Page 1 of 3 The hard and simple maths of crisis
By Julian Delasantellis
It's probably been this way through history, that humans are always faced with
two choices on how to accomplish something - an easy way and a hard way.
Certainly according to Homer's Iliad, this was the choice facing
Achilles in deciding his fate.
"My mother Thetis tells me that there are two ways in which I may meet my end.
If I stay here and fight, I shall not return alive but my name will live for
ever: whereas if I go home my name will die, but it will be long ere death
shall take me."
Achilles chose what was, for him anyway, the easy choice, to go fight and die
in the Trojan Wars.
In our present day, the principle is illustrated by two, diametrically
different, equally valid explanations for the world financial crisis. One is
chock full of arcane and esoteric mathematical formulae, how they rose, and how
they fell. That's the hard-to-understand reason.
The easy to understand reason is simplicity itself. The financial crisis
happened because people ran out of money.
David X Li, born in the early 1960s as Xiang Lin Li in China, might, in some
way, be considered something of a real-life Forrest Gump, for, twice in the
past 50 years, on opposite sides of the globe, he has been present during
disasters of truly epic proportions - the first witnessed as a child, the
second as a key participant. As a small boy in Mao Zedong's China, he was sent
with his family to live in the countryside when his father, a minor police
official, was purged during the Cultural Revolution.
When the insanity ceased, young Xiang found he was then in an environment where
he could prosper. After taking a Master's degree in economics at Nankai
University in Tianjin, he was sent by a Chinese government now hungry to learn
more about how market economies work to study in Canada. There, he earned an
MBA from Laval University in Quebec, then a Master's in actuarial science and a
PhD in statistics from the University of Waterloo in Ontario. Along the way, he
changed his name to David X Li.
The fates were aligning to bring Li down from Ontario, where he was working at
the Canadian Imperial Bank of Commerce, to Wall Street, the center of global
world finance. The US investment management industry was tiring of the old,
"dartboard", model of fund management, where investment choices were made
according to non-rigorous hunches and feelings - in essence, like throwing
darts onto a dartboard. They wanted new, scientific, quantitative,
formula-based investment strategies. Not even the September 1998 implosion of
the Long Term Credit Management (LTCM) hedge fund, with the economics Nobel
Prize winners who created the field of quantitative investment, Myron Scholes
and Robert Merton, on LTCM's board, did much to shake the Street's devotion to
the new faith.
What the new quantitative investment analysts, or, as they came to be known,
the "quants", were trying to do was the investment game's version of alchemy -
boosting total investment returns without an accompanying increase in risk. If
you had a new addition to the catechism, it would generally not be accepted
until it was peer reviewed and then approved for publication in one of the many
prestigious academic journals set up to be the guardians of the canon of
quantitative finance. In March, 2000, in the Journal of Fixed Income, Li
submitted his candidate gospel, "On Default Correlation: A Copula Function
Approach."
Judging by the e-mails I have received from many of you, I know what a varied,
literary bunch you all are. I suppose this diversity extends to what type of
writing many of you prefer of an, err, intimate nature. Maybe some of you are
into classics like Fanny Hill, or Jacqueline Susan's Valley of The Dolls,
maybe you're an aficionado of one of the many new, high-class porn blogs being
produced these days in the Cultural Studies departments of the Ivy League.
But when Wall Street read this line from Li, "We show that the current
CreditMetrics [where Li was working at the time] approach to default
correlation through asset correlation is equivalent to using a normal copula
function," the Masters of the Universe on the Street got hotter than
12-year-old boys who just found their dad's old Playboy magazines.
In 1983, Rabbi Harold Kushner's book, When Bad Things Happen to Good People,
since it so obviously gave the impression that those who read it were good,
appealed to an America still suffering from the tailend of the early 1980s'
recession. For a mathematician like Li, the answer to Kushner's implied
question was easy. Excluding environmental factors, if the number of bad people
and good people was roughly the same, bad things should happen to good people
in about the same proportion as they happen to bad people.
Cancer should befall both the good and bad in equal numbers, as long as one
group doesn't smoke or work with asbestos dust. If two houses are on a
shoreline facing an approaching tidal wave, their probability of getting
swamped is not determined by which homeowner is good or bad. They both will
face a high probability of getting flooded, while houses a few miles away, on
top of a steep hill, will face a much smaller probability of disaster, even if
it's occupied by the worst, meanest, most morally degraded and corrupt SOB in
town.
If we were graphing the probabilities of disaster on a bell curve, what
mathematicians call a Gaussian Copula, the homeowners on the shore, most
exposed to the storm's fury, would be sitting right at the apex of the curve,
while the gentleman on the hill would be down on the thin tail, since it was
very unlikely that he was going to suffer any of the fury of the sea.
