Unexpected loan losses have been lower for loans to small and mediumsized enterprises (SMEs) than for those to large enterprises in about 2/3 of the period reviewed in this article. In the remaining period, including two of the years during the banking crisis, unexpected losses were higher for loans to SMEs. The results depend in part on the models and calculation methods used. Consequently, we do not have a basis for concluding that unexpected losses are generally lower for loans to SMEs than for loans to large enterprises. Under the Basel II framework, the capital requirements for loans to SMEs have been reduced ("SME discount"). We do not take a concrete position on this discount. The results of our analysis indicate, however, that an SME discount cannot necessarily be rejected.

Introduction
In its assessment of credit risk, a bank normally distinguishes between expected and unexpected loan losses. Expected loan losses are the losses that banks expect to incur based on their model predictions. These losses can be looked upon as an ordinary cost associated with lending activity, and should therefore be priced into the interest rate on loans. However, it is unrealistic to expect a bank's modelbased predictions to be 100 per cent accurate. There will most likely be some difference between expected losses in a loan portfolio and actual losses. This difference can be referred to as unexpected loan losses.
In this article, we analyse differences between unexpected loan losses for SMEs and large enterprises in Norway. One reason why we look at SMEs and large enterprises is that banks' exposures to SMEs will receive a lower capital requirement (SME discount) under the new capital adequacy rules. We do not take a concrete position on this discount. Our analysis is a contribution to the discussion on whether it is appropriate to lower the capital requirement for exposures to SMEs.
In section 2, we describe the method, model and data used in our analysis. In the following section we estimate expected loan losses and losses relating to bankruptcy, and on this basis estimate unexpected losses on loans to SMEs on the one hand and large enterprises on the other. In section 4, we analyse the differences between SMEs and large enterprises in greater detail. In the Norwegian version, section 5 provides a description of the SME discount under the new capital adequacy rules. This section was included as background material for those who are not familiar with the discount. This section has been omitted in the English version and we refer our readers to the BIS website (www.bis.org)

Method, model and data
2.1 Method
In section 3, we estimate expected losses, losses related to bankruptcy and unexpected losses. Expected losses are estimated by multiplying the bankruptcy probability in each individual enterprise by a bank debt of NOK 1 million (2). Unexpected losses are then totalled for all the enterprises in the group and calculated as a percentage of the group's total bank debt. Losses relating to bankruptcy are calculated by tallying the number of (actual) bankruptcies for the same group of enterprises in the three subsequent years. (3) We assume that an individual bankruptcy gives rise to loan losses of NOK 1 million. We have not taken into account that banks may recover portions of the loan amount by realising any collateral. Bankruptcy losses are then totalled for all the enterprises in the group and calculated as a percentage of the group's total bank debt. (4) Unexpected losses is the difference between the sum of bankruptcy losses and the sum of expected losses. If bankruptcy losses are larger (smaller) than expected losses, the unexpected loss will be positive (negative). Finally, unexpected losses are calculated as a percentage of the total bank debt of the group.
2.2 Model
The bankruptcy probability that is used to estimate expected losses is calculated using Norges Bank's bankruptcy prediction model Sebra. (5) The model is a quantitative model that predicts enterprisespecific bankruptcy probabilities. Bankruptcy probabilities are calculated as a function of various key figures in annual corporate accounts and the age, size and industry characteristics of the company. (6) Initially, we also intended to estimate default probabilities, but owing to data limitations this was not possible. The Sebra model was initially estimated over the period 19901996. In autumn 2003, the model was reestimated for the period 19902000. The model showed relatively little change as a result of the reestimation and we have used the initial model in this article.
2.3 Data
We define SMEs as enterprises with annual sales of less than NOK 83 million (i.e. about EUR 10 million), while enterprises with annual sales in excess of this amount are defined as large. The analysis covers all limited companies in Norway that have submitted approved accounts and that have bank debt recorded on the balance sheet in the period 19882001. We have not included years subsequent to 2001 as it takes up to 3 years to tally bankruptcies. In the period prior to 1999, the annual accounts contained less detailed information about enterprises' debt to banks. As a result, the number of enterprises covered in the years 19881998 is smaller than in 1999 and subsequent years. (7) Moreover, the quality of the bankruptcy data for the period 19881990 is poorer. In addition, the registration of bankruptcies in our database was changed as from 1999. Owing to these factors, the periods prior to and following 1999...