Sunday, 30 May 2010

The Goldman Case – 2: CDOs

The Goldman case revolves around the CDOs. So, we must begin with these vehicles.

A CDO, or collateralized debt obligation, is a security, only more complex than traditional securities such as stocks and bonds. The complexity is not conceptual, as in, say, quantum mechanics, but procedural and functional. It can be measured by the words that are needed, as per requirement of the law, to describe the structure, pay off pattern and risks of the CDOs in the offering memoranda. These documents can run into hundreds of pages of legalese and still not cover all the material facts. The SEC’s charge against Goldman is precisely this “failure to disclose”, which constitutes fraud under the securities law.

A procedural/functional complexity can best be shown via an an example.

Take a bank which has lent the following amounts to 5 home buyers. The monthly payment for each loan is shown in brackets.

1: $200,000 [$1,150]
2: $240,000 [$1,250]
3: $250,000 [$1,300]
4: $300,000 [$1,700]
5: $260,000 [$1,600]

The total value of the mortgages is $1,250,000; their combined monthly payment, $7,000.

Mortgages are long-term loans, ranging from 10 to 30 years. So, the bank has locked $1,250,000 of its assets for at least a decade. Of course, in that period, it will receive interest and principal which is what banking is all about. But capital is locked and the bank’s ability to lend is reduced. If we assume the bank’s total lending assets to be $100 million and a typical mortgage around $250,000, then the bank can only make 95 loans – and no more. Afterwards, unless it could grow, it would have to seize lending.

We, as a group of investors, approach the bank and offer to buy the mortgages at their full value. The bank welcomes the idea because it would unlock its capital. With the $1,250,000 it gets from us, it could make 5 new loans and generate additional closing fees. In this way, the bank is out of the picture. We are now the owner of a pool of debt totaling $1,250,000 that brings in $7,000 a month.

Money is fungible, which is why we could speak of “one” loan of $1,250,000. We could also divide. For example, we could divide the pool into 10 equal parts of $125,000, with each bringing in $700 in monthly payments. In fact, that would be the math we had to follow if our investor group had 10 partners.

With the total mortgages ($1,250,000) and monthly payments ($7,000) remaining the same, the number of “pieces” the original pool is divided into determines the principal amount and the monthly payment of each piece. If the pool is divided into 100 pieces, each will be worth $12,500 with $70 expected monthly payment.

Such “slicing and dicing” is one of the technical conditions for securitization: selling private, illiquid assets and liabilities to investors. But securitization, precisely because it involves sales, requires the knowledge of market conditions, so that the product would appeal to potential buyers. The list of items to be considered in that regard is a legion. But two factors stand out above the rest.

One is the number of “slices”. Obviously, the more pieces a given pool is divided into, the smaller the principal amount and the monthly payment of each slice. If our pool is divided into 1000 pieces, each will be worth $1,250 with a monthly payment of $7. But, needless to say, if we divide the pool into 1000 pieces, we must sell 1000 pieces. For that, we would need a sales network, a critical factor to consider as few financial institutions have such networks in place. A large volume of products with low principal and monthly payments, further, is a retail product, while a product with a relatively large principal of $125,000 and only in 10 lots, is more geared towards the institutions or “sophisticated investors”. This technical phrase is pivotal to the Goldman case, so we will return to it. I only note here that the retail products, i.e., products that are offered to public, are governed by stricter disclosure requirements.

The other factor to be considered in securitization is the “risk appetite” of the CDO buyers: the yield they seek vs. the risk they are willing to accept. The fact remains that under the best of economic conditions, some borrowers would default. The reasons for default – a loss of job, disability or even death – do not concern us. But if that were to happen, if, for example, borrower 5 were to default, the pool would receive $1,600 less in monthly payments. That would reduce the pool’s annual return from 6.72% (7000 x 12/125,000) to 5.20% (5,400 x 12/125,000). That is a 23% decline, a tremendous loss in the fixed income world. Such potential volatility would keep away many investors. To appeal to them, we must reduce the uncertainty.

Finance professors speak of “risk averse” and “risk appetite” as if they were psychological and genetic attributes of investors. In reality, they are the investing parameters of mutual and pension funds which forbid them from buying any security not rated AAA. As these funds are the largest investors in the CDOs – because they sit on large piles of cash – their concerns must be taken into account.

