtosis. We theoretically investigate the false alarm rate using Edgeworth expansion and also numerically evaluate the performance through simulation studies. 공정의 이상 유무를 탐지하기 위해 제안된 관리도는 최근 다양한 분야에서 널리 응용된다. 특히 Shewhart의 X-bar 관리도는 현재까지 유용한 품질 관리 도구들 중 하나로 사용되고 있으며, 품질 특성치가 정규성을 만족할 때 좋은 성능을 발휘한다. 하지만 현업에서 수집되고 있는 품질 특성치들을 살펴보면 정규성을 만족하지 않는 경우가 많은 비중을 차지하고 있음을 확인할 수 있다. 이러한 문제점을 해결하기 위해, 품질관리 데이터분석을 선도하는 미니탭과 같은 통계소프트웨어는 정규변환(normal transformation)을 추천하고 있으며, 정규변환 후 X-bar 관리도에 활용하는 방법은 현업에서 널리 사용되고 있는 방법 중 하나이다. 하지만 대부분의 정규 변환 방식은 분포를 대칭으로 변환하는데 목적이 있으므로, 첨도로 인해 발생되는 비정규성 문제에 대해서는 효과적이지 못할 것이다. 따라서 본 논문에서는 공정이 관리상태일 때 첨도의 변화에 따른 비정규성의 정도가 X-bar 관리도의 성능에 미치는 영향을 탐구해 보기 위해, Edgeworth 전개를 이용한 X-bar 관리도의 가짜 알람률(false alarm rate; FAR)을 살펴보았다. 또한 모의실험을 통해 첨도의 변화에 따른 평균 런길이(average run length; ARL)의 변화를 관측함으로써 X-bar 관리도의 성능을 평가해보기로 한다.

DEMON 스펙트럼의 Kurtosis를 이용한 프로펠러의 케비테이션 발생속도 평가방법 개발

한형석(HyungSuk Han),전수홍(SooHong Jeon),이경현(KyoungHyun Lee),박성호(SungHo Park) 한국소음진동공학회 2017 한국소음진동공학회 학술대회논문집 Vol.2017 No.4