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Asymmetric volatility varies in different dry bulk freight rate markets under structure breaks
Physica A 505 (2018) 316–327
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Physica A journal homepage: www.elsevier.com/locate/physa
Asymmetric volatility varies in different dry bulk freight rate markets under structure breaks Junlin Liu a,b , Feier Chen a,c, * a
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China b College of Computing, Georgia Institute of Technology, Atlanta, United States c Department of Human and Engineered Environmental Studies, Graduate School of Frontier Sciences, the University of Tokyo, Japan
highlights • Two stages of multiple structural break model and improved A-MF-DFA model are applied to investigate the asymmetric volatility of bulk shipping market.
• Asymmetric properties vary in different vessel sizes of bulk ships. • The switching points detected by improved A-MF-DFA gather around the structural breaking points. • Combination of two methods could detect the unobvious switching points.
article
info
Article history: Received 9 November 2017 Received in revised form 30 December 2017 Available online 6 March 2018 Keywords: Volatility Bulk shipping market Multiple structure break A-MF-DFA Asymmetric analysis Switching point
a b s t r a c t The past decade has experienced the historical boom and recession in the dry bulk shipping market, which is extremely volatile and more complex than ever before. The asymmetric correlations analysis within the shipping market can provide an understanding of the asymmetric features of risk, which would be helpful for portfolio diversification and risk management. This paper investigates the asymmetric volatility characteristics in dry bulk freight market during the 2008 world financial crisis, which may impose significant impacts on the mechanism of market volatility. First, we apply multiple structural change model to detect the breaking points. Then an improved A-MF-DFA (Asymmetric Multifractal Detrended Fluctuation Analysis) model is applied to capture the asymmetric volatility of the dry bulk shipping market brought by the financial crisis. The empirical results suggest that the financial shocks on the market have a different magnitude of influence on volatility of different vessel types, and the breaking point positions also varies. The positions and scales of the switching points (SPs) of the fluctuation trend detected from A-MF-DFA method also suggest highly asymmetric characteristics in the indices. These findings supply new perspectives for investors in understanding the underlying market risks, crisis effects on bulk shipping market and detailed volatility characters for specific vessel types. © 2018 Elsevier B.V. All rights reserved.
1. Introduction The international dry bulk shipping market, one of the most practicable and cost-effective means of large volume cargo transportation is the major component of shipping market, which derives from the world trade market [1–4]. The world
*
Corresponding author at: State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China. E-mail address: [email protected] (F. Chen). https://doi.org/10.1016/j.physa.2018.02.165 0378-4371/© 2018 Elsevier B.V. All rights reserved.
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dry bulk market is characterized as a highly risky and volatile market because of the uncertainty caused by factors such as world trade volume and pattern, the global economy and inter-government policies [5,6]. Unlike world container shipping market, the dry bulk market with highly competitive and fierce freight rate volatility is hardly predictable, while has brought various opportunities and risks for market players to gain and lose [7–9]. The Baltic Dry Index (BDI) reached its historical top at 11771 in May 2008, and nearly all the market participants could make profits during that boom [10]. However, beyond most operators’ expectations again, the bulk market turned to decrease suddenly in late 2008 below 1000 within less than 6 months [11]. Since then, the world dry bulk shipping market has been struggling in the downturn. Many ship owners had to abandon their vessels to survive. The BDI, which stands for the freight rate level in the dry bulk shipping market, could best reflect the market volatility characteristics, and has always been the hot research topic in shipping finance and risk management. Thus, it is crucial to investigate the inherent volatile characteristics in the dry bulk market, especially when the market experienced its great booms and recessions in the last 10 years. The 2008 world financial crisis also resulted in a structure break in the bulk shipping market [12,13], but in the long-term time series, there may exist more than one change. Both the statistics and econometrics literature contain a vast amount of work on issues related to structural change [5,14,15], most of which specifically designed for the case of a single change [16]. The problem of multiple structural changes has received an increasing attention [17]. A structural break appears in time series when an unexpected shift happens in the macroeconomic background. This may lead to huge forecasting errors and unreliability of the model in general [18]. Perron [19] analyzed the American economy history and concluded that sudden financial and economic crisis may induce sudden impulse to the economy, which may generate fake unit root by the traditional ADF (Augmented Dickey–Fuller) test. Then he introduced the structural change points to the literature to explain financial time series changing during crisis. Bai and Perron, Bai and Perron [20,21] illustrated the procedures for modeling with multiple structural changes, which is applied in various empirical applications [22–25]. We apply this method to investigate the multiple changes in time series of bulk shipping market and divide the research periods scientifically into boom and recession under financial crisis. Financial markets may react asymmetrically to news [26,27]. Asymmetric volatility studies attracts special attention in recent years [28,29]. This is mainly because asymmetric characteristic acts as a key feature in analyzing long-range correlation, switching points, fat-tailed distribution and many other data properties. The research on the asymmetric features of risk are widely applied to enhance the portfolio in terms of diversification and risk management [29]. The two trends of stock market, namely bullish and bearish markets should be treated differently in analyzing the multifractal scaling behavior. However, studies focusing on measuring the asymmetric multifractality are quite limited, especially for the shipping market. DFA method [30] and its extensions of MF-DFA [31], MF-DCCA [32,33] among others [34,35] are effective in detrending high order fluctuations and detecting long-term power-law correlations within a time series via Hurst exponent or generalized Hurst exponent. These DFA based methods are widely applied in physics, finance and many other interdisciplinary fields for its robustness and high reliability [36,37]. For the asymmetric characteristics, A-DFA (Asymmetric Detrended Fluctuation Analysis) method is proposed [38] by introducing two new indices to analyze the positive and negative fluctuation trends separately. For further detecting the asymmetric multifractality of the dry bulk market, A-MF-DFA method [39] is constructed to analyze the asymmetric characteristics within the Chinese stock market. New volatility mechanism may have derived from the world dry bulk market in the post-2008 world financial crisis period, which really interests us. This paper aims to fill the gap in the literature and to do a thorough investigation into the dry bulk freight market to seek the distinct volatility nature during the great market boom and great recession within the past decade. This study proposes a two-stage research methodology. First, we use the Bai and Perron’s multiple structural change model to detect the precise structural breaking points in the dry bulk freight market. By dividing the research periods into boom and recession under financial crisis, then we apply the improved A-MF-DFA model to investigate the asymmetric volatility effects on the freight rate market by the financial crisis. The two-stage research could detect the unobvious switching points neglected by only one method. In addition, the switching points from A-MF-DFA gather around the breaking points from structural change model implying the validity of both methods. The rest of the paper is organized as follows. Section 2 lists processed data and their statistical features. Section 3 introduces the methodology applied in this paper. Section 4 represents the empirical results. Section 5 makes conclusions. 2. Data description In the past decade, the world dry bulk shipping market has seen a dramatic development with vicissitudes. The BDI stood at 11 771 on its historical record in May 2008 but suddenly shrank more than 90% to be less than 1000 in December 2008. The market condition is so unique and fluctuant that no past experience could compare. We divide the dry bulk market into 3 sectors by vessel sizes, namely Supramax sector, Capesize sector and Panamax sector. Different sized vessels are involved in different commodity trades and shipping routes in the world, and have their unique transportation and risk characteristics. We choose BCI (Baltic Capesize Index), BPI (Baltic Panamax Index) and BSI (Baltic Supramax Index) from the Clarksons to analyze the volatility mechanisms in the 3 sectors to seek the dry bulk shipping market internal rule. The sample daily data of BSI, BPI and BCI are from 07/01/2005 to 02/26/2015 with 2412 observations as shown in Fig. 1. The data properties displace in Table 1. The raw data processed by log first order difference is by Eq. (1). Vt = ln It − ln It −1
(1)
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Fig. 1. Freight rate indexes from 07/01/2005 to 02/26/2015. Table 1 Statistical properties for freight rate indexes.
Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis
BSI
BPI
BCI
2051.698 1572.5 6956 389 1473.837 1.5182 4.6007
2879.001 2063 11713 418 2468.178 1.5992 4.9122
4258.938 3143 19687 311 3639.619 1.7833 5.7805
Table 2 Statistical properties for freight rate volatility.
Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis
V_BSI
V_BPI
V_BCI
−0.000588
−0.000615 −0.000844
0.000720 −0.00142 0.3644 −0.1921 0.0380 0.7173 11.4206
0.000 0.2028 −0.1166 0.0162 0.4103 21.9404
0.1389
−0.2162 0.0279
−0.0934 8.5301
In Eq. (1), It and It −1 are the freight rate index at time t and t −1, Vt is the volatility (or daily return). The volatilities of the three sector time series are denoted as V_BSI, V_BPI and V_BCI. Fig. 2 and Table 2 describes the results and their properties. The similarities and differences exist in three vessel types, which need further analysis. 3. Methodology 3.1. Structural break model In this paper, the structural change model [21] is improved and applied to detect the breaking points of the freight rate index during the 2008 world financial crisis. Consider m breaks in the following multiple linear regression model (m + 1 regimes): yt = x′t β + zt′ δj + ut t = Tj−1 + 1, . . . , Tj ; j = 1, . . . , m + 1
(
)
(2)
In this model, yt is the observed dependent variable at time t; xt and zt are vectors of covariates; β and δj (j = 1, . . . , m + 1) are the corresponding vectors of coefficients; ut is the disturbance at time t. The indices (T1 , . . . , Tm ), or the breakpoints, are explicitly treated as unknown (we use the convention that T0 = 0 and Tm+1 = T ). The purpose is to estimate the unknown regression coefficients together with the breaking points when T observations on (yt , xt , zt ) are available. ′
′
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Fig. 2. Freight rate index volatility for BSI, BPI and BCI.
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J. Liu, F. Chen / Physica A 505 (2018) 316–327 Table 3 Breaking points of dry bulk shipping freight rate indices.
UDmax WDmax No. of breaking points Breaking point date
BSI
BPI
BCI
3332.349* 4964.116* 2 04/19/2007; 09/08/2008
2895.462* 4599.914* 2 04/24/2007; 09/10/2008
2584.717* 3595.963* 2 07/31/2007; 09/05/2008
Notes: Significant at 5% critical level.
3.2. A-MF-DFA method In this paper, A-MF-DFA method [39] is applied to capture asymmetric volatility effects in the dry bulk shipping market brought by the financial crisis. This model will analyze the asymmetric characteristics as well as the multi-fractality within V_BSI, V_BCI and V_BPI shown in Section 2. For a time series x (t ) (t = 1, 2, . . . , n), we first calculate its cumulative deviation y (t ) to filter out the random component in the time series: y (t ) =
n ∑
(x (t ) − x)
(3)
t =1
∑n
Where x is the average of x (t ), x = 1n t =1 x (t ). The time series can be divided into m boxes of length s, that is m = n/s. If n is not divisible by s, we can try a bigger s and allow a certain extent of overlap. The frequency that every number is used is not necessarily the same. For every box v , calculate the intercept a and slope b in linear fitting: yv (i) = ayv + byv i, i = 1, 2, . . . , m, yv = 1, 2, . . . , m
(4)
Here we only filter out the first-order trend and calculate its variance: F 2 (v, s) =
s 1∑
s
{y [(v − 1) s + i] − yv (i)}2 , v = 1, 2, . . . , m
(5)
i=1
Then calculate DFA fluctuation function:
( F (s) =
) 12
m 1 ∑
m
F (v, s) 2
(6)
v=1
If there are long-term power-law correlations within the time series, F (s) follows the power law: F (s) ∼ sH
(7)
Where H is Hurst index. Hurst index is usually obtained from the slope in linear fitting of(ln (s) , ln (F (s))). When calculating F (s), consider:
⎞ 21
⎛ F + (s) = ⎝
1 m+
∑
F 2 (v, s)⎠
(8)
byv >0
2 We sum all the F 2 (v, s) in the boxes with byv > 0 to obtain F + (s), where m+ represents the number ( of F (v, ( s) with )) − + − byv > 0, and we can get F s in a similar way. H and H are obtained from the slope in a linear fitting of ln s , ln F + (s) ( ) ( ) ( ( − )) and ln (s) , ln F (s) . In this paper, x (t ) is the Vt shown in Section 2. However, we can only get one H + and H − value if we use the whole time series. Therefore we improve the method by using the sliding window procedure to define local indices H + (t ) and H − (t ). We first define a window length L, and use L + 1 points around a given time t0 , L/2 left and L/2 right rather than the whole x (t ) to calculate H + and H − , and we call the two values H + (t0 ) and H − (t0 ). Thus when the window slides from the front to the end of the time series, we will get a series of H + (t ) and H − (t ) values. Actually curves of H + (t ) and H − (t ) are able to analyze the upward and downward fluctuations, but not clear enough to show the scale of switching points and the asymmetric characteristics. We use the improved A-DFA method described in [40] to solve this problem. In order to precisely of and the ( pair)the peaks ( switching ( ) the indices ) ( points, ) as well as to make + − the result more evident, consider H (t ) = H + t − 2L H + t + 2L and H (t ) = H − t − 2L H − t + 2L , and then calculate
+
−
∆H (t ) = H (t ) − H (t ). For a width l and t = 1, 2, . . . , l, if ∆H (t0 − t ) < ∆H (t0 ) > ∆H (t0 + t ) or ∆H (t0 − t ) > ∆H (t0 ) < ∆H (t0 + t ), ∆H (t0 ) is a local extreme. For all ∆H (t ), if it is not an extreme, we set z (t ) = 0. If it is an extreme, we record this value t
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and identify it as Ti , and then set z (i) = ∆H (Ti − 1) − 2∆H (Ti ) + ∆H (Ti + 1). In this paper, we set l = 10 to note small fluctuations, which is tested to be a reasonable value according to Rivera-Castro et al. [40]. The positions of z (i) ̸ = 0 pairs the positions of switching points in the fluctuation trend, and their magnitudes gauge their strength. To show a clear graph of the switching points and their asymmetric characteristics, we only plotted those z (Ti ) values whose |z (Ti )| are larger than a certain level and ignore the small fluctuation trend changes. Furthermore, we can replace the exponents in Eq. (6) and Eq. (8) with f (q) and rewrite them as Eq. (9) and Eq. (10):
