Volatility of shipping stock return the case of Maersk

THE INTERNATIONAL CONFERENCE ON MARINE SCIENCE AND TECHNOLOGY 2016 HỘI NGHỊ QUỐC TẾ KHOA HỌC CÔNG NGHỆ HÀNG HẢI 2016 568 Volatility of shipping stock return the case of Maersk Pham Van Huy Vietnam Maritime University, huypv.kt@vimaru.edu.vn Abstract This paper studies the volatility of Maersk’s stock return series. Data is collected for the period of more than 16 years, with more than 4000 observations obtained to secure the stability of model estimation. It is worth noticed that the largest volatility occurs during the global finance crisis. The author finds that ARCH effects exist in the series. Thus, GARCH models are employed for further estimation. While GARCH (1,1) helps remove all ARCH effects of the process, TGARCH (1,1) suggests that asymmetric effects exist in the series. In other words, bad news tends to have larger effect on Maersk’s stock return than good news does. This suggests the plausibility of employing GARCH models in estimating volatility of shipping stock return. Keywords: Maersk, Shipping, Stock, Volatility, GARCH model. 1. Introduction Stock return is one of the critical criteria in assessing the corporate’s financial performance. This is why it has been the major concern for not only corporate‘s shareholders but also the regulators and academic researchers over the last couple decades. Thus, a number of mathematical models have been introduced to help explain the volatility of stock return. In recent years, generalized autoregressive conditional heteroscedasticity (GARCH) family models have been widely employed to address this issue. These models have the advantage of capturing the volatility cluster effect existed in stock return series, which are often characterized by high skewness and kurtosis in distribution. In Vietnam, GARCH models have been mainly employed to investigate the volatility of major markets’ stock return such as VN index, HNX index, VN30 index and UPCOM index. There have been not many domestic researches dedicated to investigate the volatility of an individual equity, especially the case of shipping companies. To further contribute to Vietnamese literature, this paper employs TGARCH model in estimating the stock return of A.P. Moller-Maersk Group, which is a multinational enterprise operating in Vietnam since the open shipping era. The paper is presented in 3 sections. The first introduces methodology, the second explains about data collection and the final section is about findings and conclusion. 2. Methodology 2.1. Garch(1,1) Bollerslev (1986) introduced the generalized autoregressive conditional heteroskedasticity model (GARCH), which has been widely employed to capture stock return’s volatility. GARCH(1,1) is given as follows: 1 2 0 1 1 1 1 / (0, ) * * t t t t t t t t t r u e e I N h h a a e b h         Where tr is the stock return, tu is the mean of stock return series. te denotes error with conditional variance th under the past known information 1tI  . 0a , 1a and 1b are set to be nonnegative. THE INTERNATIONAL CONFERENCE ON MARINE SCIENCE AND TECHNOLOGY 2016 HỘI NGHỊ QUỐC TẾ KHOA HỌC CÔNG NGHỆ HÀNG HẢI 2016 569 2.2. Tgarch(1,1) Glosten, Jaganathan and Runkle (1993) introduced the TGARCH model to capture the asymmetric effect of financial time series ‘volatility. The assumption is that bad news tends to have larger impact on the time series than good news does. The only difference between TGARCH(1,1) and GARCH(1,1) is in the conditional variance formula as follow: 2 2 0 1 1 1 1 1 1* *d * *t t t t th a a e e b h       Where 1d t = 1 if 1te  < 0 (bad news) and 1d t = 0 if 1te   0 (good news).  