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# The Cost of Credit Risk and the Risk Premium

The cost of risk includes two components: the statistical loss, or average loss due to defaults ("expected loss"), and the cost of losses in excess of the average loss. The statistical loss is the average loss due to defaults (or "expected loss"), as a percentage of the balance of the loan. Expected loss depends on the borrower's credit risk. It is equal to the loss rate of DP x EAD.

The cost of losses in excess of average loss is measured by capital, either regulatory (Basel 2) or economic "risk-based capital" from models. Both can serve as reference. The cost of (equity) capital is the target return on capital (ROC) or of equity (ROE). If the loan were risk-free, there would be no capital charge and both the statistical loss from default and the loss in excess of this average would be zero. The cost of risk would be zero.

If there is credit risk, capital is required, in addition to expected loss. The percentage cost of the capital allocated to the transaction is the cost of equity for the bank, k. The overall financing combines debt and capital. The cost of credit risk capital is the cost of substituting capital K to debt Z), as shown in Figure 29.3. All costs or mark-up for cost of risk should be expressed as a percentage of the asset since we look for a target rate. Furthermore, since such rate is pre-tax, all costs should be pre-tax, including the cost of equity capital. Assume that the cost of capital is 25% pre-tax and that the cost of debt pre-tax is 7%.

The cost of funding or transfer price is / 7%. The additional cost of substituting capital to debt is:

K(k-i)=Kx (25%-1%)

This additional "cost" is called the risk premium due to credit risk. If regulatory capital is 4% of loan 1000 (the former Cooke ratio), or 40, the risk premium in € is:

40(25% - 7%) = 7.2€

TABLE 29.3 Components of risk-based prices

 Components % Transfer price 7.00% Operating costs 0.50% = All-in cost of funds 7.50% Expected losses 0.50% + Risk-based premium 0.72% = Target risk based price 8.72% + Commercial incentives 0 = Target customer rate 8.72%

For moving from the required return on capital to the target margin of the loan, we find the required mark-up in percentage of loan balance over all-in cost. This percentage is the ratio of risk premium to loan. The ratio uses the ratio of capital to loan, which is fixed (4% for Cooke ratio):

(k - i) (Moan) in % of loan = 4% x (25% - 7%) = 0.72%

The risk premium, (k- i)KIA, is proportional to capital and to the excess of cost of capital over debt. The risk premium is also dependent on the target return on capital.

Note that, in this calculation, we ignored the fact that capital should be reinvested risk-free. Otherwise, if capital funds loans or any risky asset, it would bear an additional credit risk, which would require additional capital. This adjustment for reinvesting capital at the risk-free rate is fully detailed in the risk-adjusted performance chapter, Chapter 55. It assumes that the loan is entirely funded by debt and that capital has a return, in addition to the loan return that is the risk-free rate.

Starting from the pure transfer price, the cost of debt mirroring the loan, we add operating cost. Next we add the cost of risk, with its two components, the expected loss and the risk premium for using up capital. Finally, we could add any commercial incentives, negative or positive, for obtaining the final price. This final price is not the risk-based price which is the all-in cost of funds plus the cost of risk, unless commercial incentives are zero, as in the example (Table 29.3).

This calculation is bottom-up, summing up all percentage items, for finding the target customer rate and the target spread, which is, in percentage terms, the spread over the transfer price or 8.72% - 7% — 1.72%. From the above example, it is easy to conduct a top-down calculation starting from interest revenue and checking that the ROC is effectively 25% before tax (Table 29.4). For a loan of 1000, the capital base is 40 and, under the above assumptions, the debt is 1000-40 = 960, to which the interest rate is applied. The other items follow by applying above percentages to the loan value 1000. Taking the Euro value of all items results in earnings before tax of 10, a value that matches the 25% return over the capital base 40.

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