( Fq (s) =
m )q 1 ∑( 2 F (v, s) 2 m
v=1
⎛ Fq+ (s) = ⎝
1
∑ (
m+
) 1q
⎞ 1q q ) F 2 (v, s) 2 ⎠
(9)
(10)
byv >0
Where variable q can take any real number except zero. Specially, we can define:
( F0 (s) = exp
m 1 ∑
2m
⎛ F0+ (s) = exp ⎝
) ) ln F 2 (v, s) (
(11)
v=1
1 2m+
⎞ ∑ ( ) ln F 2 (v, s) ⎠
(12)
byv >0
Thus, we can get different Hurst indexes Hq , Hq+ and Hq− for any different q. In general, Hurst index H represents the long-term power-law correlations within the time series. H + and H − represents the upward and downward trends of the time series. If H + ̸ = H − , we say the time series is asymmetric. Hq represents the scaling behavior of large fluctuations for q > 0 and small fluctuations for q < 0. When q > 0, large fluctuations are characterized by a smaller Hq and when q < 0, small fluctuations are characterized by a larger Hq . This principle is detailed in [41]. If Hq remains the same for different q, the time series is monofractal. Otherwise, the time series is multifractal. In this way, we can analyze both the multifractality and the asymmetric characteristics in the dry bulk market index with Hq+ and Hq− simultaneously. 4. Empirical results 4.1. Structural breaks With the structural change model, we can get the breaking points of freight rate indices for each vessel type. The detailed statistics are processed with Gauss 8.0 and listed in Table 3. The results reveals that during the past decade, the world dry bulk shipping market experienced three structural periods under the financial crisis influence, which is divided by two main breaking points for each index respectively. To investigate the 2008 world financial crisis effect on freight rate volatility, for each vessel type, we solely extract the second breaking point in 2008. Thus, the focused time series was separated into two parts: first period from 04/19/2007 to 09/08/2008 and second period from 09/09/2008 to 02/26/2015 for supramax; first period from 04/24/2007 to 09/10/2008 and second period from 09/11/2008 to 02/26/2015 for panama; first period from 07/31/2007 to 09/05/2008 and second period from 09/06/2008 to 02/26/2015 for capsize. We apply the A-MF-DFA model in freight rate volatility asymmetric effect and multifractality analysis. V_BCI1 and V_BCI2 stand for capesize freight index volatility in the first and second period respectively, and so on for V_BPI1, V_BPI2, V_BSI1, and V_BSI2. Correspondingly, V_BCI, V_BPI and V_BSI stand for the whole time series. 4.2. Asymmetric volatility
∆H (t ) described in Section 3.2 is applied here to show the asymmetric characteristics of dry bulk shipping freight rate + − indexes. The results are shown in Fig. 3. Since ∆H (t ) = H (t ) − H (t ), when ∆H (t ) > 0, the asymmetric volatility effect is positive and vice versa. In the first research period of BSI, ∆H (t ) tends to be negative and becomes more volatile as the second breaking point approaches. In the second research period of BSI, there is also a volatile region around the year 2014, but not as turbulent as the year 2008, when financial crisis and the breaking point appear. In the first research period of BPI, the overall trend of the asymmetric volatility is not very clear, because ∆H (t ) first turns negative and later positive as time approaches the second breaking point. Similar complex volatility happens in V_BPI2 and V_BCI2, where overall trend is not easy to conclude. For V_BCI1, the positive and negative trend are of the same level. Thus no obvious asymmetric characteristic is detected. From this analysis we can also conclude that ∆H (t ) is not satisfactory to demonstrate asymmetric volatility. As a result, a further discussion with z (t ) in Section 4.3 is applied.
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Fig. 3. ∆H (t ) for dry bulk shipping freight rate indexes BSI, BPI and BCI of two periods.
4.3. Switching points Switching points imply upward and downward trends, which is also a key feature to analyze the asymmetric characteristics of freight rate volatility. We applied A-MF-DFA model on the whole time series V_BCI, V_BPI and V_BSI. Fig. 4 compares the results of z (t ) and ∆H (t ) for V_BPI as an example. The asymmetry is obvious from Fig. 4, where the peaks of positive and negative switching points have different numbers and scales. The majority of switching points from z (t ) are detected where ∆H (t ) becomes more turbulent, and z (t ) is more evident than ∆H (t ) to show the characteristics of dry bulk shipping freight rate indexes, showing the validity of the improved method. Fig. 5 shows all the switching points from 07/04/2005 to 02/26/2015 of all the indexes, and there are also switching points gather around the breaking points that we detected in the first stage study, which indirectly verifies the structural change model. We extract the data of V_BSI1, V_BSI2, V_BPI1, V_BPI2, V_BCI1 and V_BCI2, and summarize the result in Table 4. In all market sectors (capesize, panamax and supramax), the freight indexes are time-varying. In the supramax sector, the asymmetric volatility effect is negative in the first period and positive in the second period. In the panama sector, the asymmetric volatility effect is positive in the first period and there was no asymmetric volatility effect in the second period. In capesize sector, there was no asymmetric volatility effect in the first period and the effect is negative in the second period. For V_BPI2 and V_BCI1, although we can still detect a certain level of asymmetric characteristic, there are too few switching points or the average of all switching point level is too small. Therefore we mark they have no asymmetric effects. This is also shown in Table 5 when comparing the results between during and after the financial crisis.
