Comparing Spread-Implied Probability of Default with Realized Default Rates
Hi Everyone, I am trying to calculate spread-implied probabilities of default (POD) for the iTraxx Xover index and compare with actual, realized default rates to analyse the correlation. I'm using the spread/(1-Recovery Rate) formula to determine approximate PODs. Today Xover is trading at 302bp, and assuming a recovery rate of 40%, I calculate a POD of 5% (entering the spread as a % instead of bp). This seems too low, and performing the same calculation on the CDSW calculator on the Bloomberg reveals a POD in the low 20s%. What am I doing wrong? I know the two rates will be different - the CDSW producing a more accurate result, but gap is too big.
Also, would anyone be able to advise on the relationship between market-implied PODs and realised defaults?
Thank you.
AFAIK, risk-neutral default probability is calculated by: P = 1 - exp(-Spread * Maturity / (1-Recovery)). Basically, don't forget the time...
Thank you Martinghoul, I applied this formula for spreads on the xover index, assuming 5yr maturity. Using the following figures: Spread = 300bp; Maturity = 5yr; Recovery = 40%, I calculate the exponential term as: exp(-300*5/0.6) = exp(-2500) = 0.00, leaving P = 1 I must be using the wrong units for one of the parameters.
Spread of 300bp is 0.03, not 300. Remember all quantities are in %ages, years, etc. Just common sense (and dimensional analysis) should tell you that the spread units shouldn't be different to recovery units.
Thank you very much for your assistance
If I was to use the spread-implied PODs to calculate a predicted default rate, how would I go about doing this? I just want to compare spread-implied default rates with actuals
Do you want the whole academic shebang? This paper talks about comparing implied default rates to actual ones: http://www.bis.org/publ/work173.pdf
I hope it helps.
Thank you very much for the link to this paper.
On a related note: if I were to buy protection on an index like the iTraxx XO 5yr, does this mean that I am protected against default on any of the index constituents? So if one name defaults, am I paid the full notional of the contract - say $10million for 1 contract?
And if the spread on the same index gives a probability of default of 25%, can I just multiply this by the total outstanding bond volume from issuers XO issuers to get a sense for the volume of bonds that could default? Or is this too aggressive? An alternative could be to multiply the POD by the volume of B- and lower rated bonds outstanding from XO issuers - however the spread is pricing the risk of the entire index. Any advice would be really appreciated.
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