This study seeks to respond to the need for better credit risk modeling for a portfolio of consumer loans in the Kenyan banking sector. To do this, the study briefly elucidates the credit risk models currently in use by Kenyan bankers and seeks to modify them through adapting the Semi-Markov approach to modeling credit risk. The study seeks to empirically establish a case for the adoption of the Semi-Markov credit risk framework in modeling through modeling credit rating migration patterns and establishing how the modeling of credit risk influences the solvency and capital adequacy of banks in Kenya in light of the Basel solvency requirements.

Credit risk management has been noted as the single most important role of a banks’ management owing to their nature of business. Credit creation is the main income generating activity of banks, Kargi (2011). However, the downside to credit creation is the inherent credit risk that the bank is exposed to. Increasing variety in the types of counterparties and the expansion in the variety of the forms of obligations has necessitated the jump of credit risk management to the forefront of risk management activities carried out by firms in the financial service industry (Ali and Iraj, 2006). The financial crisis of 2008-2009 revealed that improper estimation of credit risk can lead to dramatic effects on the world’s economy (Munnixl, 2011). A better estimation of credit risk is therefore important, a phenomenon addressed through credit risk modeling (Bluhm, 2002; Duffie, 2003; Giesecke, 2004; Lando, 2004; McNeil, 2005). Munnixl (2011) distinguished two fundamentally different approaches to modeling credit risk: the structural and the reduced form models.

Structural models have a long history, going back to the work of Black and Scholes (1973) and Merton (1974). Reduced form models attempt to capture the dependence of default and recovery rates on macroeconomic risk.

The Kenyan banking sector has experienced a boom in the last few years marked with growth in net assets, branch network, regional expansion, growth in level of loans issued and an increase in the level of depositors, which is not typical to the pre-financial crisis banking sector in the developed economies such as the US.

CBK (2013) notes in its March, 2013 Credit Report Survey that credit risk is the single largest factor affecting the soundness of financial institutions and the financial system as a whole and lending is the principal business activity for most banks. A view re-echoed by Kargi (2011). CBK (2013) notes that the total percentage of loans to total assets for the period ended 31st March, 2013 was 57%, which prima facie, is good for business, however poses a potential threat to the industry if more loans became non-performing. Thus the need to effectively manage credit risk is inherent to the business of a bank. Credit risk modeling underpins this management.

With the newly issued risk guidelines, CBK (2013), the Central Bank of Kenya identifies internal rating models for banks as being key for effective credit risk management. This study’s modeling of credit risk will therefore be a proxy of what a plausible portfolio of consumer loans’ internal rating model, for credit risk management, could be. According to Jansen (2007), the credit risk problem can be seen as a reliability problem. In light of this, the rating process, carried out by a rating agency, gives a reliability degree of a firm bond. Moreover, the default state can be seen as a down state and an absorbing state. It is within this framework that Semi-Markov credit risk models become handy. Limnios (2000) specifies a critical application of Semi-Markov processes as being in reliability of mechanical systems. With the hypothesis that the next transition only depends on the immediate last one, this problem falls within the Markov processes framework. However, Limnios (2000) points out that, for a mechanical system, transition between two states usually happens after a random duration, not necessarily discrete time consequently, making the Semi-Markov environment a better fit than the Markov one. The study’s results are of paramount importance to commercial banks, whose main business is credit creation, the regulator, CBK, as well as other corporate lenders, for instance corporate bond issuers.

The objective here is to articulate the conceptual foundations of the study. First is a survey of existing theoretical and empirical literature on the need for effective credit risk management. Next is a discussion of the current credit risk models in use within the Kenyan jurisdiction. Thereafter, an exploration of the need for better credit risk modeling techniques is presented, establishing a case for the Semi-Markov credit risk models.

The need for effective credit risk management

CBK (2013) annotates that credit risk is the current or prospective risk to earnings and capital arising from an Obligor’s failure to meet the terms of any contract with a bank or if an obligor otherwise fails to perform as agreed. It further emphasizes that a bank’s assets largely comprise loans making the management of credit risk extremely important. Njanike (2009) establishes that poor credit risk management was the chief reason that resulted in the demise of over ten banks in Zimbabwe during the 2003/2004 bank crisis in the southern African nation. The same can be said of the banking crisis in Kenya in the 1980s and in Spain in the 1990s.

While agreeing with Njanike (2009), Marrison (2002) articulates that the main activity of bank management is not mobilization of deposits and issuance of credit; however, risk management is paramount. He outlines that effective credit risk management reduces the risk of customer default. Moreover, they both add that the competitive advantage of a bank is dependent on its capability to handle credit valuably. Conducting a similar study in Spain, De Juan (2008) argues that banking failures were caused by poor credit risk management which was aggravated by the concentration of the loan portfolio in the group in which the bank itself belonged. Fredrick (2012), while using the CAMEL[1] model as a proxy for credit risk established that credit risk management had an impact on the financial performance of commercial banks. He cites that the goal of credit risk management is to maximize a bank’s risk adjusted rate of return through maintenance of credit risk exposure within acceptable limits. He articulates the need for credit risk management to be at the center of banks operations and cries foul at the lack thereof.

