PORTFOLIO CREDIT RISK MANAGEMENT (CASE STUDY)

The usages of credit derivatives for portfolio management are multiple: increasing diversification by taking synthetic new exposures as well hedging existing excess exposures and risk concentrations. By doing so, they also alter the portfolio return. The economics of the transactions should enhance, in the end, the return on capital (ROC).

Enhancing the ROC results from the joint effect of credit derivatives on the capital base, which depends on exposures hedged or gained, and on return, through fees paid for hedging or fees received from selling credit protection. "Regulatory arbitrage" is a classical example. Regulatory arbitrage is the direct outcome of differing prices for the same credit risk. As pointed out in Chapter 55, the capital-based price of credit risk and the market price of the same credit risk will not match in general. By taking advantage of such discrepancies, it becomes feasible to enhance the ROC. The same type of arbitrage applies to securitizations, for which an example is provided in the next chapter. Both are examples of credit portfolio management of which main purpose is to increase the risk-adjusted return by using credit derivatives.

We expand the example using regulatory capital. The weight assigned to corporations is 100% and the weight with a banking counterparty drops to 20% under the Basel 1 regulations. The capital charge with a direct loan is 4% (50% x 8%) and becomes 1/5 of 4% = 0.80% for a bank. Next consider two banks. Bank A is the lending bank and bank B is the counterparty for buying and selling credit derivatives. Bank A's pre-tax revenue decreases by the fee paid when it buys credit protection from bank B, say 0.80%, while bank B's revenue increases by the same fee. Bank B has no funding cost but earns the recurring fee from the sale of the CDS. The capital charge for a sold credit derivative is identical to a direct exposure to a corporation, if the underlying asset is a corporate issue, and equal to the full 4%, identical to lending directly to a corporation. Bank A can also sell a CDS for minimizing its cost. It earns the recurring fee for the CDS sold but has an additional exposure to credit risk, which offsets partially the gain of credit exposure from the bought CDS for credit protection purpose. By entering into such trades, the bank might enhance its risk-adjusted return.

For making explicit the economics of such transactions, we use a typical case study.

A credit portfolio of 1000 has an average risk weight of 100% and uses up 4% capital or 40. The spread on loans over funding cost is 100 bps. The cost of regulatory or economic capital is the product of the required return on capital (k) by capital, or k x K. The original return on capital is 25% before tax. Table 59.1 provides some lines for adding protection bought and protection sold, which are zero initially.

According to these data, the economic income statement shows the initial return on capital, equal to the target return. The original return is that of the original portfolio or 100 bps x 1000 = 10 (Table 59.2).

TABLE 59.1 Initial situation: capital

Capital calculation

Notional

Risk weight

Capital

Portfolio

1000

100%

40.0

Credit trading

Protection bought

0

20%

0.0

Protection sold

0

100%

0.0

Capital from trading CDS

0.0

Capital after trading CDS

40.0

TABLE 59.2 Initial situation: earnings

Initial situation: earnings

TABLE 59.3 Initial situation: economic income statement and return on capital (ROC)

Economic income statement

Original portfolio

Net capital after trading CDS

40.0

Net P&L after trade

10.0

ROC

25.00%

The capital is calculated as 4% of the original portfolio risk-weighted 100% and return of capital is calculated with original values. Note that, for return to capital, we ignore expected loss, which means that we consider returns as net of expected loss (Table 59.3).

It is possible to hedge the portfolio with credit derivatives issued by a bank. The cost of the protection bought is 60 bps. The risk weight applicable to the bank is 20%, or a capital charge of 20% x 4% 0.8% multiplied by the amount of protection acquired. It is also possible to sell protection through credit derivatives. The purpose of such a sale would be to reduce the cost of the hedge for example. In such case, the banks earns a spread estimated to 80 bps (the premium of the CDS), but this protection sold has a capital charge corresponding to a 100% risk weight or 100% x 4% = 4%.

The cost of a credit risk hedge (a credit default swap, CDS) includes two cost components. The direct cost is the premium of CDS times the exposure hedged. The second component is the cost of the Basel 1 or Basel 2 capital allocated to the exposure to the seller of the CDS, a bank with risk weight 20% instead of 100%. Under Basel 2, such a capital charge would depend on the rating of the bank. But only numerical values would change and we can proceed as if we are subject to Basel 1 capital charges. Selling a CDS provides the premium but costs additional capital, as if the bank were exposed to the underlying asset risk weighted 100%.

If the bank buys a credit protection of 1000 for the total portfolio, earnings decline by the cost (premium) of the CDS bought, but capital also declines. The bank can also buy a protection for 1000 (total portfolio) and sell a credit protection for 300 in order to offset some of the cost of the protection. Again, earnings, capital and return on capital change.

We now proceed for the calculations of earnings, capital and return on capital in the two cases:

• when buying full protection for the portfolio

• when buying and selling protection.

 
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