We received several requests to explain how some major synthetic tranches of credit indices such as CDX and LCDX get adjusted when defaults take place. The best way to go over this is to look at an example. Consider the loan index LCDX-12 (if you want to brush up on credit indices, please see the primer in this post). Here are the original tranches of LCDX-12:
0-8% (equity)
8-15% (junior mezz)
15-30% (senior mezz)
30-100% (senior)
That means that on $100 worth of the index, the tranche notionals are:
$8
$7
$15
$30
Each tranche can be traded on its own, allowing someone to go long or short a specific part of the capital structure of this loan index of 100 credits. But since the index was launched, 7 names have defaulted. One key parameter needed here is the average recovery rate, which in this case was 80%. Note that such high recovery is a fluke for leveraged loans this year, but it just happened to be the recovery for these specific names.
Note that as names drop out of the index due to defaults, the equity takes the full loss, while the most senior tranche is reduced in notional. This is equivalent to a static cash CLO deal, where recoveries from defaulted collateral go to pay down the most senior tranche.
With 7 defaults (each name representing 1% of the index) and an 80% recovery rate on $100 index notional, we would expect $7 of defaults, $1.4 in losses, and $5.6 of recoveries. The easiest way to think about this is that losses reduce the most junior tranche, while recoveries reduce the most senior tranche notional. The tranches in the middle stay intact. So here are the new amounts:
$6.6 (8 - 1.4)
$7
$15
$64.4 (70 - 5.6)
But the total notional is no longer $100; it is now $93 (7 names defaulted). Thus the tranche percentages of the lower notional become as follows:
0 - 7.1%
7.1 - 14.6%
14.6% - 30.7%
30.7% - 100%
This index capital structure has changed due to defaults as well as names taken out of the index, and can be significantly different from the original structure.
