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According to the RuG’s faculty of Management and Organisation, publication of a final papers is
compulsory. So, the highly confidential and sensitive information the original paper contained have been
rewritten.
Abstract
Banking institutions are always at risk of loosing their money: “credit risk”. Credit risk arises from any non-payment or rescheduling of a debt by a borrower. Ever since banks were first organised, managing this credit risk has formed a core expertise and still the credit risk evolution in the current economy is one of the most important issues in the world of banking.
As a result of the importance of credit risk, almost all international banks came on an agreement, so-called “The Accord or Basel I”. The agreement obliged banks to protect themselves against the financial risk, in particular credit risk. The Latest agreement, so called “The New Accord or Basel II” contains proceeding steps for among other things, the use, and development of credit risk models. Such a credit risk model consists of some modified models for the Probability of Default (PD) and for the Loss Given Default (LGD).
Within this framework in this paper, under authority of the FICTITIOUS (short sea) shipping department for the determination of the collateral, a valuation model for short sea shipping vessels, has been developed and described. The purpose, as part of the collateral calculation, of such a valuation model is to estimate the valuation of a short sea-shipping vessel of a certain age.
Key words: Credit Risk, Basel Accord, Short Sea Shipping, and Valuation Model
List of Figures ...6
List of Tables ...7
1. Introduction... 8
2. Banking Risks... 10
2.1 Introduction ...10
2.2 Credit Risk ...10
2.2.1 Expected Loss ...11
2.2.2 Unexpected Loss ...12
2.2.3 Transfer Risk ...12
2.2.4 Market Risk ...13
2.2.5 Business Risk ...13
2.2.6 Operational risk...14
2.3 Credit risk in practice...14
2.3.1 Credit ratings...14
2.3.2 Credit rating models used and developed by the FICTITIOUS BANK……….15
3. The New Basel Capital Accord ... 17
3.1 Introduction ...17
3.2 Need for more flexibility and risk sensitivity ...17
3.3 Structure of The New Accord...18
3.3.1 The first Pillar: minimum capital requirement ...19
3.3.1.1 The standardised approach for credit risk ...19
3.3.1.2 The internal ratings based approach (IRB) ...20
3.3.2 The second pillar: supervisory review process...20
3.2.3 The third pillar: market discipline...21
4. Short Sea Shipping... 22
4.1 Introduction ...22
4.2 Fleet...22
4.3 Supply and Demand...24
4.4 Importance of short sea shipping for the Netherlands ...25
5 Ship valuation models for Short Sea Shipping vessels ... 26
5.1 Introduction ...26
5.2 Raw Data...26
5.2.1 Data collection...27
5.2.2 Description ...27
5.2.2.1 Financial variables...27
5.2.2.2 Technical variables ...28
5.2.2.3 Market segments variables...28
5.2.2.4 Macro economic variables ...29
5.2.2.5 Time variables ...29
5.3 Data analysis ...30
5.3.1 Missing observations & Missing variables ...30
5.3.2 Analysis of the dataset ...31
5.3.2.1 Financial variables...31
5.3.2.1.1 New building Prices ...31
5.3.2.1.2 Selling price of vessels ...33
5.3.2.1.3 EBITDA ...34
5.3.2.2 Technical variables ...35
5.3.2.2 Technical variables ...35
5.3.2.3 Market segment variables ...36
5.3.2.4 Macro economic variables ...36
5.3.2.5 Time variables ...36
5.3.3 Final dataset...37
5.4 Model estimation and selection ...38
5.4.1 Three depreciation methodologies ...38
5.4.1.1 Simple depreciation ...38
5.4.1.2 Simple depreciation according to ShipbrokerA...38
5.4.1.3 Discounted Cash Flow valuation methodology ...39
5.4.2 Model definition and estimation results...40
5.4.2.1 Model definition...40
5.4.2.2 Estimation results Model I ...41
5.4.2.3 Estimation results Model II...43
5.4.2.4 Model I or Model II ...46
6 Conclusion ... 47
6.1 Conclusion...47
6.2 Discussion and Recommendation ...49
References ... 51
Bibliography ...51
Internet ...52
Appendices... 53
Appendix A Distributions of Credit Losses...53
Appendix B S&P Categories ...54
Appendix C Macro Economical Variables ...55
Appendix D Collinearity...56
Appendix E SAS Regression solutions ...57
Appendix F SAS CODES ...62
List of Figures
1.1 General overview..………...9
2.1 Banking Risks………10
2.2 Loss Distribution………11
2.3 Expected Loss (EL) and Unexpected Loss (UL)………...12
2.4 Average default rates (in %)………..15
3.1 Structure of The New Accord………19
4.1 Age structure Western European short sea fleet (in number and DWT)………...24
5.1 Ship valuation x €1000,-………27
5.2 Twenty-foot Equivalent Unit (TEU)………..28
5.3 Deadweight Tonnage (DWT)………28
5.4 AGE in years………..28
5.5 Estimated new building price x €1000,-………33
5.6 EBITDA……….34
5.7 Historical price ranges based on ShipbrokerA data for dry bulk 10,000 DWT………..39
5.8 Transformations of variables for Model I………..42
5.9 Goodness of fit Model I-3………..43
5.10 Transformations of variables for Model II……….44
5.11 Goodness of fit Model II-4………45
List of Tables
4.1 Orderbook and fleet size Western Europe (2001)……….24
5.1 Depreciation of a vessel……….32
5.2 Statistical Summary Financial Variables………...34
5.3 Statistical Summary Technical Variables………..35
5.4 Correlation DWT with LOA, BEAM and Draught………...35
5.5 Statistical Summary Time Variables……….37
5.6 Final Dataset………..37
5.7 Book values of general cargo/ multi purpose short sea vessels……….39
5.8 Solutions for Model I……….43
5.9 Solutions for Model II………...46
6.1 Final Dataset………..48
6.2 Solutions for Model I……….48
6.3 Solutions for Model II………48
A.A.1 Possible shape of the distribution of credit loss……….53
A.B.1 S&P Categories………..54
A.C.1 Real GDP (% change from previous period)……….55
A.C.2 Standardised Unemployment Rates (% of total civilian labor force)………55
A.C.3 Inflation: Consumer prices indices (% change from previous period)…………..55
1. Introduction
Banking institutions are always at risk of loosing their money: “credit risk”. Ever since banks were first organised, managing this credit risk has formed a core expertise and still the credit risk evolution in the current economy is one of the most important issues in the world of banking. It is said that credit risk is the oldest form of risk in the financial markets; it dates back at least as far as 1800 BC1.
