Decision-making process in shipping finance: A stochastic approach

Shipping markets irregularity due to high-level volatility of freight rates and asset prices increases the risk of banks’ invalid financial strategy. Risk is further increased due to the heterogeneous shipping market, despite the regulations set by the Basel Convention. Consistent with the above, the present work contributes to the existing methodological aspects of bank’s financial strategy on shipping finance by enhancing the role of the credibility theory, which balances the individual bank policy with the market as a whole. This has been primarily forwarded on by the analysis of the operational environment’s internal factors of an individual bank combined with the whole shipping banks’ loans portfolio by estimating the credibility factor to the decision of the bank to either increase or decrease financing in the relevant market. The important factors extracted from the principal components analysis are linked with interest income on loan and operating profit accounts. The final model predicts that the optimal decision is positive driven by both the aforementioned dependent variables, while the interest income on loan variable has more influence compared with that of the operating profit variable. In the absence of the influence of the dependent variables, the bank’s decision strategy matches the market’s strategy by 77% that decreases as the dependent variables increase their influence. *Corresponding author: Marina Maniati, Department of Economics, University of Piraeus, 80, M. Karaoli & A. Dimitriou St., Piraeus, Attica 18534, Greece E-mails: marinamaniati@gmail.com, mm@premiumc.gr Reviewing editor: David McMillan, University of Stirling, UK Additional information is available at the end of the article ABOUT THE AUTHORS Marina Maniati obtained her BSc and MSc in the Maritime Studies and obtained a Phd in Shipping Finance & Bank Performance from the Department of Economics of UNIPI. As an Economist & Financial Consultant, she draws on issues of Finance & Evaluation and of shipping market to frame her analysis. She has presented her academic work in different Conferences and Journals, while she has participated in several European & National Research Projects and/or Studies. Evangelos Sambracos is a professor of Transports Economics at the Department of Economics in the University of Piraeus. He graduated from the School of Engineers (Aristotle University) and obtained a DEA in the Transports Economics (University of Lyon II). In 1984 he received his PhD Diploma in the Transports Economics (University Lyon II)— Ecole Nationale des Travaux Publics de l’ Etat. He has participated in many research studies and projects and he has presented his work in different conferences and journals. PUBLIC INTEREST STATEMENT High-level volatility of freight rates and asset prices increases the risk banks undertake when getting involved in shipping finance. The relevant risk may influence the performance of corporate bank loans, especially during times of financial instability in the industry. Consistent with the above, the present work aims to contribute as a decision support tool that implicitly increases the validity of future financial strategy specifically on loan grants to shipping industry. This has been primarily forwarded by the analysis of the operational environments’ internal factors of an individual bank combined with the whole shipping banks’ loans portfolio. Finally, a specific methodological framework for shipping finance is developed that might be considered as an optimal decision of an individual bank to either increase or decrease a loan grant taking into account both its policy in the shipping market, as well as the most important variables arising from its internal operational environment. Received: 21 December 2016 Accepted: 31 March 2017 Published: 17 April 2017 © 2017 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.


PUBLIC INTEREST STATEMENT
High-level volatility of freight rates and asset prices increases the risk banks undertake when getting involved in shipping finance. The relevant risk may influence the performance of corporate bank loans, especially during times of financial instability in the industry. Consistent with the above, the present work aims to contribute as a decision support tool that implicitly increases the validity of future financial strategy specifically on loan grants to shipping industry. This has been primarily forwarded by the analysis of the operational environments' internal factors of an individual bank combined with the whole shipping banks' loans portfolio. Finally, a specific methodological framework for shipping finance is developed that might be considered as an optimal decision of an individual bank to either increase or decrease a loan grant taking into account both its policy in the shipping market, as well as the most important variables arising from its internal operational environment.

