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FRM Notes 2011 Unit IIIA Credit Risk

# FRM Notes 2011 Unit IIIA Credit Risk - Revised January 3...

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Revised: January 3, 2011 FIN 7400: Financial Risk Management III. MANAGING NON-MARKET RISKS A. Credit Risk Most of our focus until now has been on market risk, primarily the risk arising from interest rates and exchange rates. (Commodity prices and stock prices would also be sources of market risk but we have not spent any significant time on these.) But the potential for a counterparty to a transaction to default is an important risk as well. Credit risk is one of the oldest risks known to mankind. People have been lending objects and money for about as long as humans have been around and worrying about getting paid back. Now that we have introduced derivative contracts, we must also recognize that when a party enters into a derivative contract, it takes on credit risk from the possibility that the counterparty will default. Measuring and managing credit risk is a very important component of an effective risk management system. In very simple terms, credit risk is the potential for loss due to nonpayment of any amounts owed. The expected loss is given as follows: Expected loss = [probability of default] times [amount owed] times [percentage of amount owed not paid] The probability of default gives the likelihood of a default event occurring. The amount owed is a reflection of the exposure. The percentage not paid reflects the recovery rate. In other words, a party might owe a certain amount but the creditor might receive some of the amount owed. In some cases, recovery is higher due to collateral. Here is an example. A bank makes a \$1,000 loan to a company. The bank believes there is a 90% chance the company will pay back the full \$1,000 and a 10% chance the company will default. If the company defaults, the bank expects to recover \$200. The expected loss can be derived several ways. The expected payback is \$1,000(0.9) + \$200(0.1) = \$920. Thus, the expected loss is \$80. Alternatively, the probability of default is 0.1, the amount owed is \$1,000, and the percentage of the amount owed not paid is 80%. Multiplying these we obtain \$1,000(0.1)(0.8) = \$80 Now let us explore the concept of the probability of default a little more. At one time, credit risk was understood to be simply the possibility of default. A party might owe \$100 and have a 2% chance of default. The expected payoff was, therefore, \$98. But credit risk is really more complex than that. For one, default can occur over a period of time, not just at a point in time. The cumulative probability of default is potentially quite Unit IIIA Notes Page 1 of 32 D. M. Chance, LSU

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Revised: January 3, 2011 FIN 7400: Financial Risk Management different from the probability of default at a given instant. For example, suppose there is a 2% chance that a party will default in a given year. The probability of not defaulting in a given year is, therefore, 98%. What is the probability of default over a two-year period? It is 1 minus the probability that it will not default each year. The probability of not defaulting for two years is (0.98) 2 = 0.9604. Thus, the probability of defaulting over two years is 1 – 0.9604 = 0.0396. What about over ten years?
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