Charlie Alfred’s Weblog

Conceptual Distance and the 2008 Market Meltdown

Unless you, Gilligan, and the Skipper have been stranded on a remote desert island for the past 40 years (including reruns), you certainly have heard about the sub-prime mortgage crisis.  In fact, after looking at the damage it has wreaked on your investment portfolio, you may be tired of talking about it.

Please bear with me, because I’m going to bring it up again.  I am not intending to wallow in the effects, but rather to consider a few of the causes.  Greed, lack of accountability and lack of oversight are often cited as causes (as are a few others which will remain unmentioned).  However, there are a few more subtle causes that lay hidden.


George Santayana said, “Those who cannot remember the past are condemned to repeat it.” (  As we talk about the sub-prime crisis and its causes, the key question is: what does “repeat” mean in this context?  Do we refer to the next sub-prime crisis?  Or, the next big economic recession? 

Or, more simply, what about the next case where a major blunder results from what I refer to as the X^Y problem, the symbol I use when talking about the side effects of conceptual distance (  A great way to think about conceptual distance is to consider the question posed by Peter Senge, in his book, The Fifth Discipline:

“How can a room full of 120 IQ people have a collective IQ of 20?”

But what does the sub-prime mortgage crisis have to do with conceptual distance?  And what does “the X^Y problem” mean?  Read on to see these answers and more (or if you are pressed for time, just use “Find”;  I am a pragmatist, after all).

The Gaussian Copula

Felix Salmon wrote a fabulous article titled “A Formula for Disaster” which was published in the March 2009 issue of Wired magazine.  An online copy of the article appears here:

In this article, Salmon explores the underpinnings of the sub-prime mortgage crisis in a very understandable way.  For the purposes of this article, I will summarize several key points from this article here.

The story starts with mortgage portfolios – a collection of home mortgages that are packaged for sale to investors.  Why are mortgages packaged for sale?  There are several reasons, but the most basic are:

o      If a bank writes a mortgage and keeps it on their books, they retain the interest earnings, but must fund the mortgage (i.e. with deposits or some other form of borrowing).  If a bank writes a mortgage and sells it, they earn a fee, but sell the rights to the future mortgage interest income.

o      Assuming sufficient sources of investment capital in the financial markets, financial institutions that sell large percentages of their mortages can write more mortages than those who keep most of them.

o      If home construction is one of the cornerstones of our economy, then the availability of affordable mortgages is a major contributor to keeping the economy healty.

o      In short, packaging pools of mortgages for sale enables can efficiently match borrowers with investors.

The story continues with risk.

o      For mortgages, the two primary risks are interest rate and credit default.

o      Interest rate risk deals with the cost of money, as it fluctuates over the term of the mortgage (typically 15 or 30 years).   Interest rates for long-term government debt securities (e.g. 30 year Treasury Bonds) form the basis for interest rate expectations.

o      Credit default risk deals with the probability of a mortgage borrower defaulting on their mortgage.  The default risk for the mortgage holder is determined largely by resale market strength and down payment amounts.

The story includes derivatives as an important tool for risk management.

o      Derivatives are deals that are based on some underlying security.  Two popular derivative types are interest rate swaps and credit default swaps.

o      Interest rate swaps (IRS) often trade the interest from a fixed-price security against some well-known rate that fluctuates with money market conditions (e.g. Libor or Fed Funds rate).

o      A holder of 30-year mortgages can use interest rate swaps to “buy insurance” against a rise in market rates by selling a stream of fixed-rate income and buying a stream of of floating-rate income.

o      A credit default swap (CDS) is simply insurance against a default.  The insurance seller agrees to reimburse losses incurred by the buyer in the event of a default by the borrower.  This form of insurance is analagous to a typical home insurance policy, only the risk covered is credit default instead of fire, water, or wind damage.

o      Some forms of CDS are issued against a pool of debt securities, and may cover the first or last ‘n’ defaults from the pool.  The first ‘n’ provision limits the exposure of the insurer.  The last ‘n’ is a form of deductible, where the CDS buyer is willing to accept some, but not all of the risk.

o      Unlike tangible securities, swaps and derivatives are artificial instruments. The total value of swap and derivative contracts can exceed the value of the underlying securities by many times.  In other words, imagine 100 people in the outside world holding insurance policies on your home or life.

