Financial Python

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Fixed Coupon CDS is the same as CDX

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Everyone is quoting A Credit Trader these days! Felix Salmon of Portfolio (soon moving to Reuters), attempts to communicate the bottom-line of ACT’s post on the duration risk of CDS. Felix usually does a fantastic job with credit derivatives, but I thought a little helping hand might be useful on this coupon issue. If you understand how the CDX index is quoted, you already understand the fixed coupon, since it’s basically the same idea. The fixed coupon mechanism simply takes standardization a step further.

For example, the CDX index trades at a spread determined by the market, but also features a fixed coupon, or strike. This coupon is set at the beginning of each series (so the IG12 coupon was set when it was launched as the new on-the-run index). I don’t know what the new coupon is at the moment, but let’s say the coupon is set at 250 bps, and the index is trading at 250bps as well. In this case, the index is essentially trading at par since the market spread equals the coupon. Now, let’s assume the index widens to 300 bps and you want to buy protection at this level. There’s obviously a mismatch: the market wants 300 bps but the contract only demands 250 bps. What do you do? You make a small upfront payment to the dealer to clean up the mismatch (basically the present value of the difference between 300 bp and 250 bp payments). Trading upfront eliminates fiddling with duration assumptions and makes the transaction “cleaner.” This can be troublesome when trading the synthetic tranches as well, and there have been proposals to make similar changes to tranche quotes.

The “clean-up” upfront payment can get large when spreads widen a lot, thus introducing a technical slowdown in short trading since a large difference between the coupon and the market spread can make for expensive shorts. The opposite, of course, is also possible. If the index is trading tighter than the coupon, the dealer needs to pay you an upfront payment when you buy protection.

The big bang fixed coupon described by A Credit Trader and Felix follows the same logic as the index, but with standard 100bp/500bp coupons. If you are trading CDS with a 100bp coupon, you could say the CDS is trading at par when the market spread is 100bp (or trading at a discount when the market spread > 100 bp coupon). As a result, the CDS contract has become more bond-like.

See? Easy peasy.

Update: It occurs to me you can see this in action in a previous post. The CDSW screenshot shows IG11 trading at 237bps, with a coupon of 150bps. Looking at the numbers to the left of the green circle, you can see that the CDX is trading at a discount (~96) and that you need to pay ~$300k upfront to clean up the mismatch

Written by DK

March 30, 2009 at 10:32 pm

Posted in Finance

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Delta, Synthetic Tranches, and Mark to Market

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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.

Written by DK

March 17, 2009 at 10:36 pm

Posted in Finance

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