Apr 19, 2016

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

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.

Non ut repellat optio voluptates. Aut rerum eum molestiae dolores aut et minus. Excepturi voluptate non et animi.