As a result of the importance of credit risk, almost all international (commercial) banks came on an agreement, so-called “The Accord”. In 1988, the Bank for International Settlements (BIS) set up its first accord, also known as ‘Basel I’. The agreement obliged all (commercial) banks to protect themselves against the financial risk, in particular credit risk. The accord determines the minimal required amount of money (‘Economic Capital’) a bank must keep (to fulfil its obligations if a customer would repay too late, or partly or maybe not at all).
Ever since, The Basel Accord has changed into “The new Basel Capital Accord” also known as “Basel II”, “The New Accord”. This New Accord will come into force from January 1st 2007, and will be applied to banks all over the world. Thus also the FICTITIOUS BANK must fulfil the requirements of this accord.
In real this means that about 200 employees are working on the implementation of the New Accord. The New Accord contains proceeding steps for among other things, the use, and development of credit risk models. Such a credit risk model consists of some modified models for the Probability of Default (PD) and for the Loss Given Default (LGD).
Within this framework, the FICTITIOUS BANK’s (short sea) shipping department asked to design, as input for a Basel II compliant LGD model, a model which estimates the valuation of a ship (which I will refer to as “vessel”) at a certain age.
One of the main input parameters in a LGD model for the short sea shipping portfolio is the value of the vessel. Therefore, in this paper, I shall develop a model, which I will refer to simply as “valuation model”. To obtain the value of a vessel is essential, as part of the goal, to get a clear view on the “residual value” of the ship at the end of the tenor of a loan facility. Moreover, we must realize that a ship valuation model is a key subject to determine the Loss Given Default.
In order to develop a ship valuation model, we need to understand the basics of credit risk, the New Basel Accord, and short sea shipping. Moreover, we need to understand the relationship between the collateral and loss given default. These understandings are described in this paper and represented in figure 1.1.
Chapter 2 describes the basics of credit risk. Chapter 3 consists of a brief introduction to
“The New Basel Accord”. Chapter 4 documents short sea shipping, whereas Chapter 5 documents the development process and the final model(s) to estimate the value of a short sea shipping vessel. Finally, in chapter 6, I draw my conclusion.
Figure 1.1 General overview
Credit Risk
The New Basel Accord (Basel 2)
Short Sea Shipping Portfolio
Steps in designing a model, which estimates the valuation of a short sea shipping vessel of a certain age.
LGD-model
Collateral
2. Banking Risks
2.1 Introduction
In our effort to design a valuation model for short sea shipping vessels, we need to take a closer look at the banking risks, because this is one of the fundamentals to deal with in the final valuation model development.
Risk arises from any transaction or business decision whose result is uncertain. Because virtually every transaction includes some level of uncertainty, nearly every transaction contributes to the overall risk of the bank. The five types of banking risks and their characteristics are shown in the figure 2.1.
This chapter documents an explanation of these five types of banking risk and a brief inroduction to credit rating.
2.2 Credit Risk
Credit risk arises from any non-payment or rescheduling of a debt by a borrower. Two characteristics of the losses that arise from bad debts are useful when attempting to quantify the risk of a credit portfolio: the Expected Loss (EL) and the Unexpected Loss (UL).
Expected losses are defined as long-run average losses and thus can be reflected in pricing. Unexpected losses are not reflected in pricing but require capital being set aside to absorb the shock so that the organisation is not debilitated by their occurrence.2 Note that, UL sounds like a contradiction in terms. Because once a loss is quantified, it can no longer be called unexpected. However, the term really means maximum potential loss, or maximum loss at a given level of confidence, e.g. ninety-five percent.
The concept of EL and UL is shown in the loss distribution of figure 2.23. The EL is associated with the mean of the loss distribution4 of a loan or a portfolio. The UL is associated with e.g. ninety-five percent of the area under the loss curve. The area to the
2 Caoutte, J. B., I. E. Altman, and P. Narayanan (1998), Managing Credit Risk: The next financial challenge, John Wiley and Sons, Inc. New York (242-246).
3 The figure represents a single asset.
Credit Risk Unexpected Loss
Banking Risks Earnings Volatility
Transfer Risk Unexpected Transfer Loss
Market Risk Value-at-Risk
Business Risk Residual Earnings
Volatility
Operational Risk Event Loss
Volatility
Figure 2.1 Banking Risks
right is expected with such rarity that it would be uneconomical to hold 100 percent capital against that contingency.
2.2.1 Expected Loss
Expected Loss is the forward-looking expectation of the average losses due to a single loan or a portfolio of loans. It can be calculated for a specific loan or transaction as the product of three components, as represented in equation 2.1.
The probability of default (PD) is the probability that the customer or counterparty will default on a specific obligation. Default is typically defined as a failure to make a payment of either principal or interest, or a restructuring of obligations to avoid a payment failure5. This is the common definition used by most external rating agencies, such as Standard and Poors (S&P), Moody’s and Fitch.
The exposure at default (EAD), for the purposes of EL calculation, is simply the expected size of the bank’s exposure (the amount of money a bank has lend) to a customer or counterparty at the time of default. This is often higher than current outstandings, but is clearly the most relevant measure for loss calculation. When a borrower defaults, the bank does not necessarily lose the full amount of the loan.
Lost Given Default (LGD) represents the ratio of actual losses incurred at the time of default (including all costs associated with collection) to exposure amounts. LGD is in particular a function of collateral or security. Un-collateralised and unsecured loans have much higher losses per euro of exposure than collateralised or secured loans have. Note that as mentioned, due to the goal of this research, especially this parameter is of great concern.
5 www.moodys.com
EL(€) = PD x EAD(€) x LGD
Equation 2.1
Frequency
Minimum Loss (No default)
EL: For which reserve should be held.
UL: For which capital should be held
Magnitude of Credit Loss
Maximum Loss (Default)
Potential Unexpected Credit Loss against which it would be too expensive to hold equity
Figure 2.2 Loss Distribution
The “fat tail”
The descriptions about the PD, LGD and EAD given above are common. Actually, the New Basel Accord (see chapter 3) gives restrictions by creating own definitions for specific credit risk models. As for example for the probability of default specific agreements have to be entered, e.g. an obligation requirement for a bakery differs from an AEX-noted corporation. Note that for creating a model for short sea shipping we must keep this in mind.