The risk of our pool as a whole is given and cannot change; it is the risk of default of 1 or more of the 5 original borrowers. But the introduction of some “class system” solves our problem.

Let us “divide” the pool into three “tranches”. We'll call them the equity or first loss (FL) tranche, mezzanine (MZ) tranche and super senior (SS) tranche, and declare:
In the event of a default, the FL tranche, as its name implies, will have to absorb the loss. If more defaults follow, the FL tranche will continue absorbing losses until no more FL tranche is left, after which the MZ tranche will absorb the losses. The SS tranche, as the name implies (it refers to the order of being paid) will be the last piece to be affected by a default. The arrangement follows a “water fall” pattern where the $7,000 monthly income first satisfies the payment for SS, then “flows” to MZ and then, finally to FL.
The last part is the allocation of principal and yield to each tranche. Keeping in mind that the SS tranche is the most popular and that yield has to increase as the riskiness of the tranche increases, we allocate the original $1,250,000 principal and the $7,000 monthly payment in the following way among the tranches.

SS: $700,000 [$3,600]
MZ: $500,000 [$3,000]
FL: $50,000 [$400]

Based on this allocation, the yield for each tranche is as follows:

SS: 3,600 x 12 / 700,000 = 6.17%

MZ: 2,800 x 12 /500,000 = 7.2%

FL: $400 x 12/ 50,000 = 9.6%

The CDO structure is now complete. All we need at this point is to convince a rating agency – S&P’s or Moody’s – that the SS tranche that is “protected” against default by two loss absorbing layers FL and MZ, is as safe as the safest corporate bond or even the U.S. treasuries and therefore, should command AAA rating. With that, our lawyers put all these details into an offering memorandum and we begin contacting investors.

A while back, in discussing the “collapse of the whole intellectual edifice”, I mentioned Kurosowa’s Rashomon in which the director explores the relation between the narrative and Truth: what do we need to know about something so we could say we know it?

What do we now know about the CDOs?

First and foremost, it must be clear why CDOs are called “vehicle” or “structural products”. They are vehicles for transforming: i) the risk of loans from the bank to investors in capital markets; and ii) the risk profile of a given pool of securities from moderately risky to supposedly riskless and very risky – the latter would be SS and FL tranches. As for structured product, it is the very description of how we created the CDO; a CDO is nothing if not a structured product, a fact that is reflected in the limitless flexibility we have in its design.

I am not exaggerating about the limitless flexibility. Let us begin with the number of tranches. I suggested three. You could make it four. Or five. Or six. Or even seven, if you prefer.

Then there is the number of original loans in the pool. I had 5 because that was sufficient for illustration, but CDOs typically have over 100 securities in the pool. That large number is necessary to make the structure robust so that 3 or 4 defaults will not wipe out the entire pool. The ABACUS 2007-AC1 in the center of the Goldman case had 127 securities.

Then there is the matter of allocating the total pool between tranches. I had 56% of the total allocated to the SS tranche (700,000/1,250,000). You could make it 60% or 70%. Likewise with the MZ tranche. Finally, I allocated 4% to the FL tranche, which is just about standard. This tranche, also known as “toxic waste”, is the riskiest tranche and rarely finds any takers. So the originator of the CDO – Goldman, for example – is usually stuck with it. That must have been the reason why Goldman claimed that it had lost $75 million. The loss had to come from the toxic waste piece that the firm could not unload.

Now comes the most complicated part: the pricing and price behavior of the securities in each tranche. In our example, we have allocated $500,000 to the MZ tranche. Assume that we divide it into 1000 securities, each worth $500 and with $3 a month in payments. What would be the price of this security?

On one hand, the security is a simple bond. We price it using standard bond mathematics. We know if the interest rates increase, the bond price would decrease, and vice versa.

But this security is not a stand-alone bond. It is a mezzanine note from a CDO in which cash flows come from a pool of mortgages. If the default in the pool rises, it will first hit the toxic waste tranche, it is true, but by virtue of “eroding” this tranche, it will begin to threaten the MZ tranche. The MZ tranche, in other words, will be riskier. And since the yield of the bond is fixed at 7.2%, its price would drop, even if interest rates remain unchanged.

