Tuesday, September 29, 2009

Comparing Default Probabilities and Credit Default Swap Quotes: Insights from the Examples of FNMA and Citigroup

Posted on Kamakura's website by Donald van Deventer

Our blog post on September 23, 2009 was an update of a 2007 article we did in RISK on the relationship between credit default swap quotes and modern reduced form default probabilities. This post illustrates how the probability of government bailouts causes the potential losses of different liability holders to diverge sharply. A similar kind of division can be seen in the trends of default probabilities and credit default swaps. We illustrate this process using the cases of FNMA and Citigroup.

In what follows we compare 5 year composite senior debt credit default swap quotes, as reported by Markit Partners, with reduced form default probabilities The CDS quotes we report are on a “spread” basis for senior debt with “modified restructuring” documentation. The default probabilities we use are the 5 year Jarrow-Chava version 4.1 reduced form default probabilities from Kamakura Risk Information Services. These default probabilities predict the probability of failure from a combination of financial ratios, macro-economic factors, equity market returns, and company size. For more on the Kamakura Risk Information Services models see www.kamakuraco.com. These models are benchmarked on a “failure flag” that is the earliest to occur of the following events:

• Chapter 7 or 11 bankruptcy
• Delisting for reasons of obvious financial distress, such as failing to pay fees or file financial statements
• Declaration of a D or SD rating (if the latter becomes permanent)
• A credit event under the ISDA credit default swap language (for more recent modeling)

The five year default probability is assembled from 60 different logistic regressions which predict both the spot 1 month default probability and 59 forward 1 month default probabilities. The 5 year default probability is quoted on an annualized basis comparable to the credit default swap quote.

The graph below compares the CDS quotes and 5 year default probabilities for FNMA from 2007 until it entered into conservatorship in September 2008:

The blue line is the 5 year credit default swap quote and the green bars are the five year default probabilities from KRIS. By the end of the day on September 5, 2008, the KRIS default probabilities were consistent with a 42.92% five year cumulative probability of default. Annualized default probabilities on that day were in excess of 21% for 1 year and 10.61%, shown above, for the 5 year default probability. The five year credit default swap quote, by contrast, was only 38 basis points.

Which number was the best estimate of the “failure” of FNMA, broadly defined? From a common shareholder’s perspective, clearly the default probabilities were better predictors of the almost total loss taken by common shareholders (although the stock continues to trade today at slightly in excess of $1). The 38 basis point credit default swap represents something completely different—a combination of the probability of failure, risk aversion (as discussed on September 23) and other factors, and the probability of the rescue of the senior debt holders of FNMA. The senior debt holders, but not the equity holders, were bailed out. That’s why the two time series can and do diverge so sharply.

A similar pattern can be seen in the graph of 5 year default probabilities and 5 year senior debt credit default swap quotes for Citigroup from January 1, 2007 to March 31, 2009:

The five year default probabilities peak at more than 25 percent, with the senior debt CDS quotes topping out at 6.35% on March 31, 2009. Again, the CDS spreads obscure the probability of failure, because they also include the probability, contingent on effective failure, of senior debt holders being rescued. Common shareholders, by contrast, care about the raw probability of failure because they’re unlikely to be bailed out. That’s why the default probabilities are much more important than CDS spreads to investors in common stock, preferred stock, and even subordinated debt.

Best practice risk management requires transparency with respect to both the probability of failure and the potential recovery for each class of liabilities from common stock to senior debt and insured bank deposits. That’s why both CDS quotes and modern default probabilities are essential for best practice risk management.

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