Credit risk is the potential mark-to-market loss, at a chosen probability level, caused by a change in the counterpartys' credit quality. Credit risk has recently received major attention spurred by the Asian crisis and the need to integrate credit transaction analysis with the induced portfolio credit effects. One of the main frameworks proposed to model credit risk is based on default and migration probabilities. Implicit in this approach is the assumption investors are risk neutral to credit risk.
In the next two examples we show how a probability-based approach leads to mispricing. Consider the following two bets with the same expected payoff but contingent on two different events. In the first bet you receive USD100,000 if you lose your job, while in the second one you receive the same amount if you win USD100 million on the lottery. These two events, namely your job, loss and winning the lottery, have the same probability. It follows that pricing these bets, based on probabilities and expected payoffs, leads to the same value. For most people, however, the first bet is more valuable.
A similar argument can be used to formulate the following credit pricing question. Would you pay the same amount for a security likely to default during recession versus another which is likely to default during expansion, ceteris paribus? The above examples show there is an additional component in pricing, namely risk aversion, which is disregarded when pricing credit risk using a probability-based approach. In this sense the probability-based approach implies risk neutrality.
We define instead the price of credit on an arbitrage argument consistent with most derivative pricing frameworks. It is performed in two steps. First, it entails building a replicating portfolio immunized from credit risk and second, pricing this portfolio using the credit spreads available in the market. In this case the credit risk price incorporates the risk aversion factors implicit in the credit spreads. We define then credit risk as the change in price for mitigating the credit uncertainty.
The following example will illustrate the above points. Suppose we want to immunize the credit risk of a derivative transaction that will have a credit risk free current market value of USD100 in one years time and there are only two credit states, namely default versus non-default of our counterparty. Our strategy involves building a portfolio that pays USD100 in one years time irrespective of our counterparty defaulting or not. This portfolio consists of shortening the credit component by selling USD100 notional of corporate bonds issued by our counterparty and buying USD100 notional of Treasuries, at respective prices of 95 and 97.
The above example shows the credit price to be USD2, however, it is necessary to price the hedge throughout the life of the deal. In this respect the following situations can happen. First, the credit exposure stays constant but the credit spreads change. In this case we reprice the replicating portfolio using the new spreads. Second, the spread remains constant but the exposure changes. In this case the size of the credit hedge needs to be adjusted and priced accordingly. Third, both spreads and credit exposure change leading to an adjustment of the size of the credit hedge and the repricing of the whole replicating portfolio.
It is clear in this arbitrage framework the key pricing variables are the level and volatility of the underlying which determines the credit exposure; the level and volatility of the credit spreads and the correlation between the underlying and the spreads.
There are three advantages in using the arbitrage pricing framework over historical defaults which outweigh its implementation difficulties. First, the mark-to-market availability of credit spreads makes this measure immediately reactive to market changes while default and migration probabilities lag the market. The Asian crisis clearly showed rating agencies did not react as fast as credit spreads. Second, using spreads volatility for measuring credit risk allows for a feasible integration with the market risk framework. Third, spreads incorporate risk aversion which instead is excluded in the historical default approach. The major drawbacks of this approach are centered around liquidity issues, namely the difficulty in shortening credit securities and the related gapping behavior of credit spread, which is inconsistent with a log normal pricing framework. The lack of counterparty specific short bonds, or any suitable proxy, often undermines the credit pricing at the single transaction level, however, it can be circumvented at the portfolio level. The possibility of shortening many spread indexes allows us to substantially eliminate the portfolio credit systematic risk. This is the main component of credit risk in a well diversified portfolio where the credit specific risk has been minimized.
This week's Learning Curve was written by Yoav Tamirand Gabriela Soppelsaat Bankers Trust in London.