And extends to tranches and synthetic portfolios

o      Mortgage pools contain hundreds of individual mortgages.  This packaging makes it easier for large investors to buy, and (in theory) spreads out the credit default risk.

o      It is also possible to sub-divide a large mortgage pool according to risk level.  This is sort of like subdividing a side of beef into different cuts: filet mignon, rib eye, sirloin, brisket, etc: different qualities for different tastes.

o      Tranches are ways of pooling the credit default losses in a large mortgage portfolio.  For example, the riskiest tranche might have to absorb the first 10% of losses.  The next riskiest tranche might absorb the next 10%, while the safest tranche absorbes the last 10%

o      Credit Default Obligations (CDO’s) apply the tranche principle to pools of Credit Default Swaps.  This is a form of “insurance on insurance”.  A firm that writes CDS contracts to protect investors from credit default may want to mitigate their risk by selling a CDO to other insurers.  BTW, in the property and casualty insurance industry, this is known as “re-insurance.”

The story incorporates default correlation

o      A factor called default correlation determines just how spread out the risk in a portfolio is.  Default correlation asks: if an event happens to A at time T, how likely is it that an event will also happen to B?

o      For property insurance, if house A burns down, what is the likelihood that house B also burns down?  As we know, there’s no simple answer.  If house A is in the suburbs with a proficient fire department, the probability of B burning down is low.  But if A is located in the California hills, and the fire occurs during the dry season, the probability is much higher?

o      For a pool of mortgage securities, default correllation is at the heart of pricing deals (and insurance).  If borrower A defaults on their mortgage, what is the likelihood that borrower B (a member of the same portfolio) will, too?

o      This is the 64,000 question (in some denomination other than dollars), and is where the interesting story begins.

And approaches its climax with the Gaussian Copula

o      Copula is a phrase used in mathematics to represent the interaction effects between two or more variables.  Gaussian introduces probabilities (in the form of a bell curve) to model uncertainty.

o      The Gaussian Copula is a formula published by David X. Li in 2000.  It uses historical market prices of credit default swaps as a proxy for actual default data, and uses it to calculate the probability of default for two or more mortgages.

o      Because of its simplicity, and apparent usefulness, use of Xi’s Gaussian Copula exploded throughout the financial industry.

Cut to the AIG (formerly known as Cut to the Chase)

Between 2001 and 2006, many financial institutions used the Gaussian Copula to make billions on their investments.  In 2008, the financial picture in the U.S. began to unravel badly.  In October 2008, catastrophic losses on financial derivatives forced:

o      Lehman Brothers into bankruptcy,

o      Merrill Lynch to be absorbed by Bank of America, and

o      AIG to require billions in mouth to mouth rescucitation by the U.G. Government to avoid bankruptcy.

These shockwaves caused the global financial markets to go into a tailspin.  Between October 2008 and March 2009, the DJIA and Nasdaq indices fell by more than 50%.  The Gaussian Copula had triggered cardiac arrest at the global level, and the bailouts were the only defibrillator available.

What Happened, and Who was on Watch?

Like most catastrophies, this is one that also required a lot of complex situations and triggering events:

  1. Xi’s Gaussian Copula is a statistical simplification that relies on historical correlations (from prices in the CDS market).
  2. The real world of predicting mortgage defaults and default correlations is massively complicated, dealing with dozens of complex, hard to measure, variables.
  3. Correlation is not the same as causation, as the following comic from so deftly points out.  Two things can be correlated, with neither causing the other.


    4.  Many of the complex variables deal with human behavior.  Unlike forces of nature (like gravity or electricity), free will is a huge wildcard.

    5.  One major accellerant of the problem was ARM’s.  The ARM’s seemed like a great way to offer low rates to allow first time buyers to afford a mortgage.  While rates stayed low.  But as rates increased, the ability of these buyers to afford their mortgage payments was compromised.

    6.  A second major accellerant was low down payment mortgages (especially interest only).  When mortgage payments became unaffordable, many homeowners were willing and able to just walk away, leaving the mortgage holders and credit default insurers holding the bag.

    7.  Over-simiplification is seductively appealing, especially for those who lack time or have difficulty with the systems thinking needed to comprehend the underlying complexities.  As Salmon writes:

The quants, who should have been more aware of the copula’s weaknesses, weren’t the ones making the big asset allocation decisions.  Their managers, who made the actual calls, lacked the math skills to understand what the models were doing or how they worked.

    8.  Swaps and derivatives are another hugh amplifier for this problem, and the numbers are simply staggering.  As Salmon writes,

“At the end of 2001, there was $920 billion in Credit Default Swaps outstanding.  By the end of 2007, that number had skyrocketed to more than $62 trillion. The CDO market, which stood at $275 billion in 2000, grew to $4.7 trillion by 2006.”

For those without a calculator handy, in 6 years, CDS grew by 67x (105% annual compounded) while CDO’s grew by 17x (60% annually compounded).

    9.  Where are the loss reserves?  All other forms of insurance carriers are required to keep loss reserves against the aggregate value of the policies they write.  A huge part of the problem with AIG, Lehman, and Merrill is that the wrote uncovered insurance policies against credit default.

