Subject: LTCM, models and experts
Date: Fri, 11 Feb 2000 22:08:40 GMT
In article <38A42D1B.F00BCBCD@math.nwu.edu>,
on Fri, 11 Feb 2000 09:39:07 -0600,
Leonard Evens <firstname.lastname@example.org> writes:
>> I don't think this is exactly right.
>> First it is my understanding (which may be wrong) that
>> LTCM (Long-Term Capital Management, I believe this is the intended
>> name) was not in fact using sophisticated mathematical models but
>> instead rather simple minded models based on historical price
>> relationships between various financial instruments.
>I am not a financial model expert, so be warned that what I
>say may be misleading. And of course, I was not a partner
>or employee of LTCM, so I don't know what they were actually
>doing. But it is my impression---confirmed by a recent
>NOVA presentation---that LTCM used variations of the
>Black Scholes model. Although the mathematics of this model
>are relatively simple compared to many models used in physical
>science, it does involve theoretical principles which supposedly
>apply to options trading. I don't believe it is basically
>an extrapolation based on historical trends. There are of
>course assumptions built into the model, which if they fail
>to apply, then the results may be nonsense. I've read a bit
>about LTCM and also seen the NOVA presentation, and right now
>I'm a bit confused about what is supposed to have gone wrong.
>It was my impression that it was not a failure of the model
>per se but how LTCM tried to apply it in a real situation.
Of course LTCM used Black Scholes and variants. These
models have well known limitations which did not so far as I
know have anything much to do with what went wrong. What went
wrong was LTCM (like many before them and no doubt many after
them) was excessively leveraged.
It is my understanding that a typical LTCM position
was similar to the following. Suppose we, LTCM, notice
that the government has a bond outstanding which will be
redeemed in 5 years at par ($1000 per bond) and meanwhile
pays 9%. Call this the red bond. Suppose there is another bond,
the blue bond, which is absolutely identical except that for
some reason the red bond is currently selling at $900 while the
blue bond costs $1000. This looks like a price anomaly which
can exploited. How do we do this. Suppose we start with $9000.
We buy 10 red bonds. We take our bonds to the bank and request a
loan offering the bonds as collateral. Since we are LTCM and
really hot stuff the bank allows us to borrow 100% of our
collateral at 5.5% interest. This loan is open indefinitely but
we must keep it 100% collateralized. This is figured on a daily
basis. We take the $9000 from the bank and buy TBills paying 5%
interest. We find someone, X, holding blue bonds and planning
to hold them to maturity. We ask to borrow 9 blue bonds from
X and offer the TBills as collateral. As a sweetener we offer
.5% additional interest per year. Naturally we agree to keep
the loan 100% collateralized (on a daily basis) and we get the
TBill interest and X gets the bond interest. X agrees as it
appears a safe way to get an additional .5% yield. We now take
the 9 blue bonds and sell them on the open market. This gets
us our $9000 back. Now every year we owe $495 interest to the
bank and $855 to X ($810 from the borrowed 9% bonds and $45 for
the extra .5%) a total of $1350. But we receive $450 interest
on the TBills and $900 interest on the red bonds (the bank is
holding them but we still get the interest). This also totals
$1350 so our carrying cost is zero (I picked the numbers to
make it come out this way). But in 5 years when the bonds
come due and we unwind everything we end up $1000 ahead because
our 10 red bonds are now worth $10000 while the 9 blue bonds
which we borrowed are only worth $9000.
So we have increased the return on our $9000 capital
by $1000 over 5 years or about 2% a year. Of course 2% a year
does not sound all that impressive. However that is no problem,
we at LTCM are real men not a bunch of wimps. We take our $9000
and do the above deal again and again. In fact we do it 20 times.
This increases our excess return to 40% a year (simple interest)
which sounds a lot better. Now if we did this 20 times with the
same bank they might figure out what we were doing. This would
make them nervous. No problem, we deal with 10 different banks.
Now banks ask ordinary borrowers tedious questions like what
other loans they have outstanding. But fortunately we are LTCM
and it would be very gauche for some lowly loan officer to ask
us a question like that.
The above may be incorrect in detail but I believe it
captures the essential elements of the LTCM trading strategy.
Now you may ask where is the sophisticated mathematical model.
Good question. I believe the answer is "there wasn't one".
Now this is not entirely fair as in the real world it is rare
for the red and blue bonds to be absolutely identical but
differently priced. Instead you find similar but not absolutely
identical bonds and apply the same strategy. In doing this you
may create synthetic securities (consisting for example of .5
of a 4 year bond and .5 of a 6 year bond) to get sufficiently
similarly behaving pairs. This can involve elaborate models.
