FRM Part 2 – Credit Risk · FRM
Synthetic CDOs: Exposure Without a Limit
A cash collateralised debt obligation buys bonds or loans and slices their cash flows into tranches. A synthetic CDO owns nothing. It takes on the same credit exposure by selling protection through credit default swaps on a reference portfolio it never holds.
That distinction sounds technical and it has one enormous consequence. The size of a cash CDO market is limited by how many bonds have been issued. The size of a synthetic CDO market is limited only by how many contracts people are willing to write. Any number of synthetic structures can reference the same underlying pool, which is how losses in 2008 came to exceed, by a very large margin, the size of the mortgage market that caused them.
Key Takeaways
- A synthetic CDO gains credit exposure by selling protection through credit default swaps rather than by buying assets.
- Because no assets need to be sourced, any number of structures can reference the same pool, so the exposure has no natural limit.
- Losses fill the tranche stack from the bottom, governed by attachment and detachment points.
- Unfunded tranches carry no cash at inception but usually carry collateral obligations, which is how a correct position can still fail.
- Correlation does not change the portfolio expected loss. It redistributes it, so the equity tranche is long correlation and the senior tranche is short it.
- In 2008 correlation was calibrated low on benign data and realised high, which is exactly the state in which senior tranches take losses.
Cash and synthetic: what the difference actually is
In a cash CDO, a special purpose vehicle raises money from investors, uses it to buy a portfolio of bonds or loans, and pays investors from the interest and principal those assets generate. Losses on the assets flow through to the tranches in order of seniority. The vehicle owns real claims on real borrowers.
In a synthetic CDO, the vehicle sells credit default swap protection on a reference portfolio. It receives premium payments from the protection buyers, and pays out if a credit event occurs on any of the reference names. It never buys the underlying bonds and has no relationship with the borrowers, who typically have no idea the structure exists.
| Cash CDO | Synthetic CDO | |
|---|---|---|
| What the vehicle holds | The actual bonds or loans | Credit default swaps, and usually collateral |
| Source of return | Interest and principal on the assets | Credit default swap premiums, plus any collateral yield |
| What triggers a loss | An asset defaults or is written down | A credit event on a reference name |
| Assets must exist and be available | Yes, and must be bought at market prices | No. Only a willing counterparty is required |
| Maximum size referencing one pool | The size of the pool | Unbounded |
| Set-up speed | Slow. The portfolio has to be sourced | Fast. A contract can be written the same day |
The last two rows are the substance of the whole topic. Everything else is mechanics, and a candidate who can state those two rows can reconstruct most of what follows.
Why the exposure has no natural limit
A cash structure has to compete for assets. If a hundred managers want to build CDOs from the same class of mortgage bonds, they bid against each other for a fixed supply, prices rise and spreads compress until the trade stops working. The market is self-limiting because the raw material is finite.
A synthetic structure has no such constraint. Two parties can write a credit default swap referencing a bond neither of them owns, and they can do it as many times as they like. Ten synthetic CDOs can reference the same tranche of the same mortgage security, creating ten times that tranche’s notional in exposure without a single additional mortgage being originated.
This is the structural fact that explains the scale of the 2008 losses. The subprime mortgages that defaulted were a large but bounded amount of lending. The losses that flowed from them were far larger, because synthetic structures had multiplied the exposure to the same underlying pool many times over. A default on one bond can trigger payments under every contract that references it, and there is no rule limiting how many of those exist.
Two further consequences follow. Because nothing needs to be sourced, a synthetic structure can be assembled quickly, which suited a period when demand for yield exceeded the supply of assets to provide it. And because someone must take the other side, a synthetic CDO requires a party who wants to buy protection on that portfolio, which means a party with a view that the portfolio will deteriorate. A cash CDO has buyers and no obvious opposing side. A synthetic CDO has one by construction.
Tranches, attachment points and who absorbs what
Both structures allocate losses the same way, through tranches defined by an attachment point and a detachment point. A tranche absorbs losses once cumulative portfolio losses exceed its attachment point, and it is exhausted once they reach its detachment point.
Tranche loss % = min(max(L − A, 0), D − A) / (D − A)
L is the cumulative portfolio loss, A is the attachment point and D the detachment point, all as percentages of portfolio notional
A synthetic CDO references a $1,000 million portfolio with tranches at 0 to 3%, 3 to 7%, 7 to 15% and 15 to 100%. Allocate a 5% portfolio loss and then a 20% portfolio loss.
- 5% loss is $50m. Equity absorbs its full $30m and is wiped out.
