Credit Default Swaps for Dummies: Part IV - Synthetic CDOs

In Part I of Credit Default Swaps for Dummies we explained single name CDS.  

In Part II of Credit Default Swaps for Dummies we explained CDS indices. 

In Part III of Credit Default Swaps for Dummies we explained asset securitization. 

In Part IV of Credit Default Swaps for Dummies we will explain what a synthetic CDO is.

Creating a synthetic corporate bond from a CDS

First recall what a CDS is (see Part I if you forgot how these work).  Say you are a bank and you have made a five year loan of 1MM USD to company X.  You are ok with lending out 1MM for five years and you are willing to assume the interest rate risk of this loan.  But you don't like the credit risk of company X - you think there is a possibility that they may default on their debt.  What can you do?  One solution is to try to sell off the the debt to someone else - but that may be cost prohibitive.  A second solution might be to purchase a CDS for 1MM of five year protection on company X.  Each year you would pay a premium (aka  interest rate or coupon) to the CDS seller.  If company X has a "credit event" within the next five years then you would receive an insurance payment that would make up the difference between the face value of the debt (1MM USD) and the value of the debt after the credit event.

Now let us turn it around and assume that you are a portfolio manager and you have 1MM USD to invest for five years.  You could buy US Treasury debt and receive an interest rate of 0.625% - but that is pretty crummy.  In order to receive a higher interest rate you are going to need to be willing to assume some credit risk.  You like company X's business plan and you think the chance of them defaulting on their debt is pretty miniscule.  You look at the bond market and see that company X's corporate bonds are paying an interest rate of 3.625%.  If you were to purchase this bond you would  effectively receive 0.625% (the Treasury rate) to compensate you for the time value of money and for the interest rate risk, and you would be receive 3% to compensate you for the risk of a possible default by company X.  

As a portfolio manager could purchase 1MM USD face of five year bonds from company X ...or..you could synthetically recreate this same cash flows using US Treasuries and CDSs.  To do the latter you would purchase 1MM USD face of five year US Treasuries- that will get you an interest rate of 0.625% for the next five years to compensate you for time value of money and for the interest rate risk.  Then you would sell a 1MM USD face of five year protection on company X (as a CDS) to the bank.  If company X were to default on its debt then you would have to pay the bank the difference between the 1MM USD of face and the price of the debt post default.   So in the case of a default you would absorb the default loss just as if you directly held the bonds of company X.  

How much in premium should you demand to be paid in order to write this CDS protection?  By the principle of no-arbitrage one would assume that the portfolio of Treasury+CDS should pay the same interest rate as company X's bonds (3.625%).  If the Treasury+CDS portfolio were to pay less than 3.625% then no one would want to sell the CDS protection to the bank since they could instead just buy the corporate bonds, bear the same default risk and get a higher interest rate.  If the Treasury+CDS portfolio paid more than 3.625% then other agents who currently owned company X bonds should be willing to sell their bonds and instead synthetically recreate the bonds by purchasing Treasuries and selling CDS protection to the bank.  Since company X's corporate bonds pay 3.625% and Treasuries pay 0.625% then you should require 3% coupon to write the CDS protection.

Cash CDOs

Now let us extend the principle to a pool of loans. First we want to quickly review cash securitization (see Part III if you forgot how these work).  Say you are bank and you hold five year bonds for 1MM USD face for each of 1000 companies.  You are ok with loaning out 1BB USD and you are willing to assume the interest rate risk of making these loans but you don't like bearing the credit risk of these bonds, now what are your alternatives?  One solution would be to sell these bonds off individually  - but that may be prohibitive as you would have to find takers for each of the 1000 bonds.

A second solution would be to securitize the bonds. You the bank could create an SPV.  The SPV would issue its own debt to the public and use the proceeds to purchase the bonds from you the bank.  The pool of bonds would pay interest and principal to the SPV and the SPV would distribute these cash flows to the investors in the SPV.  There are a number of different ways that the SPV could structure their payouts.  

The first structure that we are interested in is a direct pass-through.  In this case there would be a single class of SPV debt.  The SPV would pass interest and principal cash flows through to investors in proportion to the percent of the SPV's debt that the investor holds.  In the case of defaults from the underlying pool an investor would absorb a share of defaults in proportion to the percent of the SPV's debt that he or she holds.

The second structure that we want to focus on is the Collateralized Debt Obligation (CDO).  In this case the SPV issues multiple classes of debt ordered in a hierarchy (super-senior, senior, mezzanine, junior, equity, etc..).  Each class of debt gets allocated a share of the principal. The most junior class of debt will absorb all defaults until the principal of that class is depleted.  After the principal of the most junior class is exhausted then the next most junior class will absorb all defaults until the principal of that class is depleted and so on.   The lower is a class in the hierarchy the higher the interest rate that it will receive but the more default risk it will be exposed to.  The most senior tranches will be exposed to very little default risk but in return they receive the lowest interest rate.  We refer to this as a "cash" CDO because it involves a securitization of the actual cash bonds.