2.2.2 Unexpected Loss
Unexpected Loss (UL) for a specific transaction is calculated as the raw volatility of that transaction, with no diversification benefits. Statistically, every default can be thought of as a random binomial variable: the borrower either defaults or does not default. The credit loss from any loan therefore follows a defined statistical distribution, see figure 2.3. Just as EL is calculated as the mean of that distribution, UL is calculated as the standard deviation of the same distribution. When measuring Unexpected Loss at the portfolio level, diversification has the effect of reducing the variance of the average UL.
2.2.3 Transfer Risk
Transfer Risk is the risk to the bank that solvent foreign borrowers will be unable to meet their obligations to the bank because of the fact that they are unable to obtain the convertible currency needed. Consequently, transfer risk refers to the economic and financial factors attributable to the country6. For instance, if a country faces a liquidity crisis, monetary authorities often place restrictions on the availability of convertible currency; this is called a
“Transfer Event”. Note that the economic health of the customer is not by definition affected in this case. Default occurs simply, because the convertible currency needed to repay the loan is unavailable. Transfer Events are the result of the inability of a country to meet its external convertible currency obligations.
6 Caoutte, J. B., I. E. Altman, and P. Narayanan (1998), Managing Credit Risk: The next financial
Time Loss
Rate
EL
UL
Figure 2.3 Expected Loss (EL) and Unexpected Loss (UL)
2.2.4 Market Risk
Market risk can be defined as the chance that an investment’s value will change in price as a result of marketplace forces.7 Like credit risk, market risk has affected financial institutions ever since.
Losses can arise from changes in the volatility, as well as the spot price, of underlying markets. In order to determine the market risk as well as the other four types of risks, the required amount of Economic Capital (EC), ensuring the target solvency standard of the bank over a one-year horizon, needs to be calculated. So the total value of the unexpected losses from the portfolio is the EC. For example the target AA rating of FICTITIOUS BANK corresponds to a default probability of 0,05%, which is to say that the bank’s economic capital will assure solvency for the coming year at the 99.95% confidence level.
The industry standard for market risk measurement is Value-at-Risk (VaR). VaR is a useful tool for a capital calculation, but it differs fundamentally from economic capital in that:
• VaR is a daily measure whereas economic capital is allocated on an annual basis,
• VaR and economic capital are defined at different confidence levels,
• VaR makes several distributional assumptions (e.g. normality of trading results) while an economic capital calculation can add levels of sophistication to underlying assumptions.
2.2.5 Business Risk
Business Risk results from a company’s uncertainty about future revenues and costs. It represents the volatility of operating results, which fundamentally stem from changes in volume, price, and costs8. Business Risk is mainly driven by the competitive environment and the market place, but can be mitigated by effective management practices. The downside to business risk lies with the fact that business unit’s net variable revenues may become insufficient to cover its fixed cost base. This is caused by the business unit’s capital. No business is free from business risk since all units’ carry some level of fixed costs and have uncertain revenues.
7 Caoutte, J. B., I. E. Altman, and P. Narayanan (1998), Managing Credit Risk: The next financial challenge, John Wiley and Sons, Inc. New York (2-3).
8 Caoutte, J. B., I. E. Altman, and P. Narayanan (1998), Managing Credit Risk: The next financial challenge, John Wiley and Sons, Inc. New York.
2.2.6 Operational risk
Operational risk represents the risk of loss due to rare events such as: major systems failure, errors and omissions, fraud, etc9. While operational risk can be limited through management controls and insurance, many events still have a substantial impact on the P&L of financial institutions.
Because operational risk is so far-reaching and because historic data on business performance tends to be scarce, operational risk is, in relation to the other risk types, much more difficult to quantify.
Similarly to credit risk, also operational risk events can be modelled, also as either happening (with a probability p) or not happening (with a probability of 1-p).
The difficulty in this issue is identifying and quantifying operational risks. As is said in its definition, these events are infrequent, and their impact varies significantly from year to year. However, estimations can be made through frequency/magnitude analyses and so-called, stress test modelling. However, in the end all remaining operational risks will be covered with capital.
2.3 Credit risk in practice
A credit rating is a product of a credit model, which is a tool to determine the level of credit risk. The following two paragraphs present a brief explanation of credit ratings and credit risk models.
2.3.1 Credit ratings
Ratings describe the creditworthiness of customers. Hereby quantitative as well as qualitative information is used to evaluate the customer or counterparty. Ratings are generally ranked in categories; letter labelled (AAA or Aaa) or numbered (1 to 10). So a rating category is a simple instrument to quantify risk. Ratings allow banks to measure credit risk and to manage a portfolio of a bank10.
The credit rating is relevant for several reasons11. The information includes, for each rating class:
• The frequencies of default, yearly and cumulative;
• The volatility across time of yearly frequencies;
• The transition matrices between rating classes;
Most banks use credit rating classes similar to models of rating agencies like, Moody’s, Standard and Poors (S&P) or Fitch. However, FICTITIOUS BANK uses self-made rating classes; these are generally defined in the middle risk range. The majority of the borrowers, which are situated in the middle class range, cause this.
9 Caoutte, J. B., I. E. Altman, and P. Narayanan (1998), Managing Credit Risk: The next financial challenge, John Wiley and Sons, Inc. New York.
10 Krahne, J.P. and M. Weber, Weber (2001), Generally accepted rating principles: A Primer, Journal of Banking and Finance 25 (3-25).
For illustration, whereas S&P12 uses rating categories differing from AAA through D, see appendix B, Moody’s uses rating classes differing from Aaa through C. Aaa is the highest rating class, meaning that the creditor ranks highest in its margins of investors safety against credit loss, even under severe economic conditions13. The lowest rating C has extremely poor chances of attaining any real investment value. Obligations rated Baa and higher are so-called “investment grade,” those rated Ba and lower are so-called
“speculative grade”.
Concerning the FICTITIOUS BANK, the average default rates of these classes over the period 1970-1998 are shown in figure 2.4. The figure represents the percentage of annual defaults in a specific rating class.