Current models and the case for semi-Markov models

CBK (2010) points to the application of the CAMEL rating system, an international benchmark, by the Central bank of Kenya in analyzing the soundness of financial institutions. Fredrick (2012) recognizes that numerous prior studies have examined the efficacy of the CAMEL ratings and they generally conclude that publicly available data combined with regulatory CAMEL ratings can identify and/or predict problem or failed banks. However, in a case study for the American International Assurance-Vietnam, (AIA), it was established that the CAMEL model overlooks the provision as well as allowance for loan loss ratios. Heuristics modeling has also been identified as a key component of most Kenyan banks’ credit risk models. However, Kithinji (2010) alludes to the fact that subjective decision-making by the management of banks may lead to extending credit to business enterprises they own or with which they are affiliated, to personal friends, to persons with a reputation for non-financial acumen or to meet a personal agenda, such as cultivating special relationship with celebrities or well-connected individuals.

Valle (2013) identifies three broad methodologies to model credit risk; structural form models (SFM), reduced form models (RFM) and factor models (FM). SFM are based upon the Black and Scholes theory for option pricing and the Merton model. Linda (2004), on the other hand, identifies two broad methodologies to modeling credit risk, an options-theoretic structural approach pioneered by Merton (1974) and a reduced form approach utilizing intensity-based models to estimate stochastic hazard rates. However, they both concur that the structural approach models the economic process of default, whereas reduced form models decompose risky debt prices in order to estimate the random intensity process underlying default. Consequently, RFM mainly focuses on the accuracy of the probability of default (PD), such that it is more important than an intuitive economical interpretation.

Under the Merton’s structural model, default occurs after ample early warning (Linda, 2004). Consequently, default occurs after a gradual descent in the assigned behavioral value for consumers or asset values for firms; to the default point. This implies that the PD steadily approaches zero as the time to maturity nears (Valle, 2013). More realistic credit spreads are obtained from reduced form models (RFM) or intensity-based models (Linda, 2004). This holds since; whereas structural models view default as the outcome of a gradual process of deterioration in asset values/behavioral value, intensity-based models view default as a sudden, unexpected event, thereby generating PD estimates that are more consistent with empirical observations (Linda, 2004). This study uses a reduced form model for credit risk.

Valle (2013) notes that RFM can be classified as an individual level reduced form model (ILRFM) and portfolio reduced form model (PRFM).He further points out that the former is based on a credit scoring system (two-state or multistate), and the latter assumes an intensity jump process. The study takes the PRFM approach. PRFMs are reported to perform better in capturing the properties of credit risk (Cheng and Zhang, 2009). Within the PRFMs, Discrete Time Markov Processes (DTMP) and Continuous Time Markov Processes (CTMP) have been used in empirical studies to model credit risk spread as two components PD and LGD, (Vallay, 2013). The suitability of Markov processes in modeling credit risk has been challenged with notable problems being; the underestimation of migration probabilities by DTMPs, the dependence of the current state where the current state may depend on various previous states assigned to a firm or consumer and not only in the previous one, the waiting time in a state; among others (Linda, 2004). The Semi-Markov processes have been postulated as a solution to some of the DTMPs and CTMPs weaknesses (Duffie, 2003; D’Amico, 2005; D'Amico, 2009; Monteiro et al., 2006; Banachewicz and Lucas, 2007). This study models credit risk within the Semi-Markov framework.

The case for better credit risk modeling techniques

Chen and Pan (2012) indicate that the new Basel Capital Accord explicitly places the onus on banks to adopt sound internal credit risk management practices to assess their capital adequacy requirements. The Central Bank of Kenya (CBK) adopted the Risk Based Supervisory (RBS) approach in 2004 in cognizance of the limitations inherent in the traditional approach which prescribed a common supervisory approach to all institutions irrespective of differences in business activities conducted and risk appetites adopted (CBK, 2013). In managing credit risk, the CBK recommends that banks must receive sufficient information to enable a comprehensive assessment of the true risk profile of the borrower or counterparty. At a minimum, among the factors the bank should consider is the borrower’s credit rating/report from a licensed credit reference bureau (CBK, 2013).

However, the ratings are bound to change, a factor that raises the credit risk to the bank, and which the CBK risk management guidelines don’t provide for. The CBK guidelines, however note that an important tool in monitoring the quality of individual credits, as well as the total portfolio, is the use of an internal risk rating system which will allow more accurate determination of the overall characteristics of the credit portfolio, concen- trations, problem credits, and the adequacy of loan loss reserves (CBK, 2013). However, no explicit mention of the working and parameterization or nature of such internal models is mentioned.

In its prudential guidelines, the CBK stipulates that capital requirements for a specific institution may increase or decrease depending upon its risk profile. An institution’s minimum capital requirement (MCR) is calculated by dividing its Core and Total Capital by the sum of the value of its Risk-Weighted Assets for Credit risk, Market risk and Operational risk, to arrive at the minimum Tier One and Regulatory capital adequacy ratios respectively (CBK, 2013).

