(Originally published at Dan Wang’s blog.)

What exactly are collateralized debt obligations (CDOs) and credit default swaps (CDSs)? This post draws from The Big Short by Michael Lewis and a study on CDOs by A.K. Barnett-Hart to summarize how these two financial instruments are structured and why they’re in part responsible for the financial crisis.

CDOs caused between $400 to $600 billion of the write-downs of banks, while the market size of CDSs peaked at $60 trillion. These two instruments have a well-deserved reputation for being very technical, but at their core they’re simple concepts. A CDO is a fancy bond, while a CDS is mostly an insurance policy. This essay explains exactly how these two instruments are structured. First we get into the CDO, then the CDS, then how they relate to each other, and finally their role in the subprime mortgage crisis.

Mortgage-backed Securities

CDOs are made up of sections of mortgage bonds, or mortgage-backed securities (MBS). So to understand the CDO you have to first understand the mortgage bond. What is a mortgage bond?

If you’re buying a house you’re probably taking out a mortgage. That means that you’re getting a loan from a bank or a lending agency and then making a payment back every month with some interest.

Interest rates on mortgages are fairly high. A 30-year U.S. Treasury Bond may yield about 3 to 6%, while a homeowner pays between 5 to 10% on her monthly mortgage payment. Mortgages offer much higher returns, and so investors are more attracted to them.

But for various reasons, it’s hard to invest in individual mortgages. They’re easier to invest when thousands of individual mortgages are bundled together to form a mortgage bond. The mortgage bonds were packaged by agencies like Fannie Mae and Freddie Mac, who bundled the mortgages from banks like Wells Fargo or lending agencies like the New Century Financial Corporation.

A mortgage bond isn’t like a corporate bond or a government bond. Instead, it’s a claim on payments from its thousands of mortgages. But just as a corporate bond can default, a mortgage bond can fail too: When enough individual mortgages failed, the entire bond won’t be able to generate its promised returns.

What happens when thousands of bonds get pooled together? Then the law of large numbers kicks in: Maybe a few mortgages will fail, but it’s unlikely that all of them will fail. The failure of a few are unlikely to sink the whole bond. So they’re pooled together to reduce the idiosyncratic risk of letting any single failure get in the way.

But there was one more problem for investors: When interest rates fall, homeowners tend to re-finance. So they pay back the old mortgage and receive a new mortgage with a new interest rate. Where does this leave the original investor? She gets a big pile of cash when she least wants it, i.e. when interest rates are low and when they can’t get great returns.

How did the creators of mortgage bonds deal with this problem?

By carving the mortgages into different segments. These segments are called tranches (it rhymes with LAUNCHES.) The bottom tranches are filled with the mortgages that are most likely to be pre-paid. Because they’re more risky for investors, they offer higher interest rates; the top tranche is expected to be safest, and they offer the lowest interest rate. Rating agencies like Moody’s and S&P gave the safest tranches their highest ratings: AAA, and put the lowest rating you can get before you’re called a junk bond to the bottom tranches: BBB.

The BBB tranche is filled with subprime mortgages. A mortgage is subprime if the homeowner for whatever reason is unlikely to make consistent mortgage payments. Perhaps her job doesn’t pay well enough, perhaps she has a history of getting into financial trouble, or perhaps she’s very strategic and will refinance when she knows it’s smart.

Let’s review mortgage-backed securities

Following along so far? Just think of an MBS, or mortgage bond, as a pool of thousands of mortgages, ordered from most to least risky for investors. The most risky tranches offer the highest interest rates, and the least risky offer the lowest interest rates.

Collateralized Debt Obligations

The first thing to understand about the CDO is that each one is its own little corporation. (It’s a special corporation that’s known as a Special Purpose Entity.) The next thing to understand is that each CDO is made up of hundreds of mortgage bonds.

To be more precise, a CDO is typically constructed from the bottom, or riskiest, tranches of a hundred different mortgage bonds. Hundreds of sections of different mortgage bonds get bundled together into a new instrument, or re-securitized.

Why would anyone package a hundred of the most risky sections of a mortgage bond together?

Think back to why individual mortgages are pooled together in the first place: When a lot of them are bundled, you’re betting on systematic risk, i.e. the health of the pool, rather than idiosyncratic risk, i.e. the health of any single mortgage. The same principle applies here. Creators of CDOs asserted that when the riskiest tranches of mortgage bonds are pooled together, the average level of risk diminishes.

Just as a mortgage bond can be tranched, the CDO can be tranched as well. A high-grade CDO, also known as a senior or super-senior CDO, would be composed of about 90% of the AAA-rated tranche of mortgage bonds. A low-grade CDO is known as a mezzanine CDO, and is composed mostly of the BBB-rated tranche of mortgage bonds.