J. Liu, F. Chen / Physica A 505 (2018) 316–327
Fig. 4. Comparison between the results of ∆H and z for V_BPI in 2008.
Fig. 5. Fluctuation trend switching points and their asymmetric characteristics of V_BSI, V_BPI and V_BCI.
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J. Liu, F. Chen / Physica A 505 (2018) 316–327 Table 4 Different volatility effect level shown from switching points (SPs).
V_BSI1 V_BSI2 V_BPI1 V_BPI2 V_BCI1 V_BCI2
Number of SPs
Average of SPs
18 46 18 76 1 27
−0.055949482 0.052688188 0.171112522 −0.023300606 0.873843479 0.185051211
Table 5 Asymmetric volatility effect s in the dry bulk shipping freight market during financial crisis (Period 1) vs. after financial crisis (Period 2).
V_BSI V_BPI V_BCI
Period 1
Period 2
Negative Positive None (Positive)
Positive None (Negative) Positive
4.4. Multifractal asymmetry Similar to Section 4.3, multifractal asymmetry feature of dry bulk freight rate is studied based on A-MF-DFA model with switching points. Here we set q from −5 to 5 and see how small and large fluctuation influence the time series. The multifractal asymmetry feature described by the number and average scale of switching points is visualized in Fig. 6. As is stated in Section 3.2, q value from negative to positive describes the effect of large fluctuation and small fluctuation on the volatility of dry bulk freight rate separately. Number and average level of switching points represent the severity of the volatility. As an overall trend, the number of switching points declines very quickly as q value increases. This demonstrates that dry bulk freight rate is multifractal asymmetric. Compared with large fluctuation, small fluctuation has much larger effect on the time series, showing the great volatility of dry bulk freight rate. It is worth to mention that in Fig. 6, the number and average level of switching points also rely on the value of window size l and minimum level z described in Section 3.2. Different values can lead to different results, but as long as the value of l and z is rational, the overall trend should be the same [40].
4.5. Source of asymmetric volatility effects Considering the number of switching points, the average of all switching point level neglecting the average switching point level of V_BPI2 and the only one SP of V_BCI1 as noted in Table 4 and Table 5, we conclude that V_BSI has the largest volatility among all the three indices. This conclusion is in accordance with Kavussanos [42] and Chen et al. [43] and Jing et al. [5]. Meanwhile, V_BCI is the least, which reveals that after the world financial crisis, the supramax shipping market is the most volatile sector whilst the capesize market is the least volatile sector. Supramax vessel is the most flexible vessel among the three types and is mainly engaged in transporting minor dry bulk cargoes, such as bauxite, alumina, fertilizer, rice and sugar. Capesize vessel is the least flexible type as capsize vessels are generally for transportation of iron ore and coal. Panamax vessel is mainly engaged in transporting coal, grain and sometimes, iron ore. Before the world financial crisis, the world shipping market has reached a historical top in late 2007; shipping firms to increase their fleet size placed many vessel orders. With the beginning of world financial crisis, the dry bulk shipping freight index tended to drop suddenly. Since then, overcapacity pervades in the world shipping market. On one side, for the capesize vessels, as they are engaged in major bulk commodities transportation, the international trade between countries and continents are relatively steady, the capesize and panamax shipping markets could resist certain kind of market shocks. On the other side, as supply overcapacity is severe in the dry bulk shipping market, even if positive market innovations arrive, freight rate is reluctant to increase, as overcapacity cannot absorb. In the panamax sub market, as panamax vessels are more flexible than capesize vessels, with the relative steady demand, shipowners could suffer less loss, and when positive information came, it could induce larger volatility than that of the same magnitude of negative information. For the supramax sector, before the financial crisis, as the shipping market continued to boom and the flexibility of supramax, ship owners could adjust their operations easily and freely to make profits. However, during the second period, as the financial crisis emerged, the minor bulk transportation market suffered heavy loss, ship owners and shipping firms cannot adjust their operation strategies freely, together with the supply overcapacity, so the volatility effect turned severe.
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Fig. 6. Number and average scale of switching points for different bulk vessels.
5. Conclusions The world dry bulk shipping market has experienced a long booming period since year 2000. However, since year 2007, the shipping market has been more complex and extremely volatile. It has been very hard for practitioners and researchers to understand the underlying essence and risks of this market. Past research on freight volatility modeling mainly focused on the pre-financial crisis booming period that they neglected the risks brought by the 2008 financial crisis. In this paper, we specialized on the dry effects on bulk market volatility by the financial crisis, aiming to clarify the market volatility characteristics before and after the crisis. We used daily BSI, BPI and BCI from 07/01/2005 to 02/26/2015 to investigate the asymmetric volatility effect within the world dry bulk shipping market. By extending A-MF-DFA model, we successfully investigated the asymmetric volatility effect in the world dry bulk shipping market during the financial crisis. The conclusion could be draw as in all market sectors (capesize, panamax and supramax), the freight indexes are time-varying. In the supramax sector, the asymmetric volatility effect is negative in the first period and positive in the second period. The asymmetric characters are different in the three types of bulk vessels. In summary, the structural break model and A-MF-DFA model are successful in detecting the breaking points as well as determining the asymmetric fluctuation characteristics of the freight indexes. The A-MF-DFA model is effective in studying
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asymmetric volatility effects in the dry bulk freight markets. However, in the future research, a more comprehensive multivariate model is needed to investigate the freight volatility, as the world dry bulk shipping market is not isolated, which is determined by international trade and global economy development. Overall, the results generated by this research could provide a new perspective on freight market volatility during the 2008 financial crisis, which may be useful for practitioners and researchers on market risk management and operation strategies decision-making. Acknowledgments We thank support from State Key Laboratory of Ocean Engineering of Shanghai Jiao Tong University and Simulation of Complex System Laboratory (SCS Lab) of the University of Tokyo. This work is sponsored by Natural Science Foundation of Shanghai. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]
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Physica A journal homepage: www.elsevier.com/locate/physa
Asymmetric volatility varies in different dry bulk freight rate markets under structure breaks Junlin Liu a,b , Feier Chen a,c, * a
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China b College of Computing, Georgia Institute of Technology, Atlanta, United States c Department of Human and Engineered Environmental Studies, Graduate School of Frontier Sciences, the University of Tokyo, Japan
highlights • Two stages of multiple structural break model and improved A-MF-DFA model are applied to investigate the asymmetric volatility of bulk shipping market.