Under PG/03 (CBK, 2013), the Internal Capital Assessment Adequacy Planning (ICAAP) requires that institutions ensure that they at all times plan their capital ahead for a minimum of three years in order to establish and maintain on an ongoing basis an adequate level of capital, which would include an appropriate buffer, as determined by the board, above the regulatory required minimum capital. This requires institutions to have in place an appropriate and proportionate capital management strategy; hence the need to monitor exposure to different risks, especially credit risk. Of interest for this study is the lack thereof of robust models for forecasting capital requirements especially for credit risk purposes; given the nature of banks business; credit creation (Kargi, 2011). The CBK requires that an institution’s Capital Adequacy Ratio must be at least 12%, of which 8% is Core Capital. In addition to the above minimum capital adequacy ratios of 8 and 12%, institutions are required to hold a capital conservation buffer of 2.5% over and above these minimum ratios to enable the institutions to withstand future periods of stress (CBK, 2013).

PG/04 (CBK, 2013) classifies loans, the major asset of banking institutions, into five categories: normal, watch, substandard, doubtful and loss. Classification is based on the number of days the loan is past its due repayment date. CBK (2013) portends that the CBK will conduct an on-site examination providing a list of reclassified accounts, some of which will be downgraded from categories earlier classified by the institution. No account from this list will be upgraded by the institution without sufficient justification.

Consequently, any classification should be in line with that of the regulator. Based on the classification, different amounts of provisioning are to be maintained. However, a prudent practice is to provide for more, in order to limit the downside risk of excessive exposure to non-performing loans. Incisive as this might be, could internal models aligned to the regulators requirements be able to capture exposure levels at different periods? Which would then inform capital adequacy and hence level of provisions made by a bank?

The strict regulation may explain the laxity in research in the area of credit risk modeling within the African jurisdiction. The non-multifariousness of most internal models due to the heavy reliance on regulatory provisions could explain the little or no use of intricate credit risk models.

However, even in light of regulation, the need to model credit risk, with its being the paramount risk that influences the capital levels of banks, is palpable. That less has been done is also ostensible.

A Semi-Markov framework will be adopted in modeling credit risk for a portfolio of consumer loans, as a proxy for an internal rating model for banks. For this study, initial rating of consumers is done through an initial score sheet that is backed by a logit model.

With considerable progress having been made in the area of modeling consumer credit risk, the use of RFMs to model credit spreads has been acclaimed as more realistic to other models. RFMs view default as a sudden, unexpected event, thereby generating PD estimates that are more consistent with empirical observations (Linda, 2004). Consequently, they are preferable. The Basel Accord recommends that banks have an internal rating model for their credit risk exposures. Meanwhile, the CBK Risk Guidelines note that an important tool in monitoring the quality of individual credits, as well as that of the portfolio, is the use of an internal risk rating system which will allow more accurate determination of the overall characteristics of the credit portfolio, concentrations, problem credits, and the adequacy of loan loss reserves (CBK, 2013).

The study concludes that indeed there is a need to model credit risk for effective credit risk management by banks. The inadequacy of the current risk management practice among Kenyan banks is apparent. Non- multifarious and highly subjective credit risk models have consistently been used and their inability to adequately capture credit risk and forecast the probability of default over longer durations has been established. It is concluded that this is a distressing trend since it implies inadequacy of capital reserves held by banks for credit risk. Under CBK (2013), the Internal Capital Assessment Adequacy Planning (ICAAP) requires that banks ensure that they at all times plan their capital ahead for a minimum of three years in order to establish and maintain on an ongoing basis an adequate level of capital, which would include an appropriate buffer, as determined by the board, above the regulatory required minimum capital.

The study further concludes that there is need for robust internal credit risk models. To respond to the need, the study adopted a PRFM, the Semi-Markov model, given the ability of PRFMs to model credit risk spread as two components PD and LGD (Valle, 2013). The study sought to pitch for the case of the Semi-Markov credit risk models in light of the aforementioned regulatory requirements and the need for more robust credit risk models.

Initial credit scoring of randomly selected consumers was done in line with the current practice in the Kenyan banking sector. To each initial credit score, an implied value which acts as the proxy for credit worthiness of the specific consumer; was then assigned. Subsequent rating was done through the Merton model through which the initial transition matrix was generated assuming past historical values for credit worthiness for a portfolio of consumer loans. The initial transition matrix was then espoused to the Semi-Markov environment. The study concludes; from the analysis, results and discussion; the Semi-Markov models not only respond to the existent need for better credit risk modeling but go as far as forecasting for periods beyond the required regulatory minimum of three years.

Whether the capital reserves computed from the Semi-Markov framework are more sufficient than the existent capital reserves for portfolios of consumer, loans computed through standard industry practice could not be verified in the study. This was due to the reluctance by banks to provide such information. Nonetheless, from the study results and discussion, the Semi-Markov framework facilitates better prediction of default probability, the extent of exposure and hence facilitates adequate capital provision prior to occurrence of loss event i.e. default. Lack of data to facilitate the modeling process, was the only challenge to the generation of results and the proceeding analysis. The use of Monte-Carlo simulated data however facilitated passable deductions.

The authors have not declared any conflict of interests.