Introduction
The presence of high risk in shipping markets due to high volatility in terms of freight rates and asset prices raises questions about banks' decisions to continue financing such an irregular and heterogeneous market, despite the regulations set by the Basel Convention (Albertijn, Bessler, & Drobetz, 2011;Sambracos & Maniati, 2013). Bank finance is an important source of capital for the financing of the shipping industry, while the relevant default risk may also lead banks to bankruptcy (Chava & Purnanandam, 2011) and influence the performance of corporate bank loans during times of financial instability in the shipping industry (Mitroussi, Abouarghoub, Haider, Pettit, & Tigka, 2016).
Classification of factors that affect the amount of loans for the shipping industry the following year (based on previous years' experience) might be critical for banks' performance. In this paper, internal factors of the operational environment of an individual bank in relation with the whole shipping banks' loans portfolio, are analysed by applying the credibility factor to the decision of a shipping bank to either increase or decrease financing in the relevant market.
Consistent with the variance of shipping loans granted, we present a stochastic model in order to estimate the premium for the next period in relation with past claims experience data (Zadeh & Stanford, 2016). This model is based on the credibility factor as a parameter used to quantify the individual bank's outcome (decision) with respect to both the internal and external financial environment.
The earliest work on credibility theory was made by Mowbray (1914) and Whitney (1918) who referred to limited fluctuation, in order to incorporate in premiums as much as individual experience as possible. Bühlmann (1967) proceeded in formalising the principles for the credibility theory based on premiums, as well as in computing credibility factors Z in the model with equal exposure units. Further analysis on credibility theory had been presented by Bühlmann and StrauB (1970), Hachemeister (1975), De Vylder (1976, Goovaerts andHoogstad (1987), andFrees (2003).
Recently, credibility models have been mainly applied in property and casualty insurance, in life insurance. Herbertsson, Meester and Sander, and Fackrell applied phase-type distributions to health care, finance and transportation infrastructure. There has been a large number of applications available concerning risk theory, where the claim sizes were frequently assumed to be phase-type distributed.
Principal component analysis (PCA), preceded in order to decrease the dimensionality of a bank's internal environment system variables by defining those most significant that explained more than 95% of system variance. PCA was first introduced by Pearson (1901), and recently has been forwarded on with a large set of data by Hanschel and Monnin (2005), Illing and Liu (2003), Canbas, Cabuk, and Kilic (2005), Ho and Wu (2009), Abu-Shanab and Pearson (2009), Baek, Balasubramanian, and Lee (2015. Ionită and Şchiopu (2010), we follow PCA based on both balance sheet and profit and loss account data, as the dimension of data is reduced without much information loss. Moreover, our work follows Shih, Zhang, and Liu (2007) that derived four measures of a bank's ability to perform the core task of financial intermediation based on PCA and, in order to understand the factors that drive Chinese bank performance. This paper reveals the most important factors that arise from a bank's internal environment based on PCA and implicitly contributes to the development of a specific methodological framework for shipping finance with respect to bank credibility. Essentially, it might be considered as a decision support tool, taking into account both the credibility factor in decision-making process, and the policy each bank wants to follow in the market, as well as the most important variables arising from its internal operational environment.

Consistent with
We found that: (i) the main factors are interest income on loan and operating profit accounts and the optimal decision is positively influenced by both variables. The first variable has more influence compared with the second one, (ii) in the absence of the influence of the dependent variables, the bank's decision strategy approaches the market's strategy by 77% and (iii) as the dependent variables increase their influence, the bank's decision to either increase or decrease shipping loans limits to its own policy.
The paper is structured as follows: Section 2 briefly describes the data and the methodology used, while Section 3 introduces the empirical results of the present study. The proposed support tool is then briefly discussed in Section 4 and some concluding remarks are provided in Section 5.

Methodological issues
Data were derived from Bloomberg and Bankscope databases and all rules and restrictions were conditioned accordingly. Technical analysis was forwarded with MATLAB TM and all statistics were processed with SPSS (IBM COM, v.22).

The credibility coefficient estimate
Considering that the market consists of m-shipping banks that grant loans to the shipping sector the last n-observed years, the credibility ∑ m j=1 R ij is the corresponding overall mean of a shipping banks portfolio. Credibility is the difference of the total loan that will be granted from the shipping bank the next year (n + 1) conditioned on a credibility factor Consistent with Bühlmann's theory, the factor Z j is in principle between values 0 and 1 and implicitly measures the amount of credence attached to the individual experience. In the current research, the lower and upper limits of the credibility factor are either extended below zero or above one. For instance, when either C j < H <R •j or R •j < H < C j then Z j < 0. On the other hand, when either H <R •j < C j or C j <R •j < H then Z j > 1.