• Asymmetric properties vary in different vessel sizes of bulk ships. • The switching points detected by improved A-MF-DFA gather around the structural breaking points. • Combination of two methods could detect the unobvious switching points.
article
info
Article history: Received 9 November 2017 Received in revised form 30 December 2017 Available online 6 March 2018 Keywords: Volatility Bulk shipping market Multiple structure break A-MF-DFA Asymmetric analysis Switching point
a b s t r a c t The past decade has experienced the historical boom and recession in the dry bulk shipping market, which is extremely volatile and more complex than ever before. The asymmetric correlations analysis within the shipping market can provide an understanding of the asymmetric features of risk, which would be helpful for portfolio diversification and risk management. This paper investigates the asymmetric volatility characteristics in dry bulk freight market during the 2008 world financial crisis, which may impose significant impacts on the mechanism of market volatility. First, we apply multiple structural change model to detect the breaking points. Then an improved A-MF-DFA (Asymmetric Multifractal Detrended Fluctuation Analysis) model is applied to capture the asymmetric volatility of the dry bulk shipping market brought by the financial crisis. The empirical results suggest that the financial shocks on the market have a different magnitude of influence on volatility of different vessel types, and the breaking point positions also varies. The positions and scales of the switching points (SPs) of the fluctuation trend detected from A-MF-DFA method also suggest highly asymmetric characteristics in the indices. These findings supply new perspectives for investors in understanding the underlying market risks, crisis effects on bulk shipping market and detailed volatility characters for specific vessel types. © 2018 Elsevier B.V. All rights reserved.
1. Introduction The international dry bulk shipping market, one of the most practicable and cost-effective means of large volume cargo transportation is the major component of shipping market, which derives from the world trade market [1–4]. The world
*
Corresponding author at: State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China. E-mail address: [email protected] (F. Chen). https://doi.org/10.1016/j.physa.2018.02.165 0378-4371/© 2018 Elsevier B.V. All rights reserved.
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dry bulk market is characterized as a highly risky and volatile market because of the uncertainty caused by factors such as world trade volume and pattern, the global economy and inter-government policies [5,6]. Unlike world container shipping market, the dry bulk market with highly competitive and fierce freight rate volatility is hardly predictable, while has brought various opportunities and risks for market players to gain and lose [7–9]. The Baltic Dry Index (BDI) reached its historical top at 11771 in May 2008, and nearly all the market participants could make profits during that boom [10]. However, beyond most operators’ expectations again, the bulk market turned to decrease suddenly in late 2008 below 1000 within less than 6 months [11]. Since then, the world dry bulk shipping market has been struggling in the downturn. Many ship owners had to abandon their vessels to survive. The BDI, which stands for the freight rate level in the dry bulk shipping market, could best reflect the market volatility characteristics, and has always been the hot research topic in shipping finance and risk management. Thus, it is crucial to investigate the inherent volatile characteristics in the dry bulk market, especially when the market experienced its great booms and recessions in the last 10 years. The 2008 world financial crisis also resulted in a structure break in the bulk shipping market [12,13], but in the long-term time series, there may exist more than one change. Both the statistics and econometrics literature contain a vast amount of work on issues related to structural change [5,14,15], most of which specifically designed for the case of a single change [16]. The problem of multiple structural changes has received an increasing attention [17]. A structural break appears in time series when an unexpected shift happens in the macroeconomic background. This may lead to huge forecasting errors and unreliability of the model in general [18]. Perron [19] analyzed the American economy history and concluded that sudden financial and economic crisis may induce sudden impulse to the economy, which may generate fake unit root by the traditional ADF (Augmented Dickey–Fuller) test. Then he introduced the structural change points to the literature to explain financial time series changing during crisis. Bai and Perron, Bai and Perron [20,21] illustrated the procedures for modeling with multiple structural changes, which is applied in various empirical applications [22–25]. We apply this method to investigate the multiple changes in time series of bulk shipping market and divide the research periods scientifically into boom and recession under financial crisis. Financial markets may react asymmetrically to news [26,27]. Asymmetric volatility studies attracts special attention in recent years [28,29]. This is mainly because asymmetric characteristic acts as a key feature in analyzing long-range correlation, switching points, fat-tailed distribution and many other data properties. The research on the asymmetric features of risk are widely applied to enhance the portfolio in terms of diversification and risk management [29]. The two trends of stock market, namely bullish and bearish markets should be treated differently in analyzing the multifractal scaling behavior. However, studies focusing on measuring the asymmetric multifractality are quite limited, especially for the shipping market. DFA method [30] and its extensions of MF-DFA [31], MF-DCCA [32,33] among others [34,35] are effective in detrending high order fluctuations and detecting long-term power-law correlations within a time series via Hurst exponent or generalized Hurst exponent. These DFA based methods are widely applied in physics, finance and many other interdisciplinary fields for its robustness and high reliability [36,37]. For the asymmetric characteristics, A-DFA (Asymmetric Detrended Fluctuation Analysis) method is proposed [38] by introducing two new indices to analyze the positive and negative fluctuation trends separately. For further detecting the asymmetric multifractality of the dry bulk market, A-MF-DFA method [39] is constructed to analyze the asymmetric characteristics within the Chinese stock market. New volatility mechanism may have derived from the world dry bulk market in the post-2008 world financial crisis period, which really interests us. This paper aims to fill the gap in the literature and to do a thorough investigation into the dry bulk freight market to seek the distinct volatility nature during the great market boom and great recession within the past decade. This study proposes a two-stage research methodology. First, we use the Bai and Perron’s multiple structural change model to detect the precise structural breaking points in the dry bulk freight market. By dividing the research periods into boom and recession under financial crisis, then we apply the improved A-MF-DFA model to investigate the asymmetric volatility effects on the freight rate market by the financial crisis. The two-stage research could detect the unobvious switching points neglected by only one method. In addition, the switching points from A-MF-DFA gather around the breaking points from structural change model implying the validity of both methods. The rest of the paper is organized as follows. Section 2 lists processed data and their statistical features. Section 3 introduces the methodology applied in this paper. Section 4 represents the empirical results. Section 5 makes conclusions. 2. Data description In the past decade, the world dry bulk shipping market has seen a dramatic development with vicissitudes. The BDI stood at 11 771 on its historical record in May 2008 but suddenly shrank more than 90% to be less than 1000 in December 2008. The market condition is so unique and fluctuant that no past experience could compare. We divide the dry bulk market into 3 sectors by vessel sizes, namely Supramax sector, Capesize sector and Panamax sector. Different sized vessels are involved in different commodity trades and shipping routes in the world, and have their unique transportation and risk characteristics. We choose BCI (Baltic Capesize Index), BPI (Baltic Panamax Index) and BSI (Baltic Supramax Index) from the Clarksons to analyze the volatility mechanisms in the 3 sectors to seek the dry bulk shipping market internal rule. The sample daily data of BSI, BPI and BCI are from 07/01/2005 to 02/26/2015 with 2412 observations as shown in Fig. 1. The data properties displace in Table 1. The raw data processed by log first order difference is by Eq. (1). Vt = ln It − ln It −1
(1)
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Fig. 1. Freight rate indexes from 07/01/2005 to 02/26/2015. Table 1 Statistical properties for freight rate indexes.
Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis
BSI
BPI
BCI
2051.698 1572.5 6956 389 1473.837 1.5182 4.6007
2879.001 2063 11713 418 2468.178 1.5992 4.9122
4258.938 3143 19687 311 3639.619 1.7833 5.7805
Table 2 Statistical properties for freight rate volatility.
Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis
V_BSI
V_BPI
V_BCI
−0.000588
−0.000615 −0.000844
0.000720 −0.00142 0.3644 −0.1921 0.0380 0.7173 11.4206
0.000 0.2028 −0.1166 0.0162 0.4103 21.9404
0.1389
−0.2162 0.0279
−0.0934 8.5301
In Eq. (1), It and It −1 are the freight rate index at time t and t −1, Vt is the volatility (or daily return). The volatilities of the three sector time series are denoted as V_BSI, V_BPI and V_BCI. Fig. 2 and Table 2 describes the results and their properties. The similarities and differences exist in three vessel types, which need further analysis. 3. Methodology 3.1. Structural break model In this paper, the structural change model [21] is improved and applied to detect the breaking points of the freight rate index during the 2008 world financial crisis. Consider m breaks in the following multiple linear regression model (m + 1 regimes): yt = x′t β + zt′ δj + ut t = Tj−1 + 1, . . . , Tj ; j = 1, . . . , m + 1
(
)
(2)
In this model, yt is the observed dependent variable at time t; xt and zt are vectors of covariates; β and δj (j = 1, . . . , m + 1) are the corresponding vectors of coefficients; ut is the disturbance at time t. The indices (T1 , . . . , Tm ), or the breakpoints, are explicitly treated as unknown (we use the convention that T0 = 0 and Tm+1 = T ). The purpose is to estimate the unknown regression coefficients together with the breaking points when T observations on (yt , xt , zt ) are available. ′
′
J. Liu, F. Chen / Physica A 505 (2018) 316–327
Fig. 2. Freight rate index volatility for BSI, BPI and BCI.
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J. Liu, F. Chen / Physica A 505 (2018) 316–327 Table 3 Breaking points of dry bulk shipping freight rate indices.
UDmax WDmax No. of breaking points Breaking point date
BSI
BPI
BCI
3332.349* 4964.116* 2 04/19/2007; 09/08/2008
2895.462* 4599.914* 2 04/24/2007; 09/10/2008
2584.717* 3595.963* 2 07/31/2007; 09/05/2008
Notes: Significant at 5% critical level.
3.2. A-MF-DFA method In this paper, A-MF-DFA method [39] is applied to capture asymmetric volatility effects in the dry bulk shipping market brought by the financial crisis. This model will analyze the asymmetric characteristics as well as the multi-fractality within V_BSI, V_BCI and V_BPI shown in Section 2. For a time series x (t ) (t = 1, 2, . . . , n), we first calculate its cumulative deviation y (t ) to filter out the random component in the time series: y (t ) =
n ∑
(x (t ) − x)
(3)
t =1
∑n
Where x is the average of x (t ), x = 1n t =1 x (t ). The time series can be divided into m boxes of length s, that is m = n/s. If n is not divisible by s, we can try a bigger s and allow a certain extent of overlap. The frequency that every number is used is not necessarily the same. For every box v , calculate the intercept a and slope b in linear fitting: yv (i) = ayv + byv i, i = 1, 2, . . . , m, yv = 1, 2, . . . , m
(4)
Here we only filter out the first-order trend and calculate its variance: F 2 (v, s) =
s 1∑
s
{y [(v − 1) s + i] − yv (i)}2 , v = 1, 2, . . . , m
(5)
i=1
Then calculate DFA fluctuation function:
( F (s) =
) 12
m 1 ∑
m
F (v, s) 2
(6)
v=1
If there are long-term power-law correlations within the time series, F (s) follows the power law: F (s) ∼ sH
(7)
Where H is Hurst index. Hurst index is usually obtained from the slope in linear fitting of(ln (s) , ln (F (s))). When calculating F (s), consider:
⎞ 21
⎛ F + (s) = ⎝
1 m+
∑
F 2 (v, s)⎠
(8)
byv >0
2 We sum all the F 2 (v, s) in the boxes with byv > 0 to obtain F + (s), where m+ represents the number ( of F (v, ( s) with )) − + − byv > 0, and we can get F s in a similar way. H and H are obtained from the slope in a linear fitting of ln s , ln F + (s) ( ) ( ) ( ( − )) and ln (s) , ln F (s) . In this paper, x (t ) is the Vt shown in Section 2. However, we can only get one H + and H − value if we use the whole time series. Therefore we improve the method by using the sliding window procedure to define local indices H + (t ) and H − (t ). We first define a window length L, and use L + 1 points around a given time t0 , L/2 left and L/2 right rather than the whole x (t ) to calculate H + and H − , and we call the two values H + (t0 ) and H − (t0 ). Thus when the window slides from the front to the end of the time series, we will get a series of H + (t ) and H − (t ) values. Actually curves of H + (t ) and H − (t ) are able to analyze the upward and downward fluctuations, but not clear enough to show the scale of switching points and the asymmetric characteristics. We use the improved A-DFA method described in [40] to solve this problem. In order to precisely of and the ( pair)the peaks ( switching ( ) the indices ) ( points, ) as well as to make + − the result more evident, consider H (t ) = H + t − 2L H + t + 2L and H (t ) = H − t − 2L H − t + 2L , and then calculate
+
−
∆H (t ) = H (t ) − H (t ). For a width l and t = 1, 2, . . . , l, if ∆H (t0 − t ) < ∆H (t0 ) > ∆H (t0 + t ) or ∆H (t0 − t ) > ∆H (t0 ) < ∆H (t0 + t ), ∆H (t0 ) is a local extreme. For all ∆H (t ), if it is not an extreme, we set z (t ) = 0. If it is an extreme, we record this value t
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and identify it as Ti , and then set z (i) = ∆H (Ti − 1) − 2∆H (Ti ) + ∆H (Ti + 1). In this paper, we set l = 10 to note small fluctuations, which is tested to be a reasonable value according to Rivera-Castro et al. [40]. The positions of z (i) ̸ = 0 pairs the positions of switching points in the fluctuation trend, and their magnitudes gauge their strength. To show a clear graph of the switching points and their asymmetric characteristics, we only plotted those z (Ti ) values whose |z (Ti )| are larger than a certain level and ignore the small fluctuation trend changes. Furthermore, we can replace the exponents in Eq. (6) and Eq. (8) with f (q) and rewrite them as Eq. (9) and Eq. (10):
