Today, GE credit spreads hit a record high of 1000 basis points, implying a 50% probability of default over the next 5 years.
I thought this milestone from a AAA (yes, still) company provides as good an opportunity as ever to write a post describing how the market comes up with default probabilities.
I remember a few years ago just as Delta and Northwest were getting in trouble, and would in short order enter the revolving door of airline bankruptcies, I was approached by the sector analyst who was about to head out to DC to testify on his outlook for the industry. He wanted to put some hard numbers around what the market thought was the likelihood that these two companies would go under.
I remember immediately asking out Airlines trader where the credit default swaps (CDS) were trading on the two names, plugging those spreads into a Bloomberg screen and reading off a term structure of default probabilities implied by those prices.
Noting much has changed since then. CDS is still the benchmark credit risk product that the market uses to gauge default risk. This is largely owed to the standardization provided by the CDS – maturities and conventions are largely the same across companies and liquidity in the vast majority of cases is much better than in bonds or loans.
Below, I review the standard way of calculating these default probabilities but also cover two others: the probabilities of default implied by bond spreads as well as the company’s rating.
Estimating Probabilities of Default
Method 1 (the Market Standard): CDS Approach
CDSW screen on Bloomberg
This is a CDSW Bloomberg screen for General Electric. This is the standard tool that is used to calculate mark-to-markets for credit default swaps. You can get to this screen via the following sequence in bloomberg:
WCDS <GO> → Enter GE in the ticker field → CDSW <GO>
One caveat to add here is that the Recovery Rate is a factor going into the calculation of the probability of default (for a given CDS spread level, the higher the assumed recovery rate the higher the probability of default and vice-versa). Here, Bloomberg defaults to a 40% recovery which is a standard assumption for high-grade credits.
In reality, the recovery as determined in either the workout process or in the CDS post-default auction process can be wildly off, especially for Financials. For example, Lehman recovery was determined to be 8.7% (roughly speaking, where the Lehman senior unsecured bonds were trading a month after the determination of default)- a far cry from the 40% assumption.
Method 2: Cohort Approach
One-year S&P credit migration matrix: 1981-2003.
This is very similar to the life-insurance actuarial approach where to calculate expected probabilities we look at the history of actual rating migrations and defaults. Row headers mark the rating at the beginning of the period and column headers mark the rating at the end of the period.
In this case, the matrix shows data for period length of 1 year. So, for example, reading from the matrix, historically a BBB-rated company was downgraded to BB a year later with a frequency of 4.74%. In this case, we are after the right-most column under D which tells us the 1-year default probability of a company with a given rating. In our case of a AAA GE, the 1-year historical probability of default is zero. What this tells us is that in the period of 1981-2003, no AAA S&P rated company has defaulted within a year.
What I say above requires a little bit of handwaving because we are ignoring the timing and intra-period sequence of ratings changes. Also, to be more precise we should really be using a sector-specific ratings migration matrix, especially in the case of Financials which tend to be more “gappy” than companies in other sectors (given that they are much more leveraged than “regular” companies and depend much more on general confidence). But it will work for our illustrative purpose here.
In order to calculate multi-year default probabilities (i.e. a default probability term structure) we need to create multi-year (2-year, 3-year, etc) version of the matrix above. We do this simply by multiplying the matrix by itself and again reading off the right-most cell (i.e. AAA→D).
The table below shows the probabilities of default using this approach (2nd column) as well as the probabilities using the CDS approach described above but with a more realistic 20% recovery assumption. As you can see, the two methods are wildly off. Though normally, there is a large risk premium (especially in high grade) priced into credit spreads over historical default probabilities, in the case of GE it’s pretty egregious.
Default probabilities implied by GE CDS spreads and its AAA rating
Method 3: Bond Approach
This is actually very similar to Method 1, however, instead of using CDS spreads, we use bond spreads. In an ideal world, bond spreads would imply the same default risk as CDS, all else equal. This is no longer the case in the current market and the difference between bond spreads and CDS spreads (called bond/CDS basis) has in the opinion of many become a proper tradable (if particularly toxic) asset class in the credit markets.
Many attribute billion-dollar losses at Deutsche Bank and hedge funds like Citadel to leveraged negative basis trades (long bond, long CDS) – I will cover the negative basis trade in a future post. In the current market, bond spreads usually trade above CDS spreads. This is largely a function of balance sheet (buying bonds takes up balance sheet and carries a risk-weighted asset charge) as well as unwinds of negative basis trades.
Below is a chart of the average bond/CDS basis in the Financials sector. Current level is around -220bps meaning 5y bonds trade around 220bps wider of CDS. This means that bonds for Financial companies actually imply a higher probability of default than the CDS market.
Financials Bond-CDS Basis
For those who want to keep score at home or don’t want to bother with Bloomberg, here’s a nifty way to calculate CDS-implied default probabilities:
Approximating default probability implied by CDS spreads