2.3.2 Credit rating models used and developed by the FICTITIOUS BANK
External agencies as described in the previous paragraph generally do not provide the credit ratings for all borrowers, for the reason that these agencies have insufficient knowledge of projects. Therefore, banking institutions have to develop their own (internal) rating based models. In developing credit risk models banks have to consider different drivers14 of the considered firm’s economic future:
• Future earnings and cash flows;
• Debt, short- and long term liabilities, and financial obligations;
• Capital structure (e.g. leverage);
• Liquidity of firm’s assets;
• Situations (e.g. political, social etc.) of the firm’s home country;
• Situations of the market (e.g. industry), in which the company has it’s main activities;
• Management quality, company structure, etc.
12 Standard & Poors (1998), Standard and Poors Corporate Rating Criteria 1998, www.standardandpoors.com
13 Moody’s (1999), Historical Default Rates of Corporate bond Issuers, www.moodys.com.
14 Bluhm, C., L. Overbeck and C. Wagner (2003), Credit Risk Modeling, Chapman and Hall / CRC, Inc.
London.
0,01 0,03 0,07 0,22
1,15 6,10
0 1 2 3 4 5 6 7
Average Default frequency
Default frequency
Default frequency 0,01 0,03 0,07 0,22 1,15 6,10
Aaa Aa A Baa Ba B
Figure 2.4 Average default rates (in %)
In addition, the FICTITIOUS BANK develops credit rating models, to provide ratings for all kind of borrowers. However, these models are restricted by the BASEL II accord (see chapter 3). So far, twelve models have been developed. Two major models are described below:
• The Plain Vanilla Large Corporate (PVLC) model, this is a credit risk model, built and in use for corporates with sales greater than €100 million. The model is based on 17 years of historical data.
• The Small Medium Enterprise (SME) model, this is a credit risk model built and in use for corporates with sales less than €100 million.
However, these models do not cover the whole portfolio. So for these uncovered portfolios, specific credit risk models are designed.
3. The New Basel Capital Accord
3.1 Introduction
More than a decade has passed since the Basel Committee on Banking Supervision (the Committee), also referred to as the Bank for International Settlements (BIS) introduced its 1988 Capital Accord (The Accord).
The accord is named after the city Basel (Switzerland), where the Committee is settled.
The goals for the Committee are stimulating and obtaining:
• Financial health of the financial sector;
• Stability of the financial sector.
The business of banking, risk management practices, supervisory approaches, and financial markets each have undergone significant transformation since then. In June 1999, the Committee released a proposal to replace the 1988 Accord with a more risk- sensitive framework: The New Basel Accord. Reflecting on comments and the results of discussions and research with the banking industry and supervisors, like DNB, the Committee presented a concrete proposal: The Third Consultative Paper (CP3). This paper is a result of earlier studies (CP1 en CP2) and reflects restrictions and guidelines for managing credit risk. This chapter documents the explanation for the existence of the New Basel Capital Accord, and provides a general and brief explanation about the structure of the New Accord.
3.2 Need for more flexibility and risk sensitivity
Safety and soundness in today’s dynamic and complex financial system can be attained only by the combination of effective bank-level management, market discipline, and supervision.15 The 1988 Accord focussed on the total amount of bank capital. This is very important in order to reduce the risk of bank insolvency and the potential cost of a failure of a bank for depositors. Due to this, the New Accord tries to improve “safety and soundness” in the financial system, through placing more emphasis on banks’ own internal control and management, the supervisory review process, and market discipline.16
Primarily the New Accord focus is on internationally operating banks. Nevertheless, because of its underlying principles the New Accord should be suitable for application to banks that are operating on different levels. Due to the international cooperation according to the development of the New Accord, the Committee thinks that the New Accord to be adhered by all banks should take place as mentioned below.
15 www.bis.org
16 Bank for International Settlements; Basel Committee on Banking Supervision (April 2003), Third Consultative Paper: Technical Guidance, www.bis.org > BIS Home > Basel Committee > The New Basel Capital Accord > Third Consultative Paper.
As a result of the fact that the Basel II implementation should be complete at January 1st 2007, the FICTITIOUS BANK and other involved banking institutions must fulfil several requirements:
• At least three years of experience is required with the rating models used; in real this means the rating models should come into force from January 1st 2004;
• Sufficient historical data must be collected (in some cases until 7 years);
• At least for one year the bank should have published according to the new method.
In real this means:
• 2003 quarter 4, publication of the final version of the Basel II Accord for the FICTITOUS Bank;
• 2004 quarter 1, the use of the new method for FICTITIOUS BANK;
• Midyear 2004, according to the Committee the goal is to complete the New Accord;
• 2006 quarter 1, primary publication to DNB according to the Basel II restriction;
• 2007 quarter 1, Basel II will come into force.
So, for the FICTITIOUS BANK the first major step should be passed at the end of December 2003. Before this date all credit risk models should be at least “Basel compliant”, which means that every model must function according to the foundation approach (see paragraph 3.3.1.2).
The 1988 Accord provided only one option for measuring the appropriate capital of internationally operating banks. The best way to measure, manage, and mitigate risks differs obviously from bank to bank. In 1996, an amendment was introduced which focussed on trading risks and allowed some banks for the first time to use their own systems to measure their market risks. The new framework provides a variety of approaches. It goes from simple to advanced methodologies for the measurement of both credit risk and operational risk in determining capital levels. The BIS says the New Accord provides a flexible structure in which banks, subject to supervisory review, will adopt approaches, which best fit to the banks´ level of sophistication, and their risk profile. The framework also deliberately builds in rewards for stronger and more accurate risk measurement.
Capital requirements that are more in line with underlying risks will allow banks to manage their businesses more efficiently.
The new framework intends to provide approaches, which are both more comprehensive and more sensitive to risks than the 1988 Accord, while maintaining the overall level of regulatory capital. In fact, the impact of this global implementation is large and huge internal changes for banking institutions and supervisors will take place.
3.3 Structure of The New Accord
The new Accord consists of three pillars, which together should contribute to safety and soundness in the financial system, shown in figure 3.1. The Committee stresses the need for rigorous application of all three pillars and plans to work actively with supervisors to achieve the effective implementation of all aspects of the Accord.
3.3.1 The first Pillar: minimum capital requirement
The first and main pillar sets out minimum regulatory capital requirements. The new framework maintains both the current definition of capital and the minimum requirement of 8% of capital to risk-weighted assets. To ensure that risks within the entire banking group are considered, the revised Accord will be extended on a consolidated basis to holding companies of banking groups.
The revision focuses on improvements in the measurement of risks, for example, the calculation of the denominator of the capital ratio. The credit risk measurement methods are more elaborate than those in the current (old) Accord. The new framework proposes for the first time a measure for operational risk, while the market risk measure remains unchanged.