( Fq (s) =
m )q 1 ∑( 2 F (v, s) 2 m
v=1
⎛ Fq+ (s) = ⎝
1
∑ (
m+
) 1q
⎞ 1q q ) F 2 (v, s) 2 ⎠
(9)
(10)
byv >0
Where variable q can take any real number except zero. Specially, we can define:
( F0 (s) = exp
m 1 ∑
2m
⎛ F0+ (s) = exp ⎝
) ) ln F 2 (v, s) (
(11)
v=1
1 2m+
⎞ ∑ ( ) ln F 2 (v, s) ⎠
(12)
byv >0
Thus, we can get different Hurst indexes Hq , Hq+ and Hq− for any different q. In general, Hurst index H represents the long-term power-law correlations within the time series. H + and H − represents the upward and downward trends of the time series. If H + ̸ = H − , we say the time series is asymmetric. Hq represents the scaling behavior of large fluctuations for q > 0 and small fluctuations for q < 0. When q > 0, large fluctuations are characterized by a smaller Hq and when q < 0, small fluctuations are characterized by a larger Hq . This principle is detailed in [41]. If Hq remains the same for different q, the time series is monofractal. Otherwise, the time series is multifractal. In this way, we can analyze both the multifractality and the asymmetric characteristics in the dry bulk market index with Hq+ and Hq− simultaneously. 4. Empirical results 4.1. Structural breaks With the structural change model, we can get the breaking points of freight rate indices for each vessel type. The detailed statistics are processed with Gauss 8.0 and listed in Table 3. The results reveals that during the past decade, the world dry bulk shipping market experienced three structural periods under the financial crisis influence, which is divided by two main breaking points for each index respectively. To investigate the 2008 world financial crisis effect on freight rate volatility, for each vessel type, we solely extract the second breaking point in 2008. Thus, the focused time series was separated into two parts: first period from 04/19/2007 to 09/08/2008 and second period from 09/09/2008 to 02/26/2015 for supramax; first period from 04/24/2007 to 09/10/2008 and second period from 09/11/2008 to 02/26/2015 for panama; first period from 07/31/2007 to 09/05/2008 and second period from 09/06/2008 to 02/26/2015 for capsize. We apply the A-MF-DFA model in freight rate volatility asymmetric effect and multifractality analysis. V_BCI1 and V_BCI2 stand for capesize freight index volatility in the first and second period respectively, and so on for V_BPI1, V_BPI2, V_BSI1, and V_BSI2. Correspondingly, V_BCI, V_BPI and V_BSI stand for the whole time series. 4.2. Asymmetric volatility
∆H (t ) described in Section 3.2 is applied here to show the asymmetric characteristics of dry bulk shipping freight rate + − indexes. The results are shown in Fig. 3. Since ∆H (t ) = H (t ) − H (t ), when ∆H (t ) > 0, the asymmetric volatility effect is positive and vice versa. In the first research period of BSI, ∆H (t ) tends to be negative and becomes more volatile as the second breaking point approaches. In the second research period of BSI, there is also a volatile region around the year 2014, but not as turbulent as the year 2008, when financial crisis and the breaking point appear. In the first research period of BPI, the overall trend of the asymmetric volatility is not very clear, because ∆H (t ) first turns negative and later positive as time approaches the second breaking point. Similar complex volatility happens in V_BPI2 and V_BCI2, where overall trend is not easy to conclude. For V_BCI1, the positive and negative trend are of the same level. Thus no obvious asymmetric characteristic is detected. From this analysis we can also conclude that ∆H (t ) is not satisfactory to demonstrate asymmetric volatility. As a result, a further discussion with z (t ) in Section 4.3 is applied.
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Fig. 3. ∆H (t ) for dry bulk shipping freight rate indexes BSI, BPI and BCI of two periods.
4.3. Switching points Switching points imply upward and downward trends, which is also a key feature to analyze the asymmetric characteristics of freight rate volatility. We applied A-MF-DFA model on the whole time series V_BCI, V_BPI and V_BSI. Fig. 4 compares the results of z (t ) and ∆H (t ) for V_BPI as an example. The asymmetry is obvious from Fig. 4, where the peaks of positive and negative switching points have different numbers and scales. The majority of switching points from z (t ) are detected where ∆H (t ) becomes more turbulent, and z (t ) is more evident than ∆H (t ) to show the characteristics of dry bulk shipping freight rate indexes, showing the validity of the improved method. Fig. 5 shows all the switching points from 07/04/2005 to 02/26/2015 of all the indexes, and there are also switching points gather around the breaking points that we detected in the first stage study, which indirectly verifies the structural change model. We extract the data of V_BSI1, V_BSI2, V_BPI1, V_BPI2, V_BCI1 and V_BCI2, and summarize the result in Table 4. In all market sectors (capesize, panamax and supramax), the freight indexes are time-varying. In the supramax sector, the asymmetric volatility effect is negative in the first period and positive in the second period. In the panama sector, the asymmetric volatility effect is positive in the first period and there was no asymmetric volatility effect in the second period. In capesize sector, there was no asymmetric volatility effect in the first period and the effect is negative in the second period. For V_BPI2 and V_BCI1, although we can still detect a certain level of asymmetric characteristic, there are too few switching points or the average of all switching point level is too small. Therefore we mark they have no asymmetric effects. This is also shown in Table 5 when comparing the results between during and after the financial crisis.