The stochastic uniform hypothesis
Consistent to heterogeneous portfolios of loans granted by m-shipping banks during the last n-years, contracts are in principle conditioned to unknown risk factors Θ ij i=1, …, n j=1, …, m that are different through years and among banks. The objective hypothesis is that all contracts are subject to a common risk factor, i.e. Θ ij = Θ, and the credibility factor Z j is commonly constrained as . The structural parameter k = E V{X|Θ } ∕V E{X|Θ } , where E V{X|Θ } and V E{X|Θ } are the mean variance and the variance of the mean, respectively, of the total loan grants X conditioned on the risk factor Θ. In terms of statistics, let a random variable (RV) X (j) i conditioned on an unknown parameter θ ∊ Θ that is the upper bound of the total loan grants of the j-shipping bank, j = 1, …, m at the year i = 1, …, n. In the absence of any well-established, prior Irrelevant to the unknown parameter θ, the variance of total loan grants of the j-bank at the i-year . Therefore, the PSF of the second moment of the unknown parameter θ, is Ê 2 = 3 ⋅ ̂2 −̂2 that subsequently leads to the point estimates of

Table 1. Summary of data of credibility and correlation coefficients
Notes: m: sample size (banks); Z •s : sample mean of the s-internal variable; Ẑ 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%. We applied both methods described above to extract the credibility coefficient for all m-banks and p-internal data variants (see Table 1). The array Z = Z j,s m×p contains the credibility coefficients estimates Z j,s of j-bank (j = 1, …, m) for the s-internal variable (s = 1, …, p) and Z •s = m −1 ⋅ ∑ m j=1 Z js is the sample mean of the s-internal variable. Similarly, the credibility coefficient constrained on the uniform hypothesis Ẑ s is for the s-internal variable. Finally, the non-parametric Wald-Wolfowitz test was applied to test the validity of the objective hypothesis that the parametric mean of credibility coefficients of an internal variable equals the corresponding estimate value conditioned on the uniform hypothesis.

Principal component analysis
Principal component analysis (PCA) was applied separately on the internal data of two sets of banks derived from: group (I) profit and loss accounts (net income, net interest income, interest income on loans, total interest expense, personnel expenses, operating profit, profit before tax, net interest) and group (II) balance sheet (total assets, corporate and commercial loans, customer deposits, total customer deposits, deposits and short-term funding, interest expense on customer deposits).
Both the Spearman correlation coefficient (r s ) and the Kaiser-Meyer-Olkin (KMO) statistics were extracted. For each set of data, the rationale behind applying PCA was to examine the relationships among covarying variables, by transforming the original data to a new set of equal number of orthogonal variables, i.e. the PCs.
PCs are derived in a decreasing order of importance, so that the first and the last PC, respectively, account for the maximal and minimal amount of variance in the original data. In addition, they linearly combine the original variables. Weight coefficients are the contributions of each original variable to each one of the PCs and in absolute terms, the original variable with the maximum contribution to a significant principal component is selected for further process. Percentages of the variation in the original set of p-variables where the PCs account for are equal to the normalised ei- . Eigenvalues s s=1, …, ,p and their corresponding eigenvectors v s s=1, …, p were computed using the MATLAB TM function eig.

PCs' statistics
Bartlett's test of sphericity was used to test the null hypothesis of equal eigenvalues of PCs. For the s p -PCs of lower importance L 1 , …, L s p with corresponding eigenvalues λ 1 < … < s p this had to be ac- is not greater than the critical value of chi-square distribution with s p − 1 s p + 2 ∕2 degrees of freedom. As Bartlett's test is insufficient for testing the significance of the last two PCs, i.e. those of the lowest importance (s = 1, 2), a port hoc test for proportion of total variance was applied. A desired proportion of the minimum of the total variance at 95.0% was selected and then excluded all PCs which accounted for less than 1% of the total variance.

