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.
THE INTERNATIONAL CONFERENCE ON MARINE SCIENCE AND TECHNOLOGY 2016 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 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 sections The first introduces methodology, the second explains about data collection and the final section is about findings and conclusion 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: rt ut et et / I t 1 N (0, ht ) ht a0 a1 * et21 b1 * ht 1 Where rt is the stock return, ut is the mean of stock return series et denotes error with conditional variance ht under the past known information I t 1 a0 , a1 and b1 are set to be nonnegative HỘI NGHỊ QUỐC TẾ KHOA HỌC CÔNG NGHỆ HÀNG HẢI 2016 568 THE INTERNATIONAL CONFERENCE ON MARINE SCIENCE AND TECHNOLOGY 2016 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: ht a0 a1 * et21 *dt 1* et21 b1 * ht 1 Where d t 1 = if et 1 < (bad news) and d t 1 = if et 1 (good news) is the leverage term Data Data in this paper is the daily closing prices (adjusted for dividends and splits) of MAERSK-B.CO stock collected from website http://finance.yahoo.com/ The series covers from Jan 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: rt ( pt pt 1 ) / pt 1 *100% Where pt and rt 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 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 and 2008 which is during the global finance crisis R 100 80 60 40 20 -20 -40 -60 500 1000 1500 2000 2500 3000 3500 4000 Figure1 Return series time plot Figure exhibits distribution statistics of the return series The series sees high skewness and kurtosis which suggests that the series is not normal distributed The JarqueBera statistics further confirm this HỘI NGHỊ QUỐC TẾ KHOA HỌC CÔNG NGHỆ HÀNG HẢI 2016 569 THE INTERNATIONAL CONFERENCE ON MARINE SCIENCE AND TECHNOLOGY 2016 2,400 Series: R Sample 4171 Observations 4171 2,000 Mean Median Maximum Minimum Std Dev Skewness Kurtosis 1,600 1,200 800 400 0.077598 0.000000 93.20793 -41.79683 2.795683 8.755201 315.1217 Jarque-Bera 16984064 Probability 0.000000 -40 -30 -20 -10 10 20 30 40 50 60 70 80 90 Figure2 Distribution statistics 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 Obs*R-squared 154.9931 149.5078 Prob F(1,4168) Prob Chi-Square(1) 0.0000 0.0000 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/19/16 Time: 15:20 Sample (adjusted): 4171 Included observations: 4170 after adjustments Variable C RESID^2(-1) R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Coefficient Std Error t-Statistic Prob 6.332783 0.189349 2.109942 0.015209 3.001401 12.44962 0.0027 0.0000 0.035853 0.035622 136.0343 77130189 -26402.80 154.9931 0.000000 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat HỘI NGHỊ QUỐC TẾ KHOA HỌC CÔNG NGHỆ HÀNG HẢI 2016 7.812649 138.5239 12.66417 12.66721 12.66525 1.986011 570 THE INTERNATIONAL CONFERENCE ON MARINE SCIENCE AND TECHNOLOGY 2016 Table2 TGARCH(1,1) estimation Dependent Variable: R Method: ML - ARCH (Marquardt) - Normal distribution Date: 05/19/16 Time: 15:23 Sample: 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)