Synthetic CDOs

An alternative way for the bank to insure the pool of bonds is with a synthetic CDO.  Recall that earlier in this post we demonstrated how we could synthetically recreate a corporate bond using US Treasuries plus a CDS.  Could we synthetically recreate a "cash" CDO using US Treasuries plus some sort of CDS like structure?  The answer is yes.

A synthetic CDO would be structured as follows.  The bank forms an SPV.  The SPV sells CDS insurance to the bank on each of its 1000 names.  In return the bank pays an insurance premium (aka coupon or interest rate) to the SPV.   The SPV distributes this premium to one or more investors.  If one of the bonds goes into default the investors are responsible to pay the SPV who in turn pays the bank the difference between the face value of the debt and the after default value of the debt.  

Just as we saw with simple cash securitizations (see Part III) there are a number of ways that the premium payments and insurance obligations can be divided amongst the investors.  The most simple structure for a synthetic CDO is as a synthetic pass-through.  In this case each each investor would be assigned a share of the total face value of the pool.  He would receive a share of the premium payments proportional to his share of the pool.  In the case of default he would be responsible to cover a share of the defaulted bonds proportional to his share of the pool.  This is structure is fairly similar to an index CDS (see Part II) if the bank were to choose the makeup of the index.

It should be obvious that we can recreate the "cash" pass-through security by combining US Treasuries with a synthetic pass-through.  Assume that a five year US Treasury yields 0.625%.  And assume that a five year cash pass-through security with an underlying pool of 1MM USD each of 1000 names pays 3.625%.  Of this 3.625% the first 0.625% compensates us for the time value of money and interest rate risk.  The remaining 3% compensates us for the default risk that we take on this pool.  Now assume that the bank were to issue a five year synthetic pass-through with an underlying pool of 1MM each of the same 1000 names.  If we were to purchase 1BB USD face of five year US Treasuries and then sell protection via this synthetic pass-through then we would be exposed to the same time value of money, interest rate risk, and default risk as if we had purchased the original cash pass-through.  The cash pass-through pays 3.65% and the Treasuries yield 0.625% so the synthetic pass-through must yield 3% else there would exist unexploited arbitrage opportunities between the cash and synthetic markets.

Alternately we could structure the SPV as a credit tranched synthetic CDO.  In this case the the SPV would create different classes (super-senior, senior, mezzanine, junior, equity, etc).  A class would be defined by its responsibility for paying out insurance in the case of defaults in the underlying pool and by the premium it receives as compensation.  Typically the responsibility for paying insurance is defined in terms of attachment and detachment points which specify what is the minimum level of defaults at which that class will start paying and what is the maximum level of defaults that that class will be responsible for.  

Since this is a bit complicated I will fully spell out an example.  Assume our bank has 1MM of debt from each of 1000 names.  1BB in total for the pool.  They create a synthetic CDO with the following structure.  An SPV is created which writes protection on the full 1BB in debt.  The SPV creates four tranches; equity, junior, mezzanine, and senior.  They are defined as follows:

• equity tranche - insures the first 50MM in defaults from the pool.
• junior tranche - insures the next 100MM in defaults  from the pool.
• mezzanine tranche - insures the next 200MM of defaults from the pool.
• senior tranche - insures the last 650MM of defaults from the pool.

The below diagram illustrates each tranches responsibility for paying out insurance in the case of defaults in the pool.

 

The bank pays the SPV a premium of 3% to insure 1BB of debt or (3% * 1BB = ) 30MM per year.  This premiums gets divided between the four tranches.  We will assume that the tranches receive premium as follows.

• equity tranche - receives 20MM or (20MM / 50MM = ) 40% return per year
  
• junior tranche - receives 7MM or (7MM / 100MM = ) 7% return per year
• mezzanine tranche - receives 2MM or (2MM / 200MM = ) 1% return per year
• senior tranche - receives 1MM or (1MM / 650MM = ) 0.15% return per year

Below is a diagram of the full transaction

In this example the Equity Tranche receives an annual return of 40% while the Senior Tranche receives an annual return of well less than 1% - that doesn't seem fair does it?  Well it depends on what you think about the probability that each tranche will end up paying out insurance to cover defaults in the pool.  As we will see in  Part V the fair price for each tranche depends sensitively on the assumptions  that you make about correlations between defaults.

We previously showed that you can mimic a long position in a corporate bond by buying a Treasury and selling CDS insurance on the same name.  And we asserted that you can mimic a long position in a cash pass-through by buying a Treasury and selling insurance on the same pool via a synthetic pass-through.  It should not come as a surprise that we can mimic a cash CDO by buying a Treasury and selling insurance on the same pool via a properly structured synthetic CDO.  In addition we can mimic the return on each tranche of a cash CDO by correctly structuring a synthetic CDO on the same pool.

Finally - although the examples that I have given above assumed that we used the synthetic CDO to fully insure the pool, in many cases a synthetic CDO will be written to only cover a small percentage of defaults (say the first 10 - 20%) in the pool.  In this case each tranche will only be responsible for a few percentage points worth of defaults in the pool.  The idea there is that in a large diversified pool it is very likely that there will be some defaults but it is very unlikely that a large percent of the pool will default (although that depends on the quality of the debt in the pool).