Defaults rates

The rate of default of infrastructure projects which depend on future customers, such as pwwer plcints, can generally be determined through the use of demographic studies. For example, the default rates of power projects can be evaluated based on the project s capacity emd energy sale agreement. See id. at 10. 

In the case where reaction / is a rate reaction, R j) is restricted to being a continuous function of the current values of the concentrations of reactants. This restriction is made because it simplifies the formulation of a solvable set of equations. The default rate expression for the /th reaction is given by ... 

Assuming default rate expressions [that is, R(l) =[A], i (2) =[A], and i (3) = [B], if data for A and B is given, SELECTOR correctly concludes that it is possible to solve for the remaining unknown parameters. However, if only data for A is given, and since the first two reactions have the same rate expression, SELECTOR incorrectly assumes that Al and A2 can be computed. If the rate expressions were different, then the calculation would have been possible. This example emphasizes that SELECTOR only identifies those reactants that are needed to compute the remaining parameters. Thus when the system reduces to an overspecified reaction system, misleading information may be given. 

Default probabilities are not known with certainty, and credit rating agencies suggest that higher risk bonds have more uncertain default probabilities. The agencies publish default rates for each rating category (which are used in credit... 

This represents the cumulative survival rate. Conversely, D, is the cumulative default rate, that is the probability that do not receive the coupon in year t. It is given by Equation (8.27) ... 

Fons, J.S., 1994. Using default rates to model the term structure of credit risk. Financ. Anal. J. 

It is often widely commentated that LTV is not an indicator of default probability. However, we would argue that a borrower with a 50% equity stake at risk from a potential forced sale of a property would have a greater incentive to maintain debt service payments than if the same borrower had an equity stake of, say, 20%, and so although it may not be the most important influence, the LTV of a loan could be expected to have some influence on the default rate. 

Oversimplified in the above example, the occurrence of a default is actually a Poisson process, with the occurrence of a default in time interval u governed by hazard function X(u), which defines the instantaneous default rate at any point in time du. The probability of survival to time t, according to the Poisson distribution, is... 

Note that for safer tranches, the probability of default will be grossed up by a stress factor to more accurately reflect tail risk. The stress factor corrects for the fact that the model assumes constant default rates, whereas actual default rates are stochastic. Using constant, long-term average rates of default tends to understate the possibility of severe, multiple-default scenarios. Therefore, to account for this tail risk the constant default rates are stressed upward. The stress increases for higher-rated tranches since losses in higher tranches will necessarily be farther out on the tail. 

EXHIBIT 26.12 Average Cumulative 5-Year Default Rates (%) for Various Rating Tiers (logarithmic scale), 1970-2000... 

The European market s deep concentration in the struggling telecommunication and cable sectors was the overwhelming catalyst behind the surge in defaults. Telecommunication and cable represented 77% and 91% of default volume in 2001 and 2002, respectively. The two had such a disproportionate impact on default statistics that excluding the two sectors, the default rate would have ended the third quarter of 2002 at just 4.2% compared to the all-in rate of 24.1%. 

Due to a combination of aggressive underwriting in the late 1990s, a meltdown in the telecommunication sector, a record number of fallen angel defaults, and a recession in manufacturing, defaults in the United States also soared in 2001 and 2002. The US default rate ended 2001 at 12.9% and the third quarter of 2002 at 14.3%, both unprecedented levels. The average annual default rate in the United States for the period 1980 through 2000 was just 3.4%, with a peak of 8.7% recorded in 1990. 

Default rates are calculated by dividing the par value of defaulted debt by the average market or sector par value for the period under observation. 

As noted above, the aggressive industry composition and rating mix of deals that made up the European market s early years was the source of its deep troubles in 2001 and 2002. Approximately 77% and 91% of default volume in 2001 and 2002, respectively, came from the telecommunication and cable sectors (see Exhibit 28.4). The two made up such a disproportionate share of defaults, that the default rate through September 2002 would have been 4.2% excluding the two rather than 24.1%. Not to be ignored, defaults in the United States also reached new heights in 2001 and 2002. The US default rate hit 12.9% on default volume of 78.2 billion in 2001, only to be topped in 2002 with a default tally of 90.5 billion and a new record default rate of 14.3% for the first nine months of the year. 

EHBIT 28.6 US High-Yield Default Rates and Volume, 1980-2002... 

Not annualized, through Septemher. The 2001 default rate excluding fallen angels was 9.7%. The Septemher 2002 year to date default rate excluding fallen angels was 11%. 

INDUSTRY DEFAULT RATES MAKE A STRONG CASE FOR DIVERSIFICATION... 

In the short-term, industry default rates are also valuable by highlighting pockets of weakness in the broader market. For example, investors with material exposures to the telecommunication sector either in the United States or in Europe experienced severe losses in 2001 and 2002. For the nine-month period ending September 2002, the European telecommunication sector produced a default rate of 30%. The US rate for the sector was 38.5%. Furthermore, the weighted average recovery... 

EXHIBIT 28.8 Long-Term Industry Default Rates in the United States, 1980-2000 ... 

In addition to the default rate rising to exceptionally high levels, other characteristics of the first batch of European high-yield defaults reveal the aggressive nature of the market s early years. Fitch observed that the aver-... 

The moral of the story is that in an efficient market a high default rate does not necessarily translate into equally dismal returns. The reality that many of the defaulted issues were trading at deep discounts at least six months before default confirms that the European high-yield market had achieved a meaningful level of sophistication by 2002. 

Table 9.5. Default rates and variables in the new mixed model...

The PV of the premium leg is straightforward to calculate, especially if there is no credit event during the life of the CDS. However the contingent leg is just that—contingent on occurrence of a credit event. Hence we need to determine the value of the premium leg at time of the credit event. This requires us to use default probabilities. We can use historical default rates to determine default probabilities, or back them out using market CDS prices. The latter approach is in fact implied probabilities. 

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