J. Liu, F. Chen / Physica A 505 (2018) 316–327
Fig. 4. Comparison between the results of ∆H and z for V_BPI in 2008.
Fig. 5. Fluctuation trend switching points and their asymmetric characteristics of V_BSI, V_BPI and V_BCI.
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J. Liu, F. Chen / Physica A 505 (2018) 316–327 Table 4 Different volatility effect level shown from switching points (SPs).
V_BSI1 V_BSI2 V_BPI1 V_BPI2 V_BCI1 V_BCI2
Number of SPs
Average of SPs
18 46 18 76 1 27
−0.055949482 0.052688188 0.171112522 −0.023300606 0.873843479 0.185051211
Table 5 Asymmetric volatility effect s in the dry bulk shipping freight market during financial crisis (Period 1) vs. after financial crisis (Period 2).
V_BSI V_BPI V_BCI
Period 1
Period 2
Negative Positive None (Positive)
Positive None (Negative) Positive
4.4. Multifractal asymmetry Similar to Section 4.3, multifractal asymmetry feature of dry bulk freight rate is studied based on A-MF-DFA model with switching points. Here we set q from −5 to 5 and see how small and large fluctuation influence the time series. The multifractal asymmetry feature described by the number and average scale of switching points is visualized in Fig. 6. As is stated in Section 3.2, q value from negative to positive describes the effect of large fluctuation and small fluctuation on the volatility of dry bulk freight rate separately. Number and average level of switching points represent the severity of the volatility. As an overall trend, the number of switching points declines very quickly as q value increases. This demonstrates that dry bulk freight rate is multifractal asymmetric. Compared with large fluctuation, small fluctuation has much larger effect on the time series, showing the great volatility of dry bulk freight rate. It is worth to mention that in Fig. 6, the number and average level of switching points also rely on the value of window size l and minimum level z described in Section 3.2. Different values can lead to different results, but as long as the value of l and z is rational, the overall trend should be the same [40].
4.5. Source of asymmetric volatility effects Considering the number of switching points, the average of all switching point level neglecting the average switching point level of V_BPI2 and the only one SP of V_BCI1 as noted in Table 4 and Table 5, we conclude that V_BSI has the largest volatility among all the three indices. This conclusion is in accordance with Kavussanos [42] and Chen et al. [43] and Jing et al. [5]. Meanwhile, V_BCI is the least, which reveals that after the world financial crisis, the supramax shipping market is the most volatile sector whilst the capesize market is the least volatile sector. Supramax vessel is the most flexible vessel among the three types and is mainly engaged in transporting minor dry bulk cargoes, such as bauxite, alumina, fertilizer, rice and sugar. Capesize vessel is the least flexible type as capsize vessels are generally for transportation of iron ore and coal. Panamax vessel is mainly engaged in transporting coal, grain and sometimes, iron ore. Before the world financial crisis, the world shipping market has reached a historical top in late 2007; shipping firms to increase their fleet size placed many vessel orders. With the beginning of world financial crisis, the dry bulk shipping freight index tended to drop suddenly. Since then, overcapacity pervades in the world shipping market. On one side, for the capesize vessels, as they are engaged in major bulk commodities transportation, the international trade between countries and continents are relatively steady, the capesize and panamax shipping markets could resist certain kind of market shocks. On the other side, as supply overcapacity is severe in the dry bulk shipping market, even if positive market innovations arrive, freight rate is reluctant to increase, as overcapacity cannot absorb. In the panamax sub market, as panamax vessels are more flexible than capesize vessels, with the relative steady demand, shipowners could suffer less loss, and when positive information came, it could induce larger volatility than that of the same magnitude of negative information. For the supramax sector, before the financial crisis, as the shipping market continued to boom and the flexibility of supramax, ship owners could adjust their operations easily and freely to make profits. However, during the second period, as the financial crisis emerged, the minor bulk transportation market suffered heavy loss, ship owners and shipping firms cannot adjust their operation strategies freely, together with the supply overcapacity, so the volatility effect turned severe.
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Fig. 6. Number and average scale of switching points for different bulk vessels.
5. Conclusions The world dry bulk shipping market has experienced a long booming period since year 2000. However, since year 2007, the shipping market has been more complex and extremely volatile. It has been very hard for practitioners and researchers to understand the underlying essence and risks of this market. Past research on freight volatility modeling mainly focused on the pre-financial crisis booming period that they neglected the risks brought by the 2008 financial crisis. In this paper, we specialized on the dry effects on bulk market volatility by the financial crisis, aiming to clarify the market volatility characteristics before and after the crisis. We used daily BSI, BPI and BCI from 07/01/2005 to 02/26/2015 to investigate the asymmetric volatility effect within the world dry bulk shipping market. By extending A-MF-DFA model, we successfully investigated the asymmetric volatility effect in the world dry bulk shipping market during the financial crisis. The conclusion could be draw as in all market sectors (capesize, panamax and supramax), the freight indexes are time-varying. In the supramax sector, the asymmetric volatility effect is negative in the first period and positive in the second period. The asymmetric characters are different in the three types of bulk vessels. In summary, the structural break model and A-MF-DFA model are successful in detecting the breaking points as well as determining the asymmetric fluctuation characteristics of the freight indexes. The A-MF-DFA model is effective in studying
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asymmetric volatility effects in the dry bulk freight markets. However, in the future research, a more comprehensive multivariate model is needed to investigate the freight volatility, as the world dry bulk shipping market is not isolated, which is determined by international trade and global economy development. Overall, the results generated by this research could provide a new perspective on freight market volatility during the 2008 financial crisis, which may be useful for practitioners and researchers on market risk management and operation strategies decision-making. Acknowledgments We thank support from State Key Laboratory of Ocean Engineering of Shanghai Jiao Tong University and Simulation of Complex System Laboratory (SCS Lab) of the University of Tokyo. This work is sponsored by Natural Science Foundation of Shanghai. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37]
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