So is this the way the world works - bell curve summit event probabilities
flanked on both sides by lower probability tail events? Mostly that is true -
except when it isn't.
Just about 26 months ago, in my first article on this website on what would
develop into what we now know as the world financial crisis (see
Rocking the subprime house of cards, Asia Times Online, March 6, 2007),
I noted how much the mortgage finance industry had changed in the previous
decades.
These days, virtually all US home mortgages are packaged and
bundled together to become what are called 'collateralized mortgage
obligations', or 'mortgage-backed securities'. The bank or other mortgage
originator that constructs these packages sells them to investors, who use them
very much as investment bonds. Thus your monthly mortgage payment, instead of
going to the bank that you write the check to, now 'passes through' as a
dividend payment to the investor who bought the package of mortgages that
contains yours.
Collateralized mortgage obligations (CMOs) are
mortgages, perhaps up to 5,000 of them, bundled together into one bond-like
security paying coupon interest. Collateralized debt obligations (CDOs) are
CMOs, with credit card loans, student loans, car and other consumer finance
loans bundled in for a bit of the spice of diversification.
If you are the note holder for just one mortgage, say, you're the bank that
wrote the mortgage and did not sell it into the secondary market - you intend
to hold it to maturity - then your profit/ loss analysis is simplicity itself.
If the homeowner keeps paying the mortgage you're fine, if he doesn't, you're
busted.
But what if you're the owner of a CMO or a collateralized debt obligation
containing 5,000 mortgages and other loans, what happens when one, or a few
more, of the loans inside it go bad? Will it be like one rotten apple causing
the whole barrel to go bad, or, is it just like the normal bell curve, with a
few bad events to be naturally expected down there on the thin tail of the
curve?
Li's argument, in the words of the 1988 Bobby McFerrin song, was to "don't
worry - be happy". Unlike rotten apples or cockroaches, his formula did not
believe that a few mortgage defaults here or there presaged a more widespread
upcoming catastrophe. It was just part of a normal, essentially random,
dispersion of expected results.
For Wall Street, the Li research was like the sweetest music being sung by the
sultriest siren. The Street interpreted Li to mean it was safe now to direct a
massive new quantity of liquidity in the direction of mortgage finance. Sure,
you'll get some defaults here and there, but with the number of individual
mortgages and other loans in the collateralized packages so huge, there was a
natural diversification effect that protected investor's returns.
Of course, this new liquidity stream hit the American and in many cases the
rest of the Anglo-Saxon and other world real estate markets, like an
afterburner bolted onto a tricycle. Home prices skyrocketed for most of this
decade, hardly affected by the 2000-01 recession that followed the dot-com
crash. The price rises were most extreme during the 2004-06 period, right after
the 2004 US Securities and Exchange Commission ruling that allowed US
investment banks to leverage up with even more CDOs and CMOs carrying Li's
implied, quantitative based Good Housekeeping Seal of Approval. Li by 2003 had
become global head of derivatives research at Citigroup.
Li's confidence in his research stemmed from his analysis of mortgage-related
credit default swaps (CDS). But the CDS market, only about 10 years old, had
never seen an actual real estate price pullback in America; the last of those
followed the collapse of the savings and loans industry in the late 1980s.
As economics blogger Felix Salmon put it in the March 2009 Wired magazine,
"Recipe for Disaster: The Formula That Killed Wall Street" [1],
Because
the copula function used CDS prices to calculate correlation, it was forced to
confine itself to looking at the period of time when those credit default swaps
had been in existence: less than a decade, a period when house prices soared.
Naturally, default correlations were very low in those years. But when the
mortgage boom ended abruptly and home values started falling across the
country, correlations soared. Bankers securitizing mortgages knew that their
models were highly sensitive to house-price appreciation. If it ever turned
negative on a national scale, a lot of bonds that had been rated triple-A, or
risk-free, by copula-powered computer models would blow up. But no one was
willing to stop the creation of CDOs, and the big investment banks happily kept
on building more, drawing their correlation data from a period when real estate
only went up. "Everyone was pinning their hopes on house prices continuing to
rise," says Kai Gilkes of the credit research firm CreditSights, who spent 10
years working at ratings agencies. "When they stopped rising, pretty much
everyone was caught on the wrong side, because the sensitivity to house prices
was huge." And there was just no getting around it. Why didn't rating agencies
build in some cushion for this sensitivity to a house-price-depreciation
scenario? "Because if they had, they would have never rated a single
mortgage-backed CDO."
Well, it looks like Li was wrong in his
most basic assumption.
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