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Historical bubbles
Investment strategies
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Author: Horatio Boedihardjo
On a sunny morning in 2001, a piece of investment plan landed on the
desk of Dick Fuld, the then Chief Executive of Lehman Brothers. The
document, compiled by a team of maths and physics PhDs, included a
calculation to show how the bank will always end up with a profit if
they invest on the real estate markets. Fuld was impressed. The next
five years saw the bank borrowing billions of dollars to invest in
the housing market. It worked. The housing market boom had turned
Lehman Brothers from a modest firm into the world's fourth largest
investment bank.
But as the housing market started to shrink, the assumptions that
the PhDs made began to break down one by one. The investment now
became a mistake, resulting in a stunning loss of $613 billion. On
September 15 2008 Lehman Brothers collapsed — "The largest
bankruptcy in the US history," as described by Wikipedia.
The money making model
Imagine that you are working for
Lehman Brothers and one morning you receive a phone call from HSBC.
"Hi! A hundred customers have each borrowed $1 million from us for a
year. We would like to buy an insurance from you which will cover us
in the case of any of them defaulting. From their application forms
we reckon they each have a 3% chance of default. How much will the
insurance cost?"
You can in fact calculate it, easily. The 100 customers each have a
3% chance of defaulting, so you expect three customers to default
next year. That is, you will need to pay $3 million next year.
Assuming the interest rate is about 3% each year, next year's $3
million would be worth 3/(3/100+1)=3/1.03=2.91 million now.
Therefore HSBC will have to pay you at least $2.91 million for the
insurance. Obviously Lehman Brothers wasn't a charity and so, to
make money, they would double the price to $5.82 million and expect
to make $2.91 million out of each of these deals on average. This
kind of insurance is called a credit default swap (CDS).
The legendary CDO
After putting down the phone, you
might be quite worried about what would happen if ten of the
borrowers defaulted, because then you would have to pay $10 million
back! In this case, consider this deal: how about paying me a
certain premium, and if more than ten defaults occur, you will only
need to pay for ten of them and I will pay for the rest. If less
than ten defaults occur, you will have to pay for all the defaults
and I won't pay anything. The type of deal that I am offering is
called the senior tranche of a collateralised debt obligation (CDO)
contract, while the one you are getting is called the junior tranche
of the CDO.
The attractiveness of the senior tranche is that almost all of the
time I don't have to pay anything, just pocketing my premium.
Imagine how unlikely it is to have more than ten borrowers
defaulting together! Senior tranches were generally considered to be
almost as safe as borrowing money from the government. Since the
senior tranche offers a better return than, but seems to be just as
safe as, putting the money in the bank, the investors just loved it.
In 2004 there were only $157.4 billion of CDO being issued, but by
2007 the amount grew to $481.6 billion.
But don't you find it a bit unfair that you can have something as
safe as bank deposits, that offers a higher return?
The pitfalls
Yes, it is unfair! In fact, CDO is a lot riskier than bank deposits,
but Lehman Brothers, like many investors, didn't seem to know that.
Let's go back to our original model. The first source of error is
that we have assumed that each investor has a 3% chance of
defaulting. How do we know that? It must be from historical data.
The problem is, there hasn't been a national drop of housing price
since the great depression in the 1920s, so the chance that a
borrower defaults was calculated on the basis of a good period when
the housing prices surged. However, the housing market crashed in
2007. Many borrowers' properties are now worth even less than the
loan they have to pay in the future, so many of them refuse to pay.
To worsen the situation, 22% of these borrowers are the so-called
subprime borrowers — those who had little income and had little hope
of returning money. Banks were not afraid of lending money to them
because even if they defaulted, the insurance would pay them back.
The participation of the subprime borrowers makes lending much
riskier than before.
In fact, the default probability in the US has quadrupled from the
3% as assumed in the model to 12% since 2007, making it four times
riskier. This means that investors like Lehman Brothers will be hit
four times harder than they have anticipated.
Actually it is worse than that. The profitability, or lack of it, of
financial products more complicated than CDS and CDO may depend on
the square of the default probability, rather than the probability
itself. Now as the default probability rises from 0.03 to 0.12, the
square of the probability increased from 0.0009 to 0.0144 — that's
an increase by a factor of 16!
There is also a second and more subtle source of error. Whether you
can make money from selling the CDO insurance for the bank depends
on whether the borrowers return the money, which in turns depends on
the economy. So if the economy goes down, you are a lot more likely
to lose money. If you are an active investor, then you probably have
invested in the stock market as well. Now if the market crashes you
lose both the money invested in the stock market and in the CDO.
Suppose, on the other hand, that instead of spending the money on
CDO, you bet on whether Manchester United will win the European
Champion League. This time in order to lose all your money you need
both the market to go down and Manchester United to lose their match
— this is less likely than just having the market go down.
Therefore, investing on CDO is a riskier choice than betting for
Manchester United. The error in our model is that we have not taken
into account this extra risk due to its dependence of CDO on the
market.
These two errors were sufficient to mask the risk in CDO. In fact,
the errors are so serious that 27 out of 30 of the CDOs issued by
Merril Lynch were downgraded from AAA (the safest investment) to
"junk" when the errors were spotted.
The fall of Lehman Brothers
Lehman Brothers, unaware of the hidden
risks, decided to invest big on CDO. It even had a 35 to 1 debt to
equity ratio, that is, it only owned $1 out of every $36 in its bank
account — the other $35 were borrowed from somewhere. This meant
that a loss of just 3% of the money on its balance sheet, would have
meant the loss of all the money it owned. After suffering heavy
losses (more than 3% of the money in its balance) from CDO,
borrowers began to lose confidence and called back the loans. As
Lehman had always relied on short-term loans, its lenders were able
to pull their cash back quickly. Now the bank was in trouble. It
borrowed much more than it was able to return and soon found itself
unable to pay back. On 15th September 2008, the world's fourth
biggest investment bank was gone, forever.
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