Assessment of investment decision in the dry bulk shipping market based on real options thinking and the shipping cycle perspective

Figures & data

Table 1. The notations and definition.

Notation	Definition	Unit
$PV$	the total present value of the investment revenue	Million dollars
$T_0$	the capital investment costs of the vessel	Million dollars
$n$	the investment horizon	N/A
$r$	the risk-adjusted discount rate	N/A
$C{F}_t$	the operating income in period t	Million dollars
$T_n$	the residual value of the vessel after depreciation	Million dollars
$C_{i,j}$	the option value during period i for situation j	Million dollars
P	the rising probability of the option value	N/A
$P^{\ast }$	the subjective rising probability judgments of the investors	N/A
u	the rising volatility	N/A
d	the falling volatility	N/A
$C{F}_i$	the sum present value of the options during period i	Million dollars
$F_s$	the freight rate of the stopping node	Dollars per ton
$F_r$	the freight rate of the restarting node	Dollars per ton
AOC	the average operating cost	Dollars per ton
SC	the stopping cost	Million dollars
RC	the restarting cost	Million dollars
Q	the vessel capacity under the operation state	Million tons
$F_t$	the operation revenue in time t	Dollars per ton
FC	the fixed cost of the vessel whether in the operation or stopping state	Million dollars
$F_{ij}$	the freight rate during period i for situation j	Dollars per ton
$T_{A\left(i,j\right)}$	the abandonment trigger during period i for situation j	Million dollars
ABC	the vessel abandonment cost	Million dollars
$A_{ij}$	the abandonment option value	Million dollars
$T_i$	the residual value of the vessel in period i	Million dollars
$R_{i,j}$	the operation revenue if investors do not exercise the abandonment option	Million dollars
p	the order of the GARCH ${\sigma }^2$ terms	N/A
q	the order of the ARCH ${ϵ}^2$ terms	N/A
${\sigma }^2$	the variance in the GARCH model	N/A
$\omega$	the constant term which means the long-term fluctuation of the sequence	N/A
R_SHP	the first-order difference SHP data	N/A

Figure 1. Binomial valuation model.

Figure 2. Abandonment trigger, $T_{A\left(i,j\right)}$. # stopping node; * restarting node.

Table 2. Volatility data for tough and peak periods.

Shipping Cycle	Time	Time span	Index	Frequency	Volume
With Shipping Cycle	Tough period	2010.07.16–2017.05.05	BDI	Weekly	347
			SHP	Weekly	347
	Peak period	2004.07.09–2008.09.12	BDI	Weekly	219
			SHP	Monthly	51
Without Shipping Cycle	Recent 10 years	2007.05.06–2017.05.05	BDI	Monthly	120
			SHP	Monthly	120
	Recent 5 years	2012.05.11–2017.05.05	BDI	Weekly	259
			SHP	Weekly	259

Source: https://sin.clarksons.net

Table 3. The statistics results and ARCH lagrange multiplier test results of the AR and GARCH models.

	AR(1)	AR(2)	AR(3)
AIC	−5.70466	−5.74064	−5.83255*
	GARCH(1,1)	GARCH(1,2)	GARCH(2,1)
AIC	−5.68208	−5.77977*	−5.65927
	AR(3) model		GARCH(1,2) model
Time lag coefficient	F-statistic	Prob.	F-statistic	Prob.
1	6.079950	0.0436	0.201109	0.6541
1	4.274157	0.0147	0.099914	0.9049
3	3.694993	0.0121	0.065330	0.9782
4	2.763627	0.0276	0.067943	0.9915
5	2.235471	0.0106	0.410995	0.8411
10	2.044006	0.0285	0.523848	0.8731

*Null hypothesis rejected (under 5% level of significance)

Table 4. Volatility parameter calculation results.

Shipping Cycle	Time	Index	Volatility ${\sigma }^2$	Rising rang u	Falling range d
With Shipping Cycle	Tough period	BDI	$6.276\times {10}^{-4}$	1.1972	0.8353
		SHP	$1.110\times {10}^{-4}$	1.0789	0.9268
	Peak period	BDI	$3.823\times {10}^{-4}$	1.1514	0.8685
		SHP	$2.816\times {10}^{-3}$	1.2018	0.8321
Without Shipping Cycle	Recent 10 years	BDI	$6.183\times {10}^{-2}$	2.3665	0.4226
		SHP	$1.177\times {10}^{-2}$	1.4563	0.6867
	Recent 5 years	BDI	$1.417\times {10}^{-3}$	1.3119	0.7623
		SHP	$2.210\times {10}^{-4}$	1.1132	0.8983

Table 5. Case study parameters.

Parameter	Value	Unit
Annual Fixed Cost (FC)	2	Million dollars
Annual Freight Volume (Q)	0.8	Million tons
Annual Stopping Cost (SC)	0.8	Million dollars
Annual Restarting Cost (RC)	0.5	Million dollars
Annual Average Operating Cost (AOC)	15	Dollars per ton
Risk-adjusted Discount Rate (r)	8%	N/A
Annual Depreciation Rate (DR)	10%	N/A
Abandonment Cost (ABC)	5	Million dollars

Table 6. Results of ROA and NPV methods.

Method	Result	Implication
NPV	-$\mathrm{\$}$2.06 million	Reject
ROA	$\mathrm{\$}$2.59 million	Accept
ROA(without shipping cycle)	-$\mathrm{\$}$0.37 million	Reject

Figure 3. Binomial freight rate and operating model.