As represented in figure 3.1, for credit risk, two principal options are being proposed. The first is the standardised approach. The second is the internal rating based (IRB) approach.
There are two variants of the IRB approach, the foundation and advanced approach. The use of the IRB approach will be subject to approval by the supervisor, based on the standards established by the Committee.
3.3.1.1 The standardised approach for credit risk
The standardised approach resembles the present Accord, but is more risk sensitive. The bank allocates a risk-weight to each of its assets and off-balance-sheet positions and produces a sum of risk-weighted asset values. For example, a risk weight of 100% means that an exposure is included in the calculation of risk-weighted assets at its full value, which translates into a capital charge equal to 8% of that value. Similarly, a risk weight of 20% results in a capital charge of 1.6% (i.e. one-fifth of 8%).
BASEL 2 The New Accord
Pillar 1
Minimal Capital Requirement
Pillar 2 Supervisory Process Review
Pillar 3 Market Review
The internal ratings based approach (IRB)
The standardised approach for credit risk
Foundation method
Advanced method
Figure 3.1 Structure of The New Accord
Individual risk weights depend on the broad category of borrower (i.e. sovereigns, banks, or corporates). Under the new Accord, the risk weights are refined by reference to a rating provided by external credit assessment institutions (such as a rating agency) that meet strict standards. For example, for corporate lending, the existing Accord provides only one risk weight category of 100% but the new Accord will provide four categories 20%, 50%, 100%, and 150%.
3.3.1.2 The internal ratings based approach (IRB)
Under the IRB approach, banks will be allowed to use their own internal estimates of borrower creditworthiness to assess credit risk in their portfolios, subject to strict methodological and disclosure standards. Distinct analytical frameworks will be provided for different types of loan exposures, for example corporate and retail lending, whose loss characteristics are different.
Under the IRB approach, a bank estimates each borrower’s creditworthiness, and the results are translated into estimates of a potential future loss amount, which form the basis of minimum capital requirements. The framework allows for both a (1) foundation method and more (2) advanced methodologies for corporate, sovereign and bank exposures. In the foundation methodology, banks estimate the probability of default associated with each borrower and the supervisors will supply the other inputs. In the advanced methodology, a bank with a sufficiently developed internal capital allocation process will be permitted to supply other necessary inputs as well. Under both the foundation and advanced IRB approaches, the range of risk weights will be far more diverse than those in the standardised approach, resulting in greater risk sensitivity.
3.3.2 The second pillar: supervisory review process
According to the new Accord, the supervisory review process requires supervisors (e.g.
DNB) to ensure that each bank has sound internal processes in place to assess the adequacy of its capital based on a thorough evaluation of its risks17. The new framework emphasises the importance of bank management developing an internal capital assessment process and setting targets for capital that are commensurate with the bank’s particular risk profile and control environment. Supervisors would be responsible for evaluating how well banks are assessing their capital adequacy needs relative to their risks. This internal process would then be subject to supervisory review and intervention, where appropriate.
The implementation of these proposals will require a much more detailed dialogue between supervisors and banks. This in turn has implications for the training and expertise of bank supervisors, an area in which the Committee and the BIS’s Financial Stability Institute will be providing assistance.
17 Bank for International Settlements; Basel Committee on Banking Supervision (April 2003), Third Consultative Paper: Technical Guidance, www.bis.org > BIS Home > Basel Committee > The New Basel
3.2.3 The third pillar: market discipline
The third pillar of the new framework aims to bolster market discipline through enhanced disclosure by banks. Effective disclosure is essential to ensure that market participants can better understand banks’ risk profiles and the adequacy of their capital positions. The new framework sets out disclosure requirements and recommendations in several areas, including the way a bank calculates its capital adequacy and its risk assessment methods.
The core set of disclosure recommendations applies to all banks, with more detailed requirements for supervisory recognition of internal methodologies for credit risk, credit risk mitigation techniques, and asset securitisation.
4. Short Sea Shipping
4.1 Introduction
The shipping market exists of a deep sea shipping and a short sea shipping segment.
Deep Sea shipping is a global industry with flows often involving both developed and emerging markets. The bulk of raw materials, half products, and finished goods are transported by sea.
Whereas deep sea shipping provides global transport, short sea shipping provides transport within regions. It contributes cargo delivered to regional centres such as Rotterdam and Delfzijl. It provides a so-called, port-to-port service, often in direct competition with land-based transport such as transport by train or truck.
Short sea shipping is a very different business from deep sea shipping. The vessels are generally smaller. In the short sea trades vessels range in size from 400 Dead Weight Tonnage (DWT) to 6000 DWT. Although there are no firm rules. The FICTITIOUS BANK defines short sea shipping as local, coastal shipping, which characterized by relatively small distances (on average 300-400 miles) for which in general, but not necessarily, smaller vessels (often < 8000 DWT) are used.18 Generally short sea vessels transport grain, fertilizer, coal, lumber, steel, clay, aggregates, containers, wheeled vehicles and passengers.19
This chapter documents a brief description about the short sea market and the involvement of the FICTITIOUS BANK portfolio. Paragraph 4.2 describes the fleet of the short sea shipping market, whereas paragraph 4.3 deals with the supply and demand.
This chapter ends in paragraph 4.4 with a short review of the importance of short sea shipping for the Netherlands.
4.2 Fleet
As mentioned short sea shipping can be defined as local, coastal shipping which is characterised by relatively small distances (on average 300-400 miles) for which in general, but not necessarily, smaller vessels (often < 8,000 tonnes DWT) are used. In line with the deep sea policy, we herewith propose to continue to deal with those short sea owners, which are active with ships > 8,000 DWT, in the same way as with deep sea owners. For the Dutch short sea shipping industry, the main trading areas are traditionally:
1. The triangular trade in the Benelux, UK/Ireland, Germany/Scandinavia/Baltic States;
2. The Intra-Mediterranean trade.
However, during the past few years the trading area has been expanding to the transatlantic trade due to the disappointing employment and rates in recent years in Western Europe. In addition, the growing capabilities of shipping companies prompted them to start operating with larger sized vessels.
18 Bruins, A. (2002), Brondocument: Kleine handelsvaart 2002, ING Bank Nederland, F&B1, Amsterdam.
In general, demand for vessels is primarily depending on economic growth cycles, which eventually determine demand for general dry bulk cargoes and container transport capacity. Moreover, demand for vessels depends on variables like the (distance of) the trade, the speed, the type and equipment of a vessel.