CDOs are organized in a waterfall model. All you need to know is that in case the bonds fail, the senior tranches get paid with whatever remains of the financing first, while the mezzanine tranches get paid if there’s anything left. So the mezzanine is more risky, and offers the highest interest rates for investors, while the senior levels are more safe, and offer lower interest rates.

What does a CDO look like?

A CDO is an investment vehicle that’s its own corporation. On average their size was about $800 million, and a CDO had an average of about 7 tranches. Typically three of these tranches would be rated AAA, and at least one would be BBB. The average tranche size is about $100 million.

CDOs can have weird and obscure names which rarely told you anything about their contents or origins. These names include Abacus 2005-3, Class V Funding, and Jupiter High Grade.

Who bought and sold CDOs?

CDOs were issued mostly by big banks, the most active of which were J.P. Morgan, which issued $128 billion of them, and Citigroup, which issued $110 billion. The banks would create a subprime-backed CDO filled with the tranches of BBB-rated bonds, then take it to rating agency which would declare it to be rated AAA or something else that indicated safety. By pooling together the riskiest tranches of mortgage bonds, banks with the help of rating agencies turned them into safe-looking investments.

And why would these banks sell CDOs? CDOs did two big things. First, a lot of people genuinely believed that risk had been engineered with a new formula that came out a decade ago called the Gaussian Copula Function. They thought that a big problem was solved. A lot of people wanted what they thought were fancy returns. Perhaps more importantly, CDOs allowed banks to securitize their loans, which gave them the chance to move their debt off their books and look in better shape than they were.

Investors would look at these subprime-backed CDOs and see a safe investments. And who were some of these investors? They included insurance companies, pension funds, farmers’ unions, university endowments, big banks themselves, and any institution with a lot of money to invest. A key characteristic of CDO investors is that they’re typically institutions who are required by their charters to buy AAA-rated securities. These CDOs were rated AAA, and they offered high returns, and so were appealing investments.

More complicated CDOs

There are more complicated CDOs than the standard CDOs described above.

One of these is the CDO-squared. A CDO-squared is composed of the bottom tranches of hundreds of other CDOs. Pool a few hundred of the bottom tranches of CDOs together, and you get a CDO-squared.

Another is the synthetic CDO. To understand a synthetic CDO, you have to first understand credit default swaps. So keep reading.

Let’s review CDOs

Individual mortgages are risky investments. But when they’re pooled together into a bond, they’re less risky because then what matters is the health of the pool, not any individual mortgage. The bottom tranche of mortgage bonds are risky investments. But if those tranches are pooled together, then they’re once more supposed to be less risky. Banks believed that these bonds weren’t highly correlated, i.e. one failure doesn’t have much to do with another failure. Eager investors believed that, and snapped them up.

Credit Default Swaps

Though there are some important differences, credit default swaps very closely resemble insurance contracts.

Let’s say that you want some insurance for your home. What happens when you buy home insurance? Your insurer sells you an insurance policy: You regularly make small premium payments to the insurer so that if say your house ever floods, the insurer covers the costs of repair.

What exactly is a CDS?

Think of a credit default swap as an insurance contract between the seller of a CDO or bond, which would be an insurance company like AIG, and the buyer of a CDO or bond, such as a hedge fund which believes that CDOs aren’t as safe as everybody says they are. AIG would sell an insurance policy on the risk of a bond default. If you bought that policy, you’d make regular premium payments to AIG so that in case the bond defaults, AIG would give you protection against the entire worth of the bond.

Let’s be more concrete.

Say you believe that a subprime-backed CDO isn’t as safe as it appears. So you purchase a credit default swap on that CDO. You’ll pay something like 150 basis points (or 1.5% of the value of the entire bond) to AIG every year to protect against the $100 million, 10-year bond from defaulting. In other words, you’ll pay $1.5 million a year to the insurer. If the CDO does not default, then you’ll have lost $15 million to premium payments. If it does default, then the insurer will give you the entire value of the CDO: $100 million.

Who bought and sold credit default swaps?

The seller of a CDS is typically a reinsurance company like AIG Financial Products, Zurich Re, and Credit Suisse Financial Products. These companies looked at certain bonds and CDOs, thought that they wouldn’t default, and offered to sell insurance on them. They thought that they could rake in a few million every single year in more or less perfect safety: They thought that the risk had been engineered away. Here’s a way to picture that behavior: Insurance companies were content to pick up nickels in front of a steamroller; they’d make small sums, but they thought that they’d never be flattened.

