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Posted by on March 21, 2008, 9:50 am
> Elle wrote:
> > ... hear the words of Paul Volker, quoted the other day in
> > the Wall Street Journal: "The market was being run by
> > mathematicians that didn't know financial markets. And you
> > keep hearing, you know, god, that event should only happen
> > once every hundred years, according to my model. But those
> > every hundred years events are coming along every two or
> > three years, which should raise some questions."
>
> My BS-ometer hits a 10 every time I read a quote about "five sigma
> events"
Such events do occur, so such a statement can be true. What you are
really objecting to is the second statement (below), I think.
> or about a financial event that "should happen once every 7,000
> years" - I actually saw that in print the other day. These are emperor's
> clothes kinds of statements that to me immediately discredit whatever is
> being talked about. At least, in the context of "event frequency".
>
> You can make those kinds of statements about, you know, fruit fly
> mutations -- how often the green eyed one has short wings or whatever.
> But the data series on finance is extremely short and lumpy.
Compared to what? Financial time series are go back further and have
less estimation error than the data used in most other social
sciences.
> Even the 25-year events couldn't be identified yet, if they came in any sort of
> describable distribution that is, which of course they don't.
As a prominent statistician has said, "all models are wrong, some
models are useful". A financial planner who wants to simulate the
probability that a client will not run out of money in retirement must
have a distribution of stock returns to draw from, for example, annual
returns normally distributed with a mean of 10% and a standard
deviation of 18%. If he samples from historical annual returns over
the last 80 years instead of assuming normality, there is still an
implicit return distribution.
What is the alternative to some kind of model?
Shifting to Elle's message, mathematicians or "quants" are needed on
Wall Street and in banks to determine interest rates on fixed rate and
adjustable mortgages that still leave the lender a profit margin.
Mortgages have considerable optionality, including the
(1) ability of the borrower to prepay when rates fall
(2) cap on interest rates often found on adjustable mortgages
(3) ability of the borrower to walk away when "underwater", especially
in non-recourse states such as California.
These options of the borrower make mortgage loans less attractive to
the lender than investing a non-callable Treasury bond, and valuing
them takes a quant. I think quants misvalued option (3), because that
option rises in value when house prices fall nationwide.
Since models of mortgages will have uncertain inputs, highly leveraged
structures of mortage-backed securities will be risky.
I think the lesson of the mortgage crisis is not to avoid mathematical
modeling but to limit leverage and ensure that modelers periodically
examine their assumptions.
Ideally, there would be software to help borrowers determine what is
the best loan for them, based on features in the checklist at
http://www.federalreserve.gov/pubs/arms/checklist_english.htm . For
example, if one ARM has a floating rate of 2% above LIBOR with a cap
10%, and another has a floating rate of 3% above LIBOR but a cap of
7%, a mathematical model is needed to determine which loan is better.
The mortgage calculators I have seen are simplistic and do not make
such comparisons.
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