The same is true for the SS tranche whose price can show no sensitivity to the defaults in the FL tranche – until it does. This is the so-called “cliff effect” that everyone in the CDO market was aware of. Financial Times, March 21, ‘06, p. 25:
[An independent consultant] describes how a CDO tranche can absorb a number of credit events, such as defaults and downgrades, and retain its level of subordination – or the size of the cushion that protects it from losses – until it reaches a point at which one further piece of bad news can push it over the edge. “Several things can go wrong in a deal and it will still be triple-A,” she say. “But then you get one more event and boom!”
You see what I mean by procedural complexity. There is nothing about the CDOs that a 6th grader cannot understand or follow. But no one can account for all the parameters that influence the price of a CDO.
  • Are the original mortgages from California, New York, Florida or Chicago? Mortgages from these geographies have different default patterns.
  • Are the houses occupied by younger or older occupants? That would impact the default rates.
  • Who wrote the mortgages and when? (If Countrywide in 2006, you’d better run for the hills).
  • How is the national and regional economy doing? Can it maintain a steady employment rate?
You can write a PhD dissertation on the subject of CDO pricing. You can devote your life to studying the correlation of defaults across the CDO tranches. You would then become a quant, a rocket scientist or a financial engineer, but you would still know nothing about the CDOs either at the individual level so that you could make money from them or at the macro level so could understand what makes these vehicles “tick”.

Here is Exhibit A, a quant with impeccable academic credentials and work experience, writing to make us “understand” the risk of synthetic CDOs. I am not picking on him. I mention him precisely because his paper is well written and a cut above others. I urge you to read it. Yet, here is what the author wrote on page 2:
These “bank balance sheet” deals were motivated by either a desire to hedge credit risk, a desire to reduce regulatory capital, or both. Following these early deals, the same synthetic CDO technology has been used to create CDO tranches with risk-return profiles that investors find attractive. These later deals, driven by the needs of credit investors rather than banks, are termed “arbitrage” deals.
He goes on to opine:
The terminology has taken hold despite the absence of a true “arbitrage,” which can be loosely defined as a risk-free investment with a positive excess return.
What the author is looking at is the genesis of speculative capital: the transformation of hedging to arbitrage; I spend the entirety of Vol. 1 explaining it. But he does not see it because his professors at Stanford and MIT failed to teach him that words have meanings. So, he does not pause on the word arbitrage to ask himself, You, horse’s behind, what does this word exactly mean and why do you have to define one of the key terms of modern finance “loosely”?

Where is the arbitrage in a CDO? You would not see it in a million years by looking at a CDO structure.

Let us return to our example where “we”, a group of investors, approached the bank and offered to buy its mortgages. Why would we do this? What is in it for us?

Taking into account the expenses of creating a CDO – in millions of dollars that we have to pay to agents like Goldman Sachs – we could find easier and better uses for our $1,250,000. So what drives the market? The answer is arbitrage. From Vol. 3:
The point is that arbitrageur, by definition, has no money. That is why he could not put it in the mattress. Yet, to exploit the arbitrage opportunity, he has to create a portfolio that requires an outlay of cash. For that, the moneyless arbitrageur has to go to a lender. He must borrow money. One blushes at emphasizing this point. But the emphasis must be made...

In the example, you assumed that “we”, the group of investors, had $1,250,000. But we did not. Even if we did, the exercise would have been pointless because of its costs.

If the transaction was consummated, we must have borrowed the money. What is more, we’d borrow the money through a Special Investment Vehicle, with a large bank such as Citi as the guarantor, which allowed us to borrow at the commercial paper market at about 2%.

Now, the mystery is solved: borrowing at 2% and lending, i.e., buying the mortgages that yield 6, or 7 or 8%. That is arbitrage for you and God Bless America. See Part 8 of the Anatomy of a Crisis for more details.

But we are not done. The CDO in the center of the Goldman case is a synthetic CDO, where there are no real mortgages. A synthetic CDO “replicates” the behavior of real mortgages. For that, credit default swaps must be brought in.