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Posts Tagged ‘delta’

Delta, Synthetic Tranches, and Mark to Market

Posted by DK on March 17, 2009

A Credit Trader recently posted a very nice exposition of AIGs mistakes in the credit default swap arena. Describing a meeting with AIG at the beginning of the post, he says:

Though mostly unmemorable, there was one moment in the meeting that I will never forget. As the marketing guys were pitching mezz tranches to the PM, I threw in a comment that if credit spreads were to widen the delta of the tranche would go up thus increasing the mark-to-market (MTM) sensitivity, and thus net credit exposure, of the trade. This the PM calmly brushed aside responding “we are not MTM sensitive” as he reached for another piece of fruit.

He goes on to discuss correlation of the underlying assets in CDOs and AIGs inability to appreciate the mark-to-market nature of synthetics. One thing he doesn’t explain, however, is the basic concept of mezzanine tranche deltas increasing as spreads widen. The relationship between tranche deltas and spreads isn’t well-understood (even among those in the credit derivative business), so here’s a shot at providing some intuition.

Expected Loss and Delta

Let’s use the standard IG11 index tranches as an example (though they were never really liquid, but whatever). The IG11 index is based on a portfolio of 125 investment grade credits. The spread of the 5Y index, currently around 237bps, reflects the market’s view of default probability, liquidity, etc. For argument’s sake, let’s just focus on implied default probability. Assuming some recovery rate, we can use the spread and a measure called SDV01 (dollar value of a basis point) to calculate an expected loss (EL) for the portfolio. EL just refers to the amount of money the market expects to lose given current spreads. As the screenshot shows, the SDV01 (circled in green) is about $4035. 237bps x $4035 gives us an expected loss of about $956,295 out of a notional of $10M, or 9.56%. Tuck this number away for later.

Technically speaking, SDV01s decrease as spreads increase, but the important thing to note is expected loss increases as spreads increase. Makes sense, right? Your expected loss should increase if you believe there’s a higher chance of default. Taking it to the extreme, if we assume an aggregate recovery of 40% for the portfolio (just roll with it), the maximum loss is 60%, even if every company in the index defaults.

An index tranche is defined by its attachment and detachment points. The equity tranche covers the first 0-3% of loss, the junior mezz 3-7% of loss, etc. The delta of a tranche describes the leverage of a tranche relative to the underlying portfolio. So if a given tranche has a delta of 3x, a one dollar swing in the underlying portfolio should result in a roughly $3 dollar swing in the value of the tranche.

Now, remember that index expected loss of 9.56% we calculated? You can map this to the attachment and detachment points of each index tranche. Without seeing any runs, we can guess that the 7-10% tranche probably has the highest delta (or close to it). Why? You could call it the “at-the-money tranche” since, intuitively speaking, the value of the 7-10% tranche is most sensitive to spread movements from current levels. Another way to look at it – index spreads are implying that the equity tranche will get wiped out (9.56% > 0-3%). As such, the equity tranche delta should be low as it is pretty much saturated in terms of loss.

If you look back at equity tranche deltas when spreads were low (sub-100bps), you’ll find that the equity tranche actually exhibited the highest delta of all the tranches (in the high teens). This high delta reflects the low level of expected loss implied by the index (<3%). I’m ignoring the impact of correlation right now, but basically all the loss was in the equity tranche. Thus, any change in expected loss would have the greatest impact on the equity tranche.

And that’s why mezz tranches gain sensitivity as spreads widen a lot. The junior-most tranches lose delta as they get saturated with loss while the “at-the-money” tranches gain delta since they are now the “new” first loss slices.

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