Decision-making process in shipping finance: A stochastic approach

Figures & data

Table 1. Summary of data of credibility and correlation coefficients

s	Internal variable	Group	m	${\overline{Z}}_{\bullet s}$	${\widehat{Z}}_s$	rs
1	Loans		91	>1	0.59^*	–
2	Net income	I	91	>1	0.71	0.52^**
3	Total assets	II	92	>1	0.61	0.65^**
4	Deposit & short funding	II	92	>1	0.62	0.49^**
5	Net interest	I	91	>1	0.64	0.71^**
6	Profit before tax	I	91	0.77	0.69	0.29
7	Interest income on loan	I	88	0.33	0.62	0.73^**
8	Interest expenses on customer deposits	II	83	0.81	0.64	0.78^**
9	Total interest expenses	I	91	>1	0.66	0.53^**
10	Net interest income	I	89	>1	0.64	0.47^**
11	Operating profit	I	91	0.73	0.7	0.66^**
12	Personnel expenses	I	81	>1	0.65	0.62^**
13	Corporate commercial loans	II	55	0.82	0.63	0.57^**
14	Customer deposits	II	81	>1	0.66	0.46^**
15	Total customer deposits	II	89	<1	0.63	0.52^**

Notes: m: sample size (banks); ${\overline{Z}}_{\bullet s}$: sample mean of the s-internal variable; ${\widehat{Z}}_s$: credibility coefficient estimate conditioned on the uniform hypothesis assigned to the s-internal variable; r_s: Spearman correlation coefficient between internal variables and loans.

^* Significance level at p < 5%.

^** Significance level at p < 1%.

Table 2. Spearman correlation coefficients between internal variables

Group I	Net interest income	Interest income on loans	Total interest expenses	Personnel expenses	Operating profit	Profit before tax
Net income	0.46	0.24	0.06	0.14	0.99	0.82
Net interest income		0.97	0.91	0.94	0.57	0.88
Interest income on loans			0.98	0.99	0.36	0.75
Total interest expenses				0.99	0.18	0.62
Personnel expenses					0.26	0.68
Operating profit						0.89
Group II	Corporate commercial loans	Customer deposits	Total customer deposits	Deposits & short term funding	Interest expenses on customer deposits
Total assets	0.98	0.86	0.96	0.99	0.83
Corporate commercial loans		0.90	0.98	0.99	0.83
Customer deposits			0.90	0.86	0.83
Total customer deposits				0.99	0.93
Deposits & short-term funding					0.88

Table 3. Results of Z_loan and estimate of ${\widehat{Z}}_{\text{loan}}$ based on the optimal model

Zloan	Int in loan	Oper prof	${\widehat{Z}}_{\text{loan}}$	Zloan	Int in loan	Oper prof	${\widehat{Z}}_{\text{loan}}$
0.028	0.677	2.366	>1	0.989	0.992	1.025	>1
0.106	0.249	−5.341	<0	0.989	0.958	1.011	0.992
0.157	−3.661	0.571	<0	0.994	0.996	1.089	>1
0.316	0.260	2.092	0.964	0.996	0.993	1.007	>1
0.318	0.300	0.091	0.403	0.997	0.938	1.010	0.983
0.406	2.574	3.882	>1	0.997	0.998	0.997	>1
0.483	0.849	1.086	0.961	0.997	1.002	1.000	>1
0.523	0.864	−9.631	<0	0.998	0.999	0.917	0.985
0.571	1.025	0.682	0.930	0.998	0.964	0.921	0.970
0.578	0.152	1.941	0.867	0.999	0.997	1.045	>1
0.585	0.757	0.823	0.840	1.000	1.000	1.001	>1
0.626	−21.711	4.090	<0	<0	−11.452	12.852	<0
0.652	0.617	1.758	>1	<0	−4.049	1.103	<0
0.683	0.302	0.855	0.626	<0	−3.489	1.532	<0
0.764	0.681	1.270	0.932	<0	−3.206	5.255	0.183
0.768	1.041	1.076	>1	<0	0.340	2.526	>1
0.768	0.341	1.356	0.790	<0	1.285	7.739	>1
0.802	0.867	1.161	0.992	>1	1.130	−37.359	<0
0.807	1.212	0.946	>1	>1	0.428	−2.678	<0
0.847	1.401	0.582	>1	>1	1.506	−4.394	<0
0.850	0.852	1.058	0.955	>1	0.639	−0.343	0.444
0.853	−1.280	1.028	<0	>1	0.868	−0.239	0.586
0.886	0.964	0.505	0.849	>1	1.114	−0.228	0.710
0.894	0.963	0.974	0.985	>1	0.652	0.673	0.745
0.905	0.893	0.975	0.950	>1	0.743	0.704	0.798
0.907	0.977	1.129	>1	>1	0.779	0.689	0.812
0.913	0.994	0.892	0.976	>1	0.817	0.688	0.830
0.918	0.835	1.092	0.956	>1	0.811	0.809	0.862
0.931	0.931	1.284	>1	>1	0.787	0.875	0.869
0.932	1.183	1.470	>1	>1	0.384	1.777	0.934
0.939	0.982	1.031	>1	>1	0.238	2.114	0.960
0.951	1.009	1.252	>1	>1	1.016	0.887	0.985
0.956	1.227	0.968	>1	>1	1.160	0.681	0.996
0.957	0.849	0.607	0.822	>1	1.015	1.069	>1
0.959	0.836	−0.346	0.539	>1	1.115	1.097	>1
0.959	1.052	1.002	>1	>1	0.990	1.367	>1
0.970	0.876	0.905	0.922	>1	1.234	1.388	>1
0.970	0.903	0.870	0.925	>1	1.183	1.614	>1
0.972	0.992	1.073	>1	>1	1.451	1.413	>1
0.973	1.106	1.136	>1	>1	1.813	1.068	>1
0.975	1.024	1.007	>1	>1	1.629	2.179	>1
0.981	0.984	0.963	0.992	>1	1.910	2.128	>1
0.982	0.952	0.988	0.983	>1	1.946	2.119	>1
0.987	1.092	0.851	>1	>1	1.400	7.840	>1

Notes: Paired values of credibility coefficients for both the independent variables interest income on loan (second column) and operating profit (third column).

Figure 1. Model’s surface regression estimate (z = 0.23 + 0.49 x + 0.29 y. R² = 0.88) versus data points of credibility coefficient on loan (z-axis) with respect to interest income on loan (x-axis) and operating profit (y-axis).

Notes: All values above 1 and below 0 are upper and lower limited to 1.01 and −0.01, respectively, in this plot.

Figure 2. Histograms of values of Z_loan when ${\widehat{Z}}_{\text{loan}}$ < 0 (top left a) and ${\widehat{Z}}_{\text{loan}}$ > 1 (bottom left c) and histogram of estimates ${\widehat{Z}}_{\text{loan}}$ when Z_loan > 1 (bottom right d). In all histograms the solid line is the normal fit curve adjusted to the data. At the top right (b) is the scatter plot (plus symbols) of ${\widehat{Z}}_{\text{loan}}$ (vertical axis) vs Z_loan (horizontal axis) together with the bisector (dashed) line.