And the buyers of CDSs? They are the protagonists of Michael Lewis’s book. They were relatively small hedge funds who believed that the risks of CDOs weren’t engineered away. These hedge funds included Frontpoint Partners, Scion Capital, Cornwall Capital, and Paulson & Co.

These investors decided that CDOs weren’t safe, and so bought lots of credit default swaps. When it turned out that they were right, they made billions. But more on that later.

What is a synthetic CDO?

Remember that a CDO is an instrument constructed out of the payment flow of mortgage bonds. In principle, though, a CDO can be constructed out of anything with regular cash flows, like the repayment of college loans, Goodlife membership dues, or credit card receivables.

Or, the premium payments that flow from credit default swaps.

That’s right, banks issued CDOs based on the cash flow from the hedge funds and other banks that bought credit default swaps. The premium payments that flow from credit default swaps replicated the cash flows of subprime-backed CDOs that they were wagered against.

The more credit default swaps outstanding, the more synthetic CDOs can be created. It was hard to issue sufficient numbers of mortgages to create a CDO, but a synthetic CDO does not face that same constraint.

These two instruments fed on each other, growing larger and larger and entangling the banks, hedge funds, and the insurance companies. With each new CDS there was a greater degree of counter-party risk.

Let’s review credit default swaps

Credit default swaps let you bet on bonds and CDOs that you don’t own. A few hedge funds determined that certain bonds and CDSs weren’t as safe as they’re claimed to be; that is, they looked at a AAA-rated CDO and didn’t believe that it could be that safe. So they bought credit default swaps from insurers like AIG. AIG believed that CDOs were so safe that they didn’t even bother posting reserve capital in case that the CDOs failed; they were happy to collect nickels in front of a steamroller. They hedge funds paid a few hundred thousand or a few million dollars every year that the CDO they bet against did not fail; if it did, then they received the entire value of the CDO from the insurer.

CDOs and CDSs in the financial crisis of 2008

By now you may be able to piece everything together. Here’s Lewis’s account of how CDOs and credit default swaps brought down the economy:

Though synthetic CDOs and CDOs-squared were far removed from homeowners, their foundations rested on homeowners making regular mortgage payments.

In 2005 there was a rash of subprime mortgages issued with two-year teaser rates. These rates would be around 4 to 6%, and then jump to 10 to 15% in two years.

When teaser rates were low, a lot of people bought houses. Lewis memorably offers the example of the Mexican strawberry picker who earned $14,000 a year and was lent all the money he needed to buy a house for $724,000. A lot of people were offered loans to buy a house beyond their means, or to buy a second or third house purely as an investment. The people who were at risk of not making their monthly payments put the subprime in subprime mortgages.

So: Teaser rates were low in 2005, and mortgage lenders jacked up these rates in 2007. Suddenly, when interest rates increased, homeowners were no longer able to make mortgage payments.

Dominoes

When individual mortgages started to fail in record numbers, the mortgage bond they make up got in worse health.

When the mortgage bond started to go down, its tranches also started to go down. And then the CDO, which is made up of the riskiest tranches of mortgage bonds, started to go down. Suddenly, the CDOs that were rated A, AA, and AAA started to fail. Assets that were supposed to be risk free were started to fail.

When the CDOs started to collapse, the CDS contracts were triggered. The hedge funds that bet against CDOs found that their bets had paid off. The annual trickle of premiums they paid gave them the claim to the billions in worth of outstanding CDOs.

The banks (including Lehman Brothers, Merrill Lynch, and J.P. Morgan) and the insurance companies (including AIG), all either owned CDOs or sold credit default swaps. They found that their CDOs had failed, and were on the hook for billions of losses because they bet wrong.

Dozens of banks failed, the most high-profile of which are Lehman Brothers and Bear Sterns. AIG declared bankruptcy. Merrill Lynch was sold to Bank of America. People started to panic, and credit markets seized up. Businesses struggled to keep their loans and get new ones.

It was at this time that Congress passed TARP, the Troubled Asset Relief Program, a $700 billion bailout of the big banks and the insurance companies. Citigroup, for example, received $45 billion; AIG received $40 billion; J.P. Morgan and Wells Fargo both received $25 billion; Goldman Sachs received $10 billion; and so on.

Meanwhile, the hedge funds that saw the crisis coming made billions.

How do the CDOs and CDSs fit into the financial crisis?

It’s important to note that the subprime mortgage crisis is only one part of the general financial crisis. The deepest recession since the Great Depression had many causes. The collapse of the mortgages precipitated a run on the shadow banking system in 2007, which some economists argue are the main reason that the financial crisis has hurt as much as it did.

To understand the causes of the recession, economists also point to the high degree of leverage of the banks; general high tail risk; and other factors. For a more complete understanding, read the report prepared by Congress on the causes of the financial crisis.