- Mezzanine covers 3% to 7%, that is $40m. Losses above 3% amount to $50 − $30 = $20m, so mezzanine loses $20m, which is 50% of the tranche.
- Senior and super senior are untouched. Check: 30 + 20 = $50m.
- 20% loss is $200m. Equity, mezzanine and senior are exhausted at $30m, $40m and $80m, totalling $150m.
- Super senior covers 15% to 100%, that is $850m. It absorbs the remaining $50m, which is 50 / 850 = 5.9% of the tranche. Check: 30 + 40 + 80 + 50 = $200m.
Answer: at a 5% portfolio loss, the equity investor loses everything and the super senior investor loses nothing. At 20%, three tranches are gone and the super senior loses under 6%. That last figure is why super senior tranches were treated as close to risk free, and it is correct arithmetic. What it does not tell you is how likely a 20% portfolio loss is, and that question has only one input.
Funded and unfunded
Synthetic tranches come in two forms, and the difference matters for who is exposed to whom.
In a funded tranche, the investor pays cash upfront. The vehicle invests it in high quality collateral, and the investor receives the collateral yield plus the credit default swap premium. If a credit event occurs, the collateral is liquidated to make the protection payment. The protection buyer has no credit exposure to the investor, because the money is already held.
In an unfunded tranche, no cash changes hands at inception. The investor simply receives the premium and undertakes to pay if losses reach their tranche. This is how super senior exposure was typically written, because the tranche was regarded as so unlikely to be hit that requiring cash against it seemed inefficient.
An unfunded super senior position looks like free premium income until the collateral agreement is read. These contracts typically required the protection seller to post collateral as the mark to market moved against them, and as their own credit rating fell. So a seller could be entirely correct that the tranche would never take an actual loss, and still be destroyed by the collateral calls generated by the market’s changing opinion of that question. That mechanism, rather than realised defaults, is what forced the rescue of AIG in September 2008.
Correlation is the whole valuation
The expected loss on the portfolio does not depend on default correlation at all. If each name has a 5% chance of defaulting, the expected portfolio loss is 5% whether the names move together or independently. Correlation does not change the average. It changes the distribution around the average, and tranches are claims on parts of that distribution.
Take 100 equally sized reference names, each with a 5% default probability and no recovery. Compare the expected loss on the equity tranche, 0 to 3%, and on the super senior tranche, 15% to 100%, under zero correlation and under perfect correlation.
- Zero correlation: the number of defaults follows a binomial distribution with mean 5 and standard deviation 2.18, so outcomes cluster tightly around five defaults.
- Three or more defaults is therefore close to certain, and the equity tranche has an expected loss of 94.6%.
- More than fifteen defaults is nearly impossible, at a probability of about 0.004%, so the super senior expected loss is essentially zero.
- Perfect correlation: either all names default, with probability 5%, or none do. The equity tranche is untouched 95% of the time, giving an expected loss of 5%.
- The super senior tranche is wiped out in that same 5% of cases, giving an expected loss of 5% as well.
Answer: the equity tranche’s expected loss falls from 94.6% to 5% as correlation rises, and the super senior tranche’s rises from essentially nothing to 5%. The portfolio expected loss is 5% in both cases. The equity investor is therefore long correlation and the senior investor is short it, and a single assumption about correlation moves value between the tranches without changing the total.
| Zero correlation | Perfect correlation | Direction | |
|---|---|---|---|
| Equity, 0 to 3% | 94.6% | 5.0% | Falls. The investor is long correlation |
| Super senior, 15 to 100% | about 0% | 5.0% | Rises. The investor is short correlation |
| Whole portfolio | 5.0% | 5.0% | Unchanged |
Read the bottom row first. The portfolio expected loss is the same under both assumptions, which is what makes this a redistribution rather than a change in the amount of risk present. Everything a tranche investor gains from a correlation assumption, another tranche investor loses.
That is why these instruments were often described as correlation trades rather than credit trades. The credit view was largely shared. The disagreement, and the money, sat in the correlation assumption.
What went wrong in 2007 and 2008
Pricing relied on copula models, most commonly the Gaussian copula, which reduces the dependence structure of a portfolio to a manageable set of parameters and in practice often to a single correlation number. The model was not secret and its limitations were discussed in the literature well before the crisis.
Three things then went wrong together. The correlation parameters were calibrated on historical data from a period in which regional house prices had not fallen simultaneously, so the estimates were low. The reference pools were far less diverse than their name counts suggested, because subprime mortgages across different regions shared one dominant driver in national house prices. And when that driver turned, realised correlation moved toward one, which is precisely the state in which senior tranches take losses.