The items in the above list represent a very incomplete analysis of what happened.  A more thorough analysis will require a small army of people who comb through the wreckage, like members of the National Transportation Safety Board do at the scene of an airline crash.  Given the magnitude of this crisis, surely this much is called for.

A Simple Experiment in Conceptual Distance

Now it is time to reveal the dual purpose of this article:

  1. The sections above described some of the causes and factors behind the all-too-familiar sub-prime default crisis.  Clearly, two big contributors to this crisis are directly related to conceptual distance:

o      Many of those responsible for important decisions thought they knew, but didn’t.  Or, they ignored their training, responsibilities, and better judgement (also known as “pilot error.”).

o      Many of those who knew, couldn’t explain clearly what they knew, or were inhibited from doing so.

    2.  This article is also a detailed experiment in conceptual distance.  I wish I could say that this was intentional, but in truth, it was a last minute accident.

Read Felix Salmon’s article (  When you are finished, mentally compare what understanding you took away from his article, and compare it with the understanding you got from my explanation above.

If you got a deeper understanding from his article, then my explanation had an “understanding leak.”  Much of what I said was a reflection of his points.

In the less likely event that you got more from mine, then there was an information enhancement (the inverse of conceptual distance).  I added a little information from my own experience to his message.

It is also possible that there was some synergy.  Perhaps something I wrote made it easier for you to understand something he said.

The fact that any of these three possible outcomes (among others) could happen directly results from the fact that I am writing to an opaque audience.  If I were communicating one on one, the lost of information should be less, since I can tune my explanation to your starting level of comprehension.

You see, “The X^Y problem” is a variation of the children’s game “I’ve Got a Secret”.  Since that name is already taken, I use “The X^Y problem” instead.  In essense:

o      X represents the amount of “leakage” of understanding that happens between two individuals, when information is conveyed.

o      Y is the number of times the information is retold.

When 0 <= X < 1, we have a loss of comprehension between what the teller knows and what the reciver gets.  Y magnifies the information loss.  For example:

o      Over 4 links, a 15% loss per link represents an total loss of about 48% (0.85 ^ 4 = 0.522)

o      Over 6 links, a 10% loss per link represents a total loss of about 47% (0.9 ^ 6 = 0.531).


Today’s failure points are driven by the search for simple answers to complex problems.  Why?  Because complex problems are too difficult for individual humans to wrestle with.  They involve too many subject matters, each of which requires comprehension that is too deep, too specialized, and too difficult to acquire.

And even if someone is able to gain a deep understanding about a piece of a complex problem.  Good luck trying to find somebody to explain it to who is outside of your immediate circle of colleagues.  They are unlikely to grasp what you are saying, unless you can “dumb it down” enough so that it matches something in their field of comprehension.

And don’t feel safe.  I am not just talking about how they have trouble grasping what you see clearly.  I am also talking about how you are unable to understand what they are talking about, too.  Yes, and I am also talking about how frequently I don’t get it either.

So what?  So what if person X doesn’t understand person Y?  This is perfectly normal.  We are a nation of specialists, aren’t we?  All we need to do is to organize ourselves into teams and encapsulate the specialties.  Let the specialists focus on whatever they are best at, and with a small amount of guidance, the right things will happen.  Right?

This is the theory, anyway.  Specialization leverages everybody’s strengths.  Communication and coordination enable the parts to mesh.  Synergy is manifest, as the whole is greater than the sum of its parts.

Unfortunately (and most of us have many stories to demonstrate this), there is an old saying that goes:

In theory, theory and practice are the same.  In practice, they are not.

For encapsulation of specialties to work, the following conditions generally hold:

  1. The interdependencies between specialties are relatively minor.
  2. Each of the encapsulated subject matters are understandable enough that non-experts can comprehend what makes them tick.
  3. In spite of their differences, various specialty areas share a common set of goals and priorities (aka a common value model).
  4. The contexts are relatively stable over time.  They don’t shift in a way that changes the goals, or the priorities, or cause the existing specializations to become inefficient.

The absence of one or more of these factors works to tighten the level of coupling in the system.  When the coupling between specialties is low, synergy is low and “the whole is little more than the sum of its parts.”  But when this coupling rises, the size of the whole is highly dependent on the relationships between its parts.

Success is no longer driven by what individual people know.  The world has gotten way too complicated for that.  Success now is much more dictated by how well we communicate what we know (and even what we don’t know), and how well we align with the direction that our peers are headed.


1 Comment

  1. […] written by Felix Salmon, is a great place to start, and I hope that the article that appears in helps to frame it properly. Possibly related posts: (automatically generated)Devsta: The […]

    Pingback by More Conceptual Distance « Charlie Alfred’s Weblog — March 21, 2009 @ 1:13 pm

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