Mitigating credit risk: modelling and optimizing co-insurance in loan pricing

ABSTRACT

Despite large-scale financial development and banks being the most important credit source globally, banking continues to be plagued by asymmetric information. This uncertainty makes credit risk assessment decisions complex and expensive. In this context, we show how discretionary borrower characteristics, such as the borrower’s network (which can co-insure), help mitigate risk and reduce costs by altering lending decisions. The literature on loan pricing remains focused on objective credit scoring models, while the network literature remains empirical, and borrower based. We fill this void by being the first to theoretically model the lender’s internal decision-making problem when borrowers display discretionary default risk-mitigating attributes such as network strength. We find that the interest rate reduces as the network strength increases. As constraints set in and borrowing becomes more competitive, banks rely even more on network information to parse out better borrowers. Finally, banks substitute monitoring effort with network strength for a more feasible interest rate. This will increase lending, even to borrowers outside the banks’ purview earlier.

KEYWORDS:

• Banking
• credit risk modelling
• decision analysis
• networks
• OR application

JEL CLASSIFICATION:

• C02
• C61
• D81
• D85
• E43
• G21
• L14

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ Refer to the article titled, Deutsche Bank and Trump: USD2 Billion in Loans and a Wary Board, available at https://www.nytimes.com/2019/03/18/business/deutsche-bank-donald-trump.html. Last accessed on 17th March 2020.

² India, the fastest-growing trillion dollar economy, is one of the top five economies in the world.

³ Refer to the article titled, Explained: Why did Yes Bank have to be bailed out?, available at https://www.thehindu.com/business/Industry/why-did-yes-bank-have-to-be-bailed-out/article31010980.ece. Last accessed on 17th March 2020.

⁴ Loans to large customers are often customized and prices negotiated, unlike other loans where prices are more objectively and competitively determined. Large customer loans are also the revenue source that requires more screening and can result in large NPAs as seen in examples such as Kingfisher Airlines (https://www.livemint.com/Companies/smvfjlMWKkl5aX6RZo9MiK/The-cases-against-Vijay-Mallya-and-Kingfisher-Airlines.html), Nirav Modi (https://www.businesstoday.in/sectors/banks/nirav-modi-case-pnb-fraud-11400-crore-scam-ed-cbi-raid/story/270708.html), and more recently, Yes Bank (discussed earlier).

⁵ This is a differential over and above the values already determined by the objective models in step 1 of the process.

⁶ We, henceforth, use the terms ‘bank’ and ‘lender’ interchangeably.

⁷ (Diamond 1984; Ramakrishnan and Thakor 1984).

⁸ More so when lending is transactional or non-recurring. We explain this further in section II.

⁹ A review of bankruptcy prediction models shows how despite the use of newer modelling techniques, information used is still restricted to direct information on the borrower (Kumar and Ravi 2007).

¹⁰ This is similar to collateral but it’s availability is not a certainty.

¹¹ Refer to the BCG article ‘Four Ways Banks Can Radically Reduce Costs’, available at https://www.bcg.com/en-in/publications/2018/four-ways-banks-can-radically-reduce-costs.aspx, last accessed on 19th December 2019.

¹² Regulatory delays, limited liability clauses and ‘missing’ borrowers are only few of the many problems banks face when retrieving funds from defaulting borrowers.

¹³ It is a new customer with no repeat interactions or other banking relations.

¹⁴ While loans with any characteristics (including borrowing objective and collateral requirement) can be explained using the model, we focus on a general purpose loan. This is akin to most large-ticket loans which are not investment-specific and require no physical collateral (though are secured against current assets of a borrower). Such a loan brings to the fore the borrower’s dependence on external financing in case of default.

¹⁵ This includes publicly available information such as financial data.

¹⁶ Where $\beta r$ is the reduction in amount borrowed when the quoted bank price $r$ is more than the borrower’s desired rate. This is akin to the borrower’s adjustment to loan amount desired given the lender’s price and so, $\beta$ can be interpreted as the borrower’s sensitivity to price.

¹⁷ The strength of a network can be quantified in multiple ways including ranking or assessing relative importance of a firm in its group using measures of distance (Kali and Sarkar 2011).

¹⁸ Without any loss of generality (since the objective function is concave), if $r^{\ast }>\frac{\alpha }{\beta }$ then the optimal value of $r^{\ast }$ will be set to $\frac{\alpha }{\beta }$ because $\alpha -\beta r$ would then be negative.

¹⁹ Given that $\beta >>\alpha$, $\frac{\beta }{\alpha +\beta }\to 1$. As the inherent macro and micro uncertainty in predicting a future default can never be completely eliminated, the chances of always successfully monitoring are negligible and so it is unlikely that $q$ will ever approach 1.

²⁰ Though at values of $r^{\ast }>\frac{\alpha }{\beta }$ the value is set at $\frac{\alpha }{\beta }$ (refer footnote 13), for the numerical exercise we have not bounded it.

²¹ Without any loss of generality (since the objective function is jointly concave in $r$ and $q$), if $q\ast >1$ then the optimal value will be set to $q^{\ast }=1$.