The historical reliance on credit ratings and credit scores, and lately, credit default swaps, has led many analysts to simple methods of comparing the credit risk of corporations or sovereigns. One often hears statements like “Company A is riskier than Company B” or “Country X is riskier than Company Y.” These statements ignore the time dimension in credit risk, because neither ratings nor credit scores have a time dimension. The same is often true of the credit default swap market and legacy Merton default probabilities, where market participants focus almost exclusively on one maturity. In the CDS market, 5 years gets the most attention.
With legacy Merton default probabilities, 1 year gets the most attention. This post explains how the full term structure of default probabilities in a modern reduced form model provides great insight and understanding of credit risk and its timing that other risk measures have obscured.
Because analysts are so used to credit measures that have either no maturity or only one maturity associated with them, they often ignore the time dimension of credit risk. Let’s turn the clock back to the best point in the recent business cycle. Kamakura’s troubled company press release for September 1, 2009 reported that April and May 2006 had the all-time lowest ratio of troubled companies to the pubic firm universe. On Friday, April 28, 2006 we compare the credit risk of Ford Motor Company with the Spanish bank Banco Santander using the fourth generation reduced form credit models on Kamakura Risk Information Services. On that day, Ford Motor Company had an annualized one month default probability of 1.74% and Banco Santander had a one month default probability of 1.70%. Someone who’s used to focusing on just one measure of credit risk might say “But Ford’s much riskier than Banco Santander—those numbers can’t possibly be right.”
That comment ignores the time dimension of credit risk that is made clear when one looks at the full term structure of default probabilities that is displayed in this graph from April 28, 2006:
Ford’s default probabilities peak at 10.91% at one year and 9.67% at two years, while Banco Santander’s default probabilities gradually decline as the maturity lengthens. The model correctly reflects the greater long term risk of Ford, and from the perspective of 2006, it indicates that 2007 and 2008 are projected to be very high risk years for the Ford shareholders and bond holders.
Plotting the five year default probabilities for both firms confirms that Ford has been consistently more risky in the long run than Banco Santander:
The same graph for 1 month default probabilities shows two things which credit analysts care about. First, the short end of the default probability should and does move around more than the longest maturity on the default probability term structure, just like interest rates. Second, the short term default probabilities for both Ford and Banco Santander can and do overlap, as they should, because when times are good, no one defaults regardless of how much risk the firms may have in the long run. Given the recent credit crisis, many observers have forgotten that in a recent two year period, not a single public firm in Europe defaulted. A perfect model would have shown that all firms had zero short term risk during this period, even though the long end of the default term structure should be much higher for riskier firms. That’s why this graph of the short term 1 month annualized default risk of Ford and Banco Santander shows so much overlap during the “good times” in this past business cycle:
Ford, of course, had much higher short term default risk in 2008 because of the well-publicized problems in the auto sector. If we compare the two firms’ term structure of default probabilities now, we see that Banco Santander is lower across the board even though Ford’s short term default probabilities have fallen to 0.35%:
The same consideration of the time dimension of default probabilities is equally important in comparing sovereign risk. This time we focus on Uganda and the United States of America. An analyst might say “The 1 month default probabilities for Uganda are 0.50% while the USA is at 0.54%. That can’t be right.” This comment again ignores the time dimension of risk. The current credit crisis has led to a multi-trillion dollar government intervention into the US financial markets, so short term risk has indeed risen. If one looks at the full term structure of default probabilities for Uganda and the United States, you can see that state of the art reduced form modeling predicts much higher long term risk for Uganda than for the United States:
Uganda’s five year default probability is 1.17% and the USA term structure of default declines to 0.26% at five years. Over time, it’s apparent that the long term risk of a default by Uganda has been consistently higher than the five year risk of default by the United States:
This graph, which goes back to 1990, shows that Uganda’s long term risk has been improving steadily due to economic growth of Uganda in particular and Africa in general. The long run risk of the USA has always been lower over this 19 year period.
If we turn to the evolution of 1 month annualized default probabilities over time, one can see clearly that the Uganda economy has improved enough (and the USA economy has deteriorated enough) that the short term risk of the two companies has overlapped in recent years.
By paying attention to the time dimension in credit risk assessment that the full term structure of default offers, analysts can distinguish clearly between short run and long run risk. A simplistic single index of risk, like credit ratings, does not offer this kind of insight.
Donald R. van Deventer
September 16, 2009