The table 4.120 illustrates the orderbook, as per April 1, 2001, and fleet size of the Western European short sea fleet. The orderbook consists of 171 vessels divided over 882,544 DWT, which is 7% of the fleet measured in DWT (3,607 vessels divided over 12,039,410 DWT).
The average age of the Western European fleet is in general old, i.e. 20 years, as shown in table 4.1 and graphically illustrated in figure 4.1. The Dutch and German fleets are relatively young; their average age is in-between 12.5 and 14.4 years. In comparison with other Western European countries, whose average age are in-between 20 and 34 years, this could be considered as an advantage for the Dutch and German fleets. Because the advantages of a young, modern fleet instead of a fleet of older vessels find their origination in the following characteristics:
• Price (value) volatility of older vessels is in general higher compared to newer vessels, and therefore requires a higher risk premium from a bank’s point of view;
• Older vessels are economically less viable:
o Efficiency (e.g. fuel costs) for newer vessels is higher;
o Dry-docking costs increase exponentially after a certain age;
o Constraints to transport of certain cargo for older (> 20 years) vessels;
• Industrial shipping requires increased performance (speed, efficiency, etc), which requires young, modern tonnage;
• Stretching possibilities of loan facilities are better available for younger tonnage (with longer remaining economical lifetimes).
20 Lloyd's Register of Shipping (2002), Register of ships 2001: supplements and new entries incorporating classification survey dates supplement, Lloyd’s Register of Shipping, London.
Table 4.1 Orderbook and current fleet size Western Europe (2001)
Country Orderbook Current Fleet
Number In % DWT In % TEU Number DWT Average Age Germany
Netherlands
Norway Denmark UK Italy Sweden Spain Finland France
65 53
8 - 23 10 2 8 - 2
38%
31%
5%
0%
13%
6%
1%
5%
0%
1%
333.481 256.590
11.291 - 146.178
63.600 9.400 45.200
- 16.804
38%
29%
1%
0%
17%
7%
1%
5%
- 2%
17.521 9.435
44 - 4.149
- - - - -
1.137 534
644 318 305 257 137 129 97 49
4.534.204 2.116.203
1.303.147 925.920 1.000.808
844.927 402.105 444.578 327.768 139.750
14.4 12.5
29.2 20,7 19.7 24.9 34.1 21.4 27.1 23.7 Total 171 100% 882.544 100% 31.149 3.607 12.039.410 20.0
A disadvantage of new buildings is the relatively high capex (capital expenditures) resulting from the high financing amount (interest payments + repayment obligations).
The graph of figure 4.1, also illustrates the trend towards larger vessels; the average size of vessels of 0 to 5 years is 5,240 DWT (=3500000/668), while older vessels (> 20 years) have an average size of 2,230 (=3500000/1570) DWT. The average size for the vessels on order is 4210 DWT, for 6 to 10 years it is 4375 DWT, for 11 to 15 years, it is 3428 DWT, and for 16 to 20 years it is 3220 DWT.
4.3 Supply and Demand
It is said that the supply of Western European tonnage, measured in DWT, has grown almost twice as fast (6%) as short sea shipping transport demand (3.6%) from 1994 onwards, even if we take into account the fact that larger vessels (> 8,000 DWT) increasingly trade outside European waters. Although Germany and the Netherlands are within Western Europe the only countries that have continued investing in their fleets, the increase of the general cargo fleet in terms of DWT has been substantial. Note that the rest of the Western European countries have been focusing on other shipping markets like ferries and ro-ro.21 The German current largely consists of container feeder vessels, while the Dutch fleet largely comprises general cargo/multi-purpose vessels.
The substantial supply growth will to some extent be mitigated by the following developments22:
• Older vessels (> 20-25 years) are becoming economically less viable, and are sold to trading areas outside Europe like e.g. the Caribbean, Middle East (Syria);
• Vessels that are older than 20 years are no longer allowed to transport e.g. grain and fertilisers, although this is a regulation that is not strictly complied with. These vessels will eventually leave the markets which require modern tonnage;
21 Ro-Ro: Roll on, Roll off a description of a ship in which cargo is worked horizontally on wheeled vehicles via a ramp and through doors in a ship’s wall.
Figure 4.1 Age structure Western European short sea fleet (in number and DWT)
0 200 400 600 800 1000 1200 1400 1600 1800
On order
0-5 6-10 11-1516-20 20+
Number
0 500 1000 1500 2000 2500 3000 3500 4000 DWT x 1000
NUMBER DWT
Age in years
From 1995 onwards, and largely due to the fiscally attractive CV-structure, Dutch shipping banks have made a considerable contribution to the current over capacity, even if assessing this in a broader Western European perspective. Therefore, we need to be increasingly careful with respect to future developments regarding fleet, age structure, orderbook and rate developments.
4.4 Importance of short sea shipping for the Netherlands
As illustrated in the table 4.1, it has become clear that the short sea shipping industry is important to the Dutch economy. This is also stated in a study23 executed for “Nederland Maritiem Land” on the economic impact and structure of the Dutch Maritime Cluster. The Dutch Maritime Cluster creates a total value-added of approximately €6.3 billion, of which
€4.5 billion is direct and €1.8 billion is indirect added value. It is estimated to employ 120,000 people of whom 86,000 are directly involved. With respect to the sea-going shipping industry, the total value-added is €0.8 billion (of which €0.6 billion is direct). It employs 15,000 people of whom 11,000 are directly involved. Other segments of the Dutch Maritime Cluster include shipbuilding, inland shipping, dredging and ports. The study also made clear that the Dutch Government’s sea-going shipping policy, in effect since January 1, 1996, has had a highly positive influence on the (re-) development of the Dutch maritime industry. The Dutch short sea market segment has contributed substantially to this industry.
Note, the ING fleet will be discussed in chapter 5.
23 Stichting Nederland Maritiem land (1997), Nederland Maritiem Land, Delft University Press, Delft.
5 Ship valuation models for Short Sea Shipping vessels
5.1 Introduction
One of the main input parameters in a LGD model for the short sea-shipping portfolio is the taxation value of the vessel. In this chapter, I develop such a model, which I will refer to simply as “valuation model”. The purpose of the evaluation model is to estimate the taxation value of a short sea shipping vessel of a certain age.
