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THE PRICE OF RISK AND ARBITRAGE

In general, the capital-based price of credit risk will not coincide with the market price of credit risk. The risk premium derived from risk-based pricing using capital as risk metric has no reason to coincide with the market price of credit risk. For example, the market spread on a 1000 loan is 0.2% while the required capital is 4% x 1000 — 40. The capital-based return should be 20% x 40 — 8, or 0.8% of the book value of the loan. It is quite different from the market spread over the risk-free rate that is 0.2%. The implied capital in the market spread is the capital that would provide the required 20% return with the actual market spread. The market spread in monetary units is 0.2% x 1000 — 2. The capital proving a 20% return with such spread is 2/20% =10, instead of 40. This is the implied bank's capital in market credit spreads. Note that, theoretically, such an issue does not exist with expected loss, since credit spreads equal the loss rate. But it does when referring to capital measuring unexpected loss.

The example illustrates the discrepancy between market price of risk and the capital-based price of risk. Neither regulatory capital nor economic capital will coincide with the market-based price of credit risk, or spreads. Referring to two prices for the same risk will mechanically generate arbitrage. In the above example, lending at 20 basis points is not profitable for the bank. It would make sense only if other clients' revenues compensate the gap between the facility spread and the required return on capital.

Arbitrage emerges in general as soon as two measures of the same risk differ. A well-known case of possibly under-priced risk is that of securitizations, such as CDOs or other securitizations. The returns provided to investors by each asset-backed note is rating based. But if banks believe that the risk is lower than the risk measured by ratings, they will generate excess returns from CDOs. The CDOs would generate revenues, net of losses, higher than the rating-based revenues required by investors because actual losses are lower than rating-based losses. More generally, securitizations are economical for the bank as soon as they allow increasing the bank's return on capital while still offering the market spread to investors matching the ratings assigned to the various tranches issued by the securitization vehicle. Chapter 59 on credit portfolio management provides examples of regulatory arbitrage, through securitizations and usage of credit derivatives, which allow banks to generate a higher return on capital by taking advantage of such discrepancies.

According to the CAPM, the required return on capital results from the market price of systematic risk of the stock. The cost of equity depends on the systematic risk of the bank's stock in the equity market. The "internal price of risk" charged to a borrower depends on its contribution to the bank's portfolio capital. It translates into a minimum all-in spread that does not match, except by chance, the market credit spread applicable to the borrower.

Bond credit spreads above the risk-free rate relate to default probabilities, recovery rates, risk aversion and bond market liquidity. There are several sources of discrepancy between the bond spreads compensating market investors for credit risk and the all-in spread compensating the bank.

First, economic capital measures the contribution of the bond to volatility of losses of the bank's portfolio and is specific to each bank. Second, the required return on capital depends only on the general risk of the bank's stock, whether capital depends on both the general risk and the specific risk of the bank's portfolio. Therefore, the bank uses a cost of capital that depends on its systematic risk only through the (3 of its stock, for defining compensation to both systematic and specific risk. Finally, the market values credit risk through the bond credit spread, which depends on factors that are not related to a particular bank. Such discrepancies between the market price of credit risk and the capital-based pricing of the same credit risk create inevitably arbitrage opportunities.

 
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