Recently we had to write a large essay on the bank loan pricing procedure of the banking system under imperfect competition (for the banking course we ‘re currently attending). The end result was quite interesting and we have posted it as a Working Paper on ssrn. The paper is heavily based on the relevant work of Ruthenberg and Landskroner (2008) which has been extended with more realistic assumptions such as a non-zero Recovery Rate on loans and a securities portfolio to match capital and reserves.

The paper first describes a few stylized facts of modern banking with sections on modern monetary policy implementation and the actual interbank market (where monetary policy acts as an interest rate cap on ‘competitive spreads’). This is followed by a general (stochastic) model for the term and credit risk premium added on loan rates.

The model assumes that a bank finances a new loan by borrowing in the interbank market under Cournot oligopoly and Basel capital requirements. We only examine the case of a properly functioning interbank market with very low excess reserves and liquidity hoarding. The end result is the following equation:

bank loan pricing under imperfect competition

where RL is the loan rate, Ps the borrower’s probability of survival, Rf the risk-free rate, θ the spread in the interbank market over the risk-free rate, k cost of equity (RoE), H the Herfindhal-Hirschman index of concentration in the loan market, ε the elasticity of demand in terms of RL for new loans by bank customers and φ is the risk premium per borrower which is equal to:

φ = PD x LGD

(PD: Probability of default or 1-Ps and LGD: Loss-Given-Default).

Based on the above equation, it is clear that the main drivers of the loan rate are the  Probability of Default and the risk-free rate (these two factors account for over 90% of the loan rate). PD enters the equation both as a ‘compounding factor’ and in the risk premium φ. The end result is that for PD higher than 5% the compounding factor increases substantially and a loan becomes very expensive. The obvious conclusion is that the PD is used as a ‘first line of defence’ by banks in order to determine if a loan will be offered in the first place and the amount made available (especially as a percentage of available collateral, proxied by the Loan-to-Value ratio).

This explains why credit crises and large recessions lead to a ‘credit crunch’ since a large enough PD will result in loan rejections and not in a (very large) increase of the offered loan rate. Updates to a borrower’s PD /LGD (after a loan has been extended) are usually large enough that a bank cannot include them in the loan rate risk premium (without pushing a borrower to an early default) and are incorporated in Loan-Loss provisions.

Under perfect competition (H close to zero) banks are not able to earn a premium over the risk-free rate (apart from the borrower risk premium) and only get their required RoE. If market power exists banks are capable of gaining an above normal profit which is rather marginal for H lower than 0.1 (usually lower than 10% of the risk-free rate). For large enough HHI the premium becomes quite significant.

Both the RoE and Basel capital requirements play a role in the loan rate offered although that depends mainly on the loan’s risk weight.

The model specification was followed by a simple application in the Greek banking system during the Euro era (and before the 2007-2008 credit crisis). Although we did not use any econometric techniques in this essay, the model performed quite well with an R² of 0.93. Given the current HHI of 0.214 it seems that banks have gained (through M & As) significant market power and are able to impose a premium of close to 30% over the risk-free rate in their quoted loan rates (based on the model’s projections).

Our next step is to use the model in order to look into the Greek banking system with more detail and estimate an econometric specification. Still, the basic stylized facts that can be drawn are quite significant and can explain why credit crises lead to a credit crunch and how higher probabilities of default eat into bank profits through loan-loss provisions. Obviously we would appreciate any comments on the paper and the outlined model.