The worked example above is the whole mechanism in miniature. Super senior tranches were priced and rated on the assumption of low correlation, which makes their expected loss essentially zero. Realised correlation went to something close to perfect, which puts their expected loss at the portfolio default rate. Nothing about the arithmetic failed. The single input it depended on was wrong, and the structure had been built so that this input carried all the weight.
The ratings themselves compounded the problem rather than catching it. A super senior tranche whose expected loss is essentially zero under the assumed correlation genuinely does look like the safest instrument in the market, and the rating followed the model. Investors who relied on the rating were not being careless in any obvious way; they were relying on an assessment that had itself been produced by the same single assumption. When one input drives both the price and the rating, the rating is not independent confirmation of anything.
The synthetic multiplication described in Section 2 then determined the scale. Every contract referencing an impaired pool had to pay, and there were far more contracts than there were mortgages.
What to carry forward
Three points survive well beyond this instrument.
First, ask what limits the size of an exposure. If the answer is the quantity of an underlying asset, the market is self-limiting. If it is the willingness of counterparties to contract, it is not, and the aggregate can grow far past anything the underlying could support.
Second, find the input that carries the weight. Tranche valuation depends on many things and is genuinely sensitive to one. A model whose output is stable across most of its inputs and swings violently on a single hard-to-estimate parameter is a model whose risk is that parameter, whatever the documentation says.
Third, separate the risk of being wrong from the risk of being early. The unfunded super senior sellers were largely right that the tranches would not experience the losses being priced. They were destroyed by collateral calls driven by mark to market movements before that question was ever settled. Solvency and liquidity fail differently, and a position can be correct and still be unsurvivable. Any risk framework that measures only the first has not measured the thing that actually ends institutions.
Expect the attachment and detachment arithmetic, and expect the correlation direction. Higher default correlation reduces the expected loss on the equity tranche and increases it on the senior tranche, leaving the portfolio expected loss unchanged. State it as a redistribution rather than an increase in risk, because that phrasing is what the question is testing.
The short version
- A synthetic CDO gains credit exposure by selling protection through credit default swaps rather than by buying assets.
- Because no assets need to be sourced, any number of structures can reference the same pool, so the exposure has no natural limit.
- Losses fill the tranche stack from the bottom, governed by attachment and detachment points.
- Unfunded tranches carry no cash at inception but usually carry collateral obligations, which is how a correct position can still fail.
- Correlation does not change the portfolio expected loss. It redistributes it, so the equity tranche is long correlation and the senior tranche is short it.
- In 2008 correlation was calibrated low on benign data and realised high, which is exactly the state in which senior tranches take losses.
Frequently Asked Questions
What is a synthetic CDO?
A structure that takes on credit exposure to a reference portfolio by selling credit default swap protection on it, rather than by buying the underlying bonds or loans. The vehicle receives swap premiums and pays out on credit events, and it never owns the assets or has any relationship with the borrowers.
How does it differ from a cash CDO?
A cash CDO raises money, buys a portfolio and pays investors from the interest and principal it generates. A synthetic CDO owns no assets. The practical difference is that a cash structure is limited by the supply of bonds available to buy, while a synthetic one is limited only by the willingness of counterparties to write contracts, so any number of them can reference the same pool.
How are losses allocated between tranches?
From the bottom up, using attachment and detachment points. A tranche starts absorbing losses once cumulative portfolio losses exceed its attachment point and is exhausted at its detachment point. On a $1,000 million portfolio with a 5% loss, an equity tranche running from 0 to 3% loses its full $30 million and a mezzanine tranche from 3 to 7% loses $20 million of its $40 million.
What is the difference between funded and unfunded?
A funded tranche investor pays cash upfront, which is held as collateral and used to make protection payments. An unfunded investor pays nothing at inception and simply receives the premium, undertaking to pay if losses reach their tranche. Unfunded positions usually carry collateral obligations that are triggered by mark to market moves and rating downgrades, which is a liquidity exposure quite separate from the credit one.
Why does correlation matter so much?
Because it redistributes losses between tranches without changing the portfolio total. With 100 names each 5% likely to default, zero correlation gives the equity tranche a 94.6% expected loss and the super senior essentially zero. Perfect correlation gives both an expected loss of 5%. The equity investor benefits from higher correlation and the senior investor is harmed by it.
Why did super senior tranches lose money in 2008?
Because they were priced and rated on low correlation estimates drawn from a period in which regional house prices had not fallen together. The reference pools shared one dominant driver in national house prices, so realised correlation moved toward one, which is exactly the condition under which senior tranches take losses. The arithmetic worked. The single input it depended on did not.
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