Multilinear regression
consists of a constant term β 0 and w-slopping coefficients such that the coefficient s w explains the influence of the credibility coefficient vector Z s w to the dependent vector variable Z. Method of ordinary least squares (ols) solves the linear regression model and estimate of the vector All diagnostic tests for residual errors were passed in order to confirm the linear, unbiased and minimum variance estimate B .

Data and empirical results
Data for eighty eight (88) banks worldwide involved in shipping finance were derived from Bloomberg and Bankscope databases for the time period 2005-2010 that the relevant industry displaced both its peak and least value.
For nine internal variables over 15 (see Table 1), the sample mean Z •s of the credibility coefficient was found to exceed the value 1 and for a single case (Customer Deposits) was found to be negative. In all other cases (5/15), the sample mean ranged from 0 to 1 and the parametric mean of the credibility coefficient for each one of the internal variables except Loan (s = 1) might be equal the corre-  By applying PCA, it found that there two significant principal components that together accounted for 99.9% of the total variance of all internal variables of group I; these were modest correlated (Table 2, Spearman's r s = 0.36, p < 0.001) variables Interest Income on Loan (s = 7, λ 1 = 5.03, 71.8%, α = 0.98) and Operating Profit (s = 11, λ 2 = 1.97, 28.1%, α = 0.99). Similarly in group II, only a single component was found that accounted for the 92.9% of the total variance; this was the Total Assets (s = 3, λ 1 = 5.57, α = 0.83). Neither Interest Income Loan nor Operating Profit was highly correlated to Total Assets (Spearman's r s = 0.58 and 0.63 < 0.7, respectively).
The univariate linear regression model of the credibility coefficient of Loans was estimated: and the step-wise method specified that the optimal model is: Table 3 contains paired values of credibility coefficients for both the independent variables Interest Income on Loan (second column) and Operating Profit (third column), that were used as inputs to the above model to estimate the credibility coefficient of dependent variable Loans (fourth column).
Finally, we preferred to show the estimated values if they were ranged from 0 to 1, while all others were qualitatively represented either as negative signed (<0) or greater than one (>1). Regarding the aforementioned model, the estimated values Ẑ loan are positioned in a plane surface (x-axis: Interest Income on Loan, y-axis: Operating Profit), that regresses through the data points (z-axis: Z loan ) with a goodness of fit R 2 = 88% (Figure 1).
Comparing Z loan data with Ẑ loan estimates, 14/88 matching cases were found where in 3 cases (pa = 3/14) both Z loan and Ẑ loan < 0 and in 11 cases (pd = 11/14) both Z loan and Ẑ loan > 1. On the other hand, 5 over 88 unmatched cases were found, where in 2 cases (pb = 2/5) Z loan < 0 and Ẑ loan > 1 and in 3 cases (pc = 3/5) Z loan > 1 and Ẑ loan < 0. The McNemar's test did not reject the null hypothesis that the two marginal probabilities for each outcome were the same, i.e. pa + pb = pa + pc and pc + pd = pb + pd (X 2 = 0.2, df = 1, p = 0.655) which implicitly states the coherency between raw data (Z loan ) end estimates (Ẑ loan ) for the values and took into account out of the interval 0-1.
In one case Z loan < 0, Ẑ loan was equal to 0.18. In 13 over 88 cases where Z loan > 1, the estimates that were found left skewed from 0 to 1 with a mean 0.81 (standard deviation 0.16). In 5 over 88 cases where values of Z loan were at the interval [0, 1] (mean and standard deviation were 0.55 and 0.32, respectively), their estimates Ẑ loan were found as negative. In 24 over 88 cases where values of Z loan ranged from 0 to 1, the estimates Ẑ loan were found greater than 1 with a mean 1.13 (standard deviation 0.23), respectively. Finally, in 26 over 88 cases both Z loan data and corresponding estimates Ẑ loan ranged from 0 to 1 with mean residual error equalled to −0.08 (standard deviation 0.22). Despite the negative sign of the mean difference Z loan -Ẑ loan , we presume that the estimates are unbiased (Student's test value = 0, t = −1.95, p = 0.063).