To obtain the valuation it is essential, as part of the collateral, to get a clear view on the
“residual value” of the ship at the end of the tenor of a loan facility. Moreover, we must realize that a ship valuation model is a key subject to determine Loss Given Default. In addition, the LGD is part of the determination of the EL. Therefore, the (values of) short sea vessels are one of the most important assets on a balance sheet of shipping companies (and the corresponding loans as liabilities).
In order to develop a ship valuation model, we need to understand the relationship between the collateral and loss given default.
This chapter describes the different steps that were taken as part of the model development process of transaction values according to the sale and purchase valuation for short sea shipping vessels. Paragraph 5.2 describes the process of obtaining the required data. Paragraph 5.3 consists of the data analysis. The following step in the model development process is the determination of the importance of a variable. Relevant issues in this context are: (1) are there sufficient observations available and (2) if not, are valid and motivated assumptions possible, “to fill in the missing links”. Note that it will be determined which specific variables will be used in the model estimation and which will be eliminated. Subsequently, a suitable method must be developed to handle the data.
Therefore, in paragraph 5.4, I develop two types of statistical models to estimate the value of a short sea shipping vessel. In the same paragraph the estimations results are represented.
5.2 Raw Data
The model developing process starts with gathering and organize the required data, which are referred to as “raw data”. This paragraph documents the steps to the final dataset with predictive power. This means that this final dataset is the required input for designing a ship valuation model.
First, I start with the process of collecting data. Subsequently, the raw data will be described and finally a quality check will be performed resulting in the final data set. For the last two procedures I divide the variables in so-called, “classes of variables” in order to get a clear view.
5.2.1 Data collection
Collecting appropriate data in the short sea shipping portfolio is notoriously difficult.
General data from external sources and companies are rarely available, due to the fact that no one has ever gathered them. Moreover, ship-owners do not wish to share their sale and purchase information. Even agencies like the Koninklijke Nederlandse Vereniging van Rederijen (KNVR) and the Short Sea Shipping Federation do not have any significant data.
Hence, I started with only three internal Excel spreadsheets provided by the FICTITIOUS BANK. The spreadsheets data have been delivered in different set-ups by the IB (intensief beheer or problem loan department), F&B1 (Fiat & Beheer afdeling 1 or risk management department 1), and the DK (district kantoor or district office) Groningen.
These three data sets were merged into the raw data set. Besides the total number of 138 observations, the raw data set contained significant information like, Deadweight Tonnage (DWT), Twenty-foot equivalent unit (TEU), name of a ship, and the year of build. Moreover, the raw data set also contained less significant data, necessary for the creation of a ship valuation model, such as the amount of exposure or the percentage parent influence. In order to create a simplified database for modelling purposes less significant data were eliminated.
Note that later in this section these data will be added to information collected from the Internet and collected from other internal resources.
5.2.2 Description
In order to provide more insight in the available information, I grouped the collected data into five classes, named “the classes of variables”: (1) financial-, (2) technical-, (3) market-, (4) macro economic- and (5) time variables. Each class and their variables will be described and explained below.
5.2.2.1 Financial variables
These variables refer to the financial characteristics of a ship. Financial variables
12.650 9.850 7.0
50 4.2 1.450 50
Frequency
100
80
60
40
20
0
Std. Dev = 3254,88 Mean = 5339 N = 307,00
obtained from the spreadsheets include the valuation of a vessel (P_val) measured by ship valuator ShipbrokerB. This variable has to be estimated. The P_val measuring took place in the years of 2000, 2001 and 2002. Out of 1380 vessels, 3070 observations have been made. Notice, as a max one vessel could be measured three times! As we can see in the figure 5.1 the mean is €2,7 million and the median is €2,1 million. So 50% ships of the FICTITIOUS BANK portfolio have a value in excess of €2,1 million.
5.2.2.2 Technical variables
These variables refer to the technical specifications of a vessel. The experts suggested that this might have a (strong) influence on the ship valuations. Technical variables obtained from the delivered data are the Deadweight Tonnage (DWT) and the Twenty- foot equivalent unit (TEU).
A twenty-foot equivalent unit, is a standardised container, and refers to its size, which is 20’ (length) x 8’0” x 8’6” (height). The amount of TEU represents the number containers that a vessel can carry. Be aware of the fact that not every vessel can transport containers.
So, for the FICTITIOUS BANK-portfolio 1310 out of 3070 observations are available, see figure 5.2.
The deadweight tonnage of a ship measures the total weight of cargo that the vessel can transport, including the weight of fuel, stores, water ballast, fresh water crew, passengers, and baggage. According to the statistics, as we can see in the histogram of figure 5.3, the average DWT measured is 4900 and the median average is 4200. Experts believe this is a very important variable to determine the valuation of a ship. They say that, the larger the deadweight tonnage the higher the price. (ceteris paribus)
5.2.2.3 Market segments variables
These variables contain information about the market or segment in which particular short sea vessels operates. The FICTITIOUS BANK makes a distinction between Market
Dead weight tonnage 10.17
5 8.075 5.975 3.875 1.775
Frequency
100
80
60
40
20
0
Std. Dev = 2368,57 Mean = 4963 N = 307,00
Twenty equivelant unit
1000 900 800 700 600 500 400 300 200 100
Frequency
50
40
30
20
10
0
Std. Dev = 204,16 Mean = 307 N = 131,00
Figure 5.2 Twenty-foot Equivalent Unit (TEU) Figure 5.3 Deadweight Tonnage (DWT)
and Segment variables. The Market variables determine whether a vessel operates in the Dry Cargo-, Container-, the Dry Cargo/Multi Purpose, or the Dry Cargo/Container segment. The second variable is the Segment variables, a DWT distinction has been made in several classes: 0-2300, 2300-3400, 3400-4500, 4500-5500, 5500-8000, and 8000- 10000.
Using the market segment variables, we can get a closer look at the distribution of the portfolio. For example, almost every vessel can transport Dry Cargo, whether or not it can also transport other cargo like containers or whether it can be used for other purposes.
5.2.2.4 Macro economic variables
Shipping experts believe that there is a positive correlation between the short sea shipping market and economical growth cycles. Due to this correlation, I obtained two kinds of variables that are important, namely: the unemployment rate and the grow of gross domestic products (GDP). The FICTITIOUS BANK’s fleet operates in parts of Europe (see chapter 4, market description) and as well as around Holland. Therefore, the unemployment rate and the grow of GDP of Europe and the Netherlands are collected (see Appendix C Macro Economical Variables).