is the leverage term. 3. Data Data in this paper is the daily closing prices (adjusted for dividends and splits) of MAERSK-B.CO stock collected from website The series covers from Jan 3 2000 to May 19 2016 yielding 4172 observations. Garch model is employed to estimate the volatility of stock return series which is computed as follows: 1 1( ) / *100%t t t tr p p p   Where tp and tr are stock price and stock return at time t respectively. This leads to the fact that the stock return series only contains 4171 observations. Figure 1 exhibits the return series time plot. All the returns fluctuate around the zero level. The series sees clustering trend as volatility exists mostly in groups. Largest volatility occurs at time t=2476 and 2477 or on December 8 and 9 2008 which is during the global finance crisis. -60 -40 -20 0 20 40 60 80 100 500 1000 1500 2000 2500 3000 3500 4000 R Figure1. Return series time plot Figure 2 exhibits distribution statistics of the return series. The series sees high skewness and kurtosis which suggests that the series is not normal distributed. The Jarque- Bera statistics further confirm this. THE INTERNATIONAL CONFERENCE ON MARINE SCIENCE AND TECHNOLOGY 2016 HỘI NGHỊ QUỐC TẾ KHOA HỌC CÔNG NGHỆ HÀNG HẢI 2016 570 0 400 800 1,200 1,600 2,000 2,400 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 Series: R Sample 1 4171 Observations 4171 Mean 0.077598 Median 0.000000 Maximum 93.20793 Minimum -41.79683 Std. Dev. 2.795683 Skewness 8.755201 Kurtosis 315.1217 Jarque-Bera 16984064 Probability 0.000000 Figure2. Distribution statistics 4. Findings and Conclusion LM-test statistics suggest the presence of ARCH(1) effects in the stock return series Table1. LM-test statistics Heteroskedasticity Test: ARCH F-statistic 154.9931 Prob. F(1,4168) 0.0000 Obs*R-squared 149.5078 Prob. Chi-Square(1) 0.0000 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/19/16 Time: 15:20 Sample (adjusted): 2 4171 Included observations: 4170 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 6.332783 2.109942 3.001401 0.0027 RESID^2(-1) 0.189349 0.015209 12.44962 0.0000 R-squared 0.035853 Mean dependent var 7.812649 Adjusted R-squared 0.035622 S.D. dependent var 138.5239 S.E. of regression 136.0343 Akaike info criterion 12.66417 Sum squared resid 77130189 Schwarz criterion 12.66721 Log likelihood -26402.80 Hannan-Quinn criter. 12.66525 F-statistic 154.9931 Durbin-Watson stat 1.986011 Prob(F-statistic) 0.000000 THE INTERNATIONAL CONFERENCE ON MARINE SCIENCE AND TECHNOLOGY 2016 HỘI NGHỊ QUỐC TẾ KHOA HỌC CÔNG NGHỆ HÀNG HẢI 2016 571 Table2. TGARCH(1,1) estimation Dependent Variable: R Method: ML - ARCH (Marquardt) - Normal distribution Date: 05/19/16 Time: 15:23 Sample: 1 4171 Included observations: 4171 Convergence achieved after 91 iterations Presample variance: backcast (parameter = 0.7) GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*RESID(-1)^2*(RESID(-1)<0) + C(5)*GARCH(-1) Variable Coefficient Std. Error z-Statistic Prob. C 0.086843 0.033152 2.619529 0.0088 Variance Equation C 0.018826 0.002541 7.407490 0.0000 RESID(-1)^2 0.005253 0.000621 8.452785 0.0000 RESID(-1)^2*(RESID(-1)<0) 0.053855 0.001380 39.02514 0.0000 GARCH(-1) 0.971774 0.000914 1063.437 0.0000 R-squared -0.000011 Mean dependent var 0.077598 Adjusted R-squared -0.000011 S.D. dependent var 2.795683 S.E. of regression 2.795698 Akaike info criterion 4.511879 Sum squared resid 32592.42 Schwarz criterion 4.519474 Log likelihood -9404.524 Hannan-Quinn criter. 4.514566 Durbin-Watson stat 2.219932 THE INTERNATIONAL CONFERENCE ON MARINE SCIENCE AND TECHNOLOGY 2016 HỘI NGHỊ QUỐC TẾ KHOA HỌC CÔNG NGHỆ HÀNG HẢI 2016 572 Thus, GARCH(1,1) model is used to remove all ARCH effects. Furthermore, TGARCH model is employed to estimate the series. The result is shown in table 2. The leverage term (0.054) is significantly different from zero at 1% significance level, indicating that good news and bad news have different impact on stock return. The estimate of conditional variance for the stock return series is: 2 1 10.018826 0.005253 0.971774t t th e h    (When the shock is positive) 2 1 10.018826 0.005253 0.053855) 0.97 77( 1 4t t th e h   (When the shock is negative) This result suggests the plausibility of employing GARCH models in estimating volatility of shipping stock return. References [1]. Bollerslev, T. (1986). “Generalized autoregressive conditional heteroskedasticity”. Journal of econometrics, 31(3), 307-327. [2]. Glosten, L. R., R. Jagannathan, and D. E. Runkle. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks." The Journal of Finance. Vol. 48, No. 5, 1993, pp. 1779-1801.