Discussion
Focusing on the most essential operational environments' internal factors of an individual bank combined with the whole shipping banks' loans portfolio that may influence its decision to either increase or decrease financing in the relevant market, we developed a specific methodological framework for shipping finance with respect to bank credibility. More specifically, we found that the most important variables from shipping bank's internal environment are linked to interest income on loan and operating profit accounts, while its decision for loan grants is related to its policy in comparison with the whole market (total of shipping banks).
According to Buhlmann's theory a decision (C) making process contains two components: the individual unit (R) and the whole population (H), that in our case is the bank and the mass of banks, respectively. They are both combined with weight coefficients Z and 1−Z and form a linear system If the Z coefficient is from 0 to 1, then the linear system illustrates how credible the individual unit is; Z = 0 means total non-credible and the decision is made based on, if the unit depends exclusively on the population (C = H); 0 < Z < 1 means partial credible; for instance, if Z = 0.5, then the decision is made based upon the average between the unit and the population units (C = (R + H)/2); and finally Z = 1 means fully credible and the decision ignores the population and is made exclusively by the unit (C = R).
For each internal factor the corresponding credibility coefficient was calculated. Consistent with the absence of any information for risk factors that influence the bank's policy, we may consider an unknown upper limit for loan grants and all grants could be randomly distributed. Thus, we selected the uniform distribution as the most appropriate probabilistic conceptualisation for the assumption of the size of the internal factor. In Table 1, for each internal factor both the classic mean (Z •s ) and stochastic (Ẑ s ) credibility coefficient were presented. Despite the wide range of means found from below 0 to above 1, the stochastic was ranged narrowly from 0.59 through to 0.71. Rejection of the credibility coefficients data normality allowed the non-parametric runs test rather than the student parametric test, and forwarded that the credibility coefficient might be insignificantly different to the stochastic value extracted under the uniform hypothesis for all 14 internal factors except the internal factor for loan grants.
Finally, we had two contradictory estimates: the mean estimate was greater than 1 and implied either a sharp aggressive or passive defensive strategy (see below). On the other hand, the stochastic value 0.59 implied balanced weights between the individual (59%) and the population market's (41%) strategy.
Since no prior work has been done regarding the issue of decision-making process strategy based on the credibility coefficients, we made two models: the "detailed" model that is fully presented here and the "lumped" model that will be explicitly analysed in forthcoming research.
The "detailed" model took into account all the single values of the credibility coefficients and all of the results in this paper are based on it. On the other hand, the "lumped" model evaluated only the stochastic values of credibility coefficients. In both models, the dependent variable is the credibility coefficient of loan grants internal factor and the independents are the most essential internal factors found from the PCA.
PCA was extracted from those internal factors which account for most of the variance of the system of all internal factors. Since large values of correlation coefficients were found between internal factors, the idea was that many of them were explained from others and that they were redundant. The aim of this analysis was to minimise the redundancy without seriously affecting the system's variance; in fact, the last was secured by setting a lower limit of 95% of the system's variance. Consistent with the method's limitations, we created two groups, each with homogeneous internal factors. To this end, PCA extracted three internal factors as the most essential: Total Assets, Interest Income on Loans and Operation Profit.
All three internal factors were used as independent variables in a linear univariate regression model for prediction of the credibility coefficients of loan grants that were used as the dependent variable (Z loan ). Stepwise regression analysis excluded the total assets variable by increasing the adjusted goodness of fit from 0.855 to 0.86. The final model predicts that (i) the values of Z loan are positively driven by each dependent variable, (ii) the interest income on loan variable has more influence compared to the operating profit variable (0.49 versus 0.29), (iii) if both variables together equal 0 or 1, i.e. reach their minimum or maximum value from zero through to one, then the Z loan equals 0.23 (the bank's decision strategy follows the market's strategy by 77%) or reaches its maximum value (the bank strictly follows its own strategy) respectively. By applying the "detailed" model in our study, we counted 55 over 88 banks (62.5%) of Z loan values from 0 to 1 and mean value of 0.8 that is actually quite close to 1. This is presumably an indication that the decision-making process on loan grants is more so based on the individual strategy rather than on the whole market statement. For those banks, about half (47.3%) were unbiased estimated by the model developed in this research, 9% were false estimated, given that estimates were found below zero and 43.7% were overestimated, given that estimates were found above 1. For the last case, the mean error estimate is about 0.12 and might be attributed to the other bank's internal factors with no significant influence to the values of Z loan .
In contradiction with the most frequent values of Z loan that were found from 0 to 1, there were also only 6 banks over 88 (6.8%) of negative signed Z loan values. In half of the cases, the Z loan values were adequately estimated from the model, in one case it was overestimated with error 0.18 and in two cases we had false estimates above 1. Negative values of Z loan two strategies regarding the next year (n + 1). One case, is the optimistic strategy that leads the bank to overcome the market's average amount of loan grants (C > H), while the previous year's had followed a pure conservative strategy by holding the average amount of loan grants below the market's corresponding (R < H). The other case, is the defensive strategy that leads the bank to grant loans below the market's average amount (C < H), while the previous year's had followed a regressive strategy by granting loans above the market's corresponding (R > H).
Finally, in 27 banks over 88 (30.6%) the Z loan values were found above 1. In 11 of those banks, Z loan values were matched from the model, in 13 banks the Z loan values were underestimated with mean error 0.18 and in only 3 banks there were false estimates, i.e. below zero. Values of Z loan above 1 implicate either an extreme aggressive or passive defensive strategy; the bank either increases (aggressive) or decreases (defensive) the loan grants the next period (n + 1) when the previous periods granted more (H < R < C) or less (C < R < H), respectively, than the population average. Both cases might be characterised as risky, since the individual policy for loan grants is further distant from the population average.
In summary, the importance of this paper concerns the methodological steps, (i) PCA as a powerful technique to find the most important internal factors that explain most of a bank's system variance and (ii) the credibility coefficient that balances the individual bank's policy with the market as a whole to either increase or decrease its loan grants to a shipping market. The main advantage of the proposed methodological framework is that it takes into account the current market trends and balances its own optimal policy concerning the loan grants.