5.2.2.5 Time variables
In addition, time variables are one of the essential variables, for the reason that vessels normally depreciate over time. The variables given are Year of valuation (Year_val) and Year of Build (Year_build). Out of these variables result the Age of valuation (Age_Val).
As mentioned in the “financial variable section”, measuring took place at three times, in the year 2000, 2001 and 2002. Hence, no exact point of measuring is known (e.g. August, November). Therefore, I assume the time in-between the measuring is one year!24
Because of the FICTITIOUS BANK’s policy, that vessels older than 10 years will not be
Age (years)
18 14 10 6
Frequency 2 120
100
80
60
40
20
0
Std. Dev = 3,98 Mean = 6 N = 307,00
Figure 5.4 Age_val in years
financed, the average age is of the fleet is quite young, 62 years. A second important in this respect is the introduction of fiscal friendly CV-structures from 1995 onwards. These resulted in a boom of ordering vessels by shipping companies, enthusiastically financed by numerous banks. The FICTITIOUS BANK’s short sea shipping portfolio increased with more than 50 % (in terms of € exposure) from €52 million in 1998 to €1465 in 2001.
Currently, the portfolio is approximately €2350 million, due to stricter lending guidelines and annual repayments of approximately €133 million.
5.3 Data analysis
The raw dataset described in the previous section contains insufficient information for model purposes. For some important variables, there are too much missing values and other variables are missing completely.
In order to solve this we have to get a clear overview of the existing data. Therefore, we need to recognise the “missing observations”. We need to underline these missing observations (importance) and if necessary solve these with valid and motivated assumptions. Having this in mind, the following paragraph first describes the importance of the missing observations and the analysis of the dataset.
5.3.1 Missing observations & Missing variables
The importance of a variable determines whether or not a variable will be added to the data set. The reason to take a variable into account depends on one hand on the expert opinions. This means that an FICTITIOUS BANK expert thinks a variable is a potential risk driver. On the other hand, a variable could be needed because of the statistical importance. This means that there is a possibility that an expert can underestimate the weight of a specific variable for it for modelling purposes.
In statistical analysis, missing data is (unfortunately) a fact. Our goal should be, to complete the data set as good as possible. Therefore, missing values need to be indicated, because it is useful to know why and what information is missing. Every variable has its own specification and every specification needs its own treatment. The question is how to deal with this. The approach I have taken is by asking questions:
• Is this variable of great importance?
• Is there a great lack of significant data? If so is it possible to fill the missing data with valid and motivated assumptions?
If it is appropriate to fill in the missing data, then there are three methods:
• By obtaining the average (mean or median) for the entire sample size;
• Taking averages for a segment25 of the variable. The outcome can replace the missing values in the same segment;
24 Note that, it is theoretically possible that, for example, a first valuation could be measured at 31-12-2000 and a second could be measured at 1-1-2001.
• If appropriate, a more complex method should be considered.
Due to the fact that the FICTITIOUS BANK dataset was incomplete, i.e. missing observations for variables, missing specific variables or missing variables deemed important by shipping experts, other resources had to be referred to. First, I consulted the Internet, especially for collecting technical data.26 Furthermore, I consulted documentation provided by the FICTITIOUS BANK. This documentation consists of annual accounts of single ship companies. Note that, obtaining data, according to these two procedures is a time-consuming exercise. Moreover, it needs to be done very carefully.
5.3.2 Analysis of the dataset
In this part, I document the final data set per class of variable. The approach to solve the missing observations and add specific variables will be determined according to the classification as being used in the former section. Within every section, key variables will be explained, helped by histograms and statistical summaries
5.3.2.1 Financial variables
Up until now, the main problem with respect to the collected data is that there is a lack of important variables. New building Prices of vessels (P_new), the sale Prices of vessels (P_sale) and the Earnings Before Interest, Taxes, Depreciation, and Amortisation (EBITDA) are essential variables, which are missing in the current data set.
5.3.2.1.1 New building Prices
If you want to determine the current price of a vessel, the new building (and sell) price is a key issue. You can imagine that if you want to obtain the change of prices starting from the year of “birth”, that besides the age, also a starting point is required. I determined these newly build vessels prices in two ways. First by (1) searching in the FICTITIOUS BANK files and annual accounts of single ship companies. But, because of the rather high amount of missing values I decided also to (2) estimate the newly build vessel prices, which is a more complex method as mentioned. This method is explained below.
The new building prices (P_new) according to the annual accounts are scarce. Only about 700 observations were available. Note that the P_new measuring took place in the years of 2000, 2001 and 2002. Out of these 700 observations, 196 observations have been made. As mentioned before this is because vessels are more than one time counted in the dataset and as a max one vessel could be measured three times! So this is the reason that
26Key pages that have been consulted: http://www.knvr.nl/, http://www.shortsea.nl/, http://www.wagenborg.nl.
the financial statistical summery in table 5.2 indicates that the number of observations is 196.
As previously mentioned, many vessels have been measured for two or three times.
Hence, it is possible to calculate the depreciation from a specific vessel over a year. Note that, because vessels only have been measured in 2000, 2001 and 2002, the depreciation over time is one or two years. In terms of percentage, I determined the depreciation for every appropriate vessel. Subsequently, I merged the vessel observations with the same ages and estimated their average depreciation, in terms of percentage difference over one year, as represented in previous the left side of table 5.1. On the right of table 5.1, the percentage depreciation according to the new build prices is exposed.
As a result of this approach an estimated new building price (P_E(new)) is obtained for every vessel. As we can see in the histogram in figure 5.5 the mean of the estimated new building price is €70,7 million. Be aware that a calculation for each vessel is made, but as mentioned earlier vessels are counted more than once. This also means that one vessel could have different estimated new building prices. For this reason, I decided to replace the vessels that are counted two or three times, by the estimated new building price based on the oldest valuation.
Age (in years)
Average over one year depreciation
(in %)
Cumulative depreciation
(in %)
0 0 100
1 7 93
2 9 85
3 7 79
4 8 75
5 11 67
6 9 61
7 7 57
8 10 51
9 10 46
19 6 43
11 10 39
12 9 35
13 14 31
14 15 26
15 N/A N/A
16 N/A N/A
17 10 18
18 11 16
Average depreciation over a year is 9%
Table 5.1 Depreciation of a vessel
