# Synthetic CDOs Demystified

#### Synthetic Debt

Before we can understand how a synthetic CDO works, we must understand how credit default swaps create synthetic exposure to credit risk. Let’s begin with an example. Assume that D sold protection on $100 worth of ABC bonds through a CDS. Assume that on the day that the CDS becomes effective, D takes$100 of his own capital and invests it in risk-free bonds, e.g., U.S. Treasuries (in reality Treasuries are not risk-free, but if they go, we all go). Assume that the annual interest rate paid on these Treasuries is R. Further, assume that the annualized swap fee is F. It follows that so long as a default does not occur, D’s annual income from the Treasuries and the CDS will be I = $100 x (R + F) until the CDS expires. If there is a default, D will have to payout$100 but will have received some multiple of I over the life of the agreement prior to default.

So, D sets aside $100 and receives the risk free rate plus a spread in exchange. If ABC defaults, D loses$100. If ABC doesn’t default, D keeps $100 plus the income from the Treasuries and the swap fee. Thus, the cash flows from the CDS/Treasuries package look remarkably similar to the cash flows from$100 worth of ABC bonds. As a result, we say that D is synthetically exposed to ABC credit risk.

But what if D doesn’t want this exposure? Well, we know that he could go out to the CDS market and buy protection, thereby hedging his position. But let’s say he’s tired of that old trick and wants to try something new. Well, he could issue synthetic ABC bonds. How? D receives $100 from investors in exchange for promising to: pay them interest annually in the amount of $100 \cdot (R + F - \Delta)$; pay them$100 in principle at the time at which the underlying CDS expires; with both promises conditioned upon the premise that ABC does not trigger an event of default, as that term is defined in the underlying CDS. In short, D has passed the cash flows from the Treasury/CDS package onto investors, in exchange for pocketing a fee ($\Delta$). As noted above, the cash flows from this package are very similar to the cash flows received from ABC bonds. As a result, we call the notes issued by D synthetic bonds.

#### Synthetic CDOs

In reality, if D is a swap dealer, D probably sold protection on more than just ABC bonds. Let’s say that D sold protection on k different entities, $E_1, ... , E_k$, where the notional amount of protection sold on each is $n_1, ..., n_k$ and the total notional amount is $N = \sum_{i=1}^k n_i$. Rather than maintain exposure to all of these swaps, D could pass the exposure onto investors by issuing notes keyed to the performance of the swaps. The transaction that facilitates this is called a synthetic collateralized debt obligation or synthetic CDO for short. There are many transactions that could be categorized fairly as a synthetic CDO, and these transactions can be quite complex. However, we will explore only a very basic example for illustrative purposes.

So, after selling protection to the swap market as described above, D asks investors for a total of $N$ dollars. D sets up an SPV, funds it with the money from the investors, and buys $n_i$ dollars worth of protection on $E_i$ for each $i \leq k$ from the SPV. That is, D hedges all of his positions with the SPV. The SPV takes the money from the investors and invests it. For simplicity’s sake, assume that the SPV invests in the same Treasuries mentioned above. The SPV then issues notes that promise to:  pay investors their share of $N - L$ dollars after all underlying swaps have expired, where L is the total notional amount of protection sold by the SPV on entities that triggered an event of default; and pay investors their share of annual interest, in amount equal to $(R + F - \Delta) \cdot (N - L)$, where $F$ is the sum of all swap fees received by D.

So, if every entity on which the SPV sold protection defaults, the investors get no principle back, but may have earned some interest depending on when the defaults occurred. If none of the entities default, then the investors get all of their principle back plus interest. So each investor has synthetic exposure to a basket of synthetic bonds. That is, if any single synthetic bond defaults, they still receive money. Thus, the process allows investors to achieve exposure to a broad base of credit risk, something that would be very difficult and expensive to do in the bond market.

## 12 thoughts on “Synthetic CDOs Demystified”

1. Kyle

Awesome as always, but you lost me at: “That is, D hedges all of his positions with the SPV. The SPV takes the money from the investors and invests it.” I thought D just took the money from the investors and put it into the SPV? I understand the general concept, but I got confused on this particular piece of the puzzle.

2. Hi Kyle,

Glad you like the article. Here it goes: D takes the money from the investors, puts it in the SPV. D enters into a series of swaps with the SPV offsetting the positions D took in the market. The SPV, not D, takes the investor’s money and invests it in Treasuries. Just leaving the money in the SPV in cash wouldn’t generate any returns, so the risk-free portion of the notes would be missing. So, the SPV needs to make some investments to cover the risk-free portion of the return on the notes. The rest comes from the swap fees.

3. Kyle

Gotcha. One other question though, I thought that D was supposed to have guaranteed the returns to investors, and that that was the problem that FRE, FNM, C, et. all ran into with their MBS issuances.

4. Hi Kyle,

It would be very unusual for a swap dealer to guarantee returns on bonds. As for Fannie and Freddie, many investors took the position that the Federal Government would guarantee their securities. In retrospect, it appears they were correct.

5. Kyle

Certainly so. Either way, so the swap dealers do not place guarantees on the spv returns. Can you give me an example of a company that would be a swap dealer in this context? So the only gain to the SPV investor is the diversification of exposure to several bonds for a much lower cost (like an etf?), while the swap dealer who controls the spv in essence just passes-through the returns, and collects a swap fee in exchange?

6. acc

Hi Charles,

Thank you for a clear exposition of a basic synthetic CDO. It has been my understanding of the product that it was the super senior CDS (i.e. reinsurance policy) covering 75% or more of the total sum insured that made synthetic deals economically viable. Was it common at some point for the industry to issue these unleveraged synthetic CDOs (i.e. without an unfunded super senior tranche)?

A few other questions that I have are: Do these special purpose entities post collateral against the decline in their CDS values? Who decides how much collateral they have to post — the sponsoring bank or the purchaser of the CDS issued by the SPV? Have any CDOs blown up because of a failure to post collateral?

7. Hi ACC,

Glad you like the article. Your questions are very good, but they ask about market practices. As a result, in order to give you a reliable answer I will have to engage in a lot of research and asking around that I just don’t have time for. Sorry about that.

That said, the example I gave has no tranches. I can say with confidence that tranched synthetic CDOs were common. Maybe I’ll write an article on how tranches work. We’ll see.

As for collateral, collateral is determined by the terms of the agreement and each swap entered into by the SPV will have its own terms (although they could be and probably would be booked under one agreement). So, again, we are back to market practice, which I just don’t have time to figure out.

8. Michael Podokshik

What D wants to do is to create as many synthetic CDO’s as possible , so D can collect the fees, well “risk-free”.
In order to do each subsequent CDO D needs liqidity. That is where I come in and short the deal(buy the CDS). we do this 3 or 4 thousand times until D and I are both satisfied. Let’s say this particular CDO contains only my mortgage. D could not sell most junior tranche(aka “nuclear waste” or my basement), so D put it in
RAV or SPV on D’s balance (off-balance sheet of course). At this point all I have to do is default on my own mortgage.
This, of course, oversimplified verison of what happens when there are whole bunch of these D’s around who want to make a lot risk-free money.
Tnanks.