Conclusions
The purpose of this study was threefold: (i) to analyse the operational environments' internal factors of an individual bank combined with the whole shipping banks' loans portfolio by estimating the credibility factor to the decision of the bank to either increase or decrease financing in the relevant market, (ii) to reveal the essential factors arising from a bank's internal environment and, finally, (iii) to develop a specific methodological framework for shipping finance with respect to bank credibility.
We found that the most important variables from shipping banks' internal environment that affect a bank's decision to either increase or decrease the shipping portfolio are linked to interest income on loan and operating profit accounts. In addition, an individual bank's decision for loan grants is related to its policy in comparison with the whole market (total of shipping banks); prices of Z loan close to or below zero mean that the bank's top management has little confidence in its own estimations and follows what its competitors do, while prices close to or above 1 show that despite, what the majority of the shipping banks decide for loan grants the following year n + 1, the individual bank will decide its own policy based on its own estimations.
Considering the aforementioned, key implications that arise from these findings concern (i) methodology, (ii) the natural basis of raw data, (iii) the significance of the improved financial strategy concerning the loan grant into the irregular and heterogeneous shipping market.
The behaviour of the model derived from the estimates supported the idea that values of Z loan implicate either an extreme aggressive or passive defensive strategy: the bank either increases (aggressive) or decreases (defensive) the loan grants the following period (n + 1) depending on its previous years' policy than the population average. The relevant formulas accumulate the internal forces within the bank, as well as the general environment of all banks. Verification is an indication of credibility of the proposed model based on: (a) the principal component analysis, (b) the regression analysis and (c) the Bühlmann credibility model applied at stochastic and empirical level. To our knowledge, this is the first model to do so.
Further understanding of the proposed decision support tool requires quantitative assessment of the most important factors deriving from the external environment of the shipping banks, e.g. shipping market analysis per sector. The definition of the most important factors related to each shipping sub-sector is expected to integrate the proposed model as it will co-estimate both internal and external factors that may influence shipping finance taking into account each individual bank's policy with respect to decision's credibility factor.