However it does nothing to eliminate the risk present even in
the simple case with identical bonds and it is this risk which
I believe did LTCM in.
What is this risk, what could possibly go wrong? Very
simple. While it is true that in 5 years the red bond will be
worth $1000 and so one would expect the price to gradually rise
from the current $900 to $1000 over the 5 year period, this does
not mean the price cannot fall temporarily. Suppose the red bond
price falls to $890. Now the collateral for your $9000 loan from
bank is worth $8900 and they want $100 like right now. Well no
problem you have $9000 capital. But wait, real men that you were,
you did the deal 20 times. So you must part with $2000 over 20%
of your capital. Ouch. But there's worse to come. Rumors start
going around Wall Street that LTCM is in trouble and may have to
unwind its positions. Furthermore somehow Wall Street has
figured out you own a gazillion red bonds which you would have
sell and have shorted a gazillion blue bonds which you would have
to buy back. So what happens, the red bond price falls a bit
more to $880 in case you are about to dump a bunch of red bonds
on the market and the blue bond price rises a bit to $1010 in case
there is about to be a shortage of blue bonds. So now your not
quite so friendly banks want another $2000 and furthermore X wants
another $1800 TBills collateral. Ouch. Ouch.
Well you get the picture.
>> sorts of financial models are somewhat similar to "key precinct"
>> type electoral models (which are based on historical relationships
>> between voting results in different precincts). There are also
>> some climate models based on historical relationships (ie El Nino
>> vrs La Nina). Such models can fail spectacularly if the system
>> moves outside the often rather limited domain they are based on.
>I am not a climatologist, so be warned that what I now say may
>be misleading because of my lack of understanding.
>I think when people talk about "climate models", they generally
>are referring the GCMs (general circulation models). These
>use well established principles in thermodynamics
>and fluid mechanics to model the Earth's atmosphere and/or
>ocean either separately or in some sort of combination.
>Unfortunately, it is necessary to make major approximations
>to get the programs to run on computers. For example,
>an awful lot of information has to be included in the form
>of so-called parameterization because it involves phenomena
>smaller in scale than the approximation grid used to describe
>the system. Such models may be tweaked using observational
>data, but they are very far from being based on historical relations.
>Or at least this is what I understand. But climate modelling is
>a sophisticated subject, constantly being improved, and I've
>probably oversimplified and ignored some important features.
Yes, but I think when you hear La Nina means a wetter
than normal winter (or whatever) is likely in the US this is
just based on historical patterns.
>> I also think it is possible to draw general conclusions
>> from the LTCM fiasco. One is that it is dangerous to rely on
>> reputations. The people involved in LTCM had glittering
>> reputations. As a result their investors and creditors failed
>> to take reasonable precautions which could have averted much of
>> the trouble.
>Nonsense. We rely on reputations all the time. That is
>extrapolating from past experience, which usually is a good
>first guide. But of course it is a mistake to rely solely
>on reputations. We must examine what anyone says about a
>situation on its own merits. We should also be careful not
>to assume that because someone is a proven expert in one area
>that what he or she says in a related area is necessarily
Ok, let me clarify to say it is dangerous to rely too
much on reputations. You have (mostly properly in my opinion)
chastised posters to this group for ignoring expert opinion.
However it is also possible to give too much weight to expert
opinion, a danger you appear much less aware of.
>As best I can tell, LTCM strategy was based on sophisticated
>hedging schemes which supposedly avoided risk. It also had
>to be done on a massive scale in order to succeed. I think
>perhaps the only reasonable precaution their investors could
>have taken would have been not to invest.
It had to use massive leverage to get impressive
returns. Investors could have been asked more questions about
the trading strategy and not settled for answers like "If we
told you we would have to kill you" or "Only three people in
the world are capable of comprehending our strategy and they
all work for us". I believe LTCM traded on its reputation to
avoid awkward questions.
>Financial schemes have a history of appearing to work in
>normal times and failing when things go awry, as they did
>in the Asian meltdown followed by the Russian failures.
>Perhaps LTCM had a more sophisticated scheme, so it may have
>worked better when it worked, but it is not surprising it
>eventually failed. I attended a course on the Black Scholes
>model, and it was clear that it was based on several crucial
>assumptions which need not always apply.
Lots of financial schemes are based on obtaining a
small gain most of the time at the risk of a small chance of
a huge loss. They work fine until you roll the snake eyes.
LTCM had more to do with arrogance and greed than any failing
in Black Scholes.
>It is important however to distinguish between models in
>physical science and models in finance. The former are based
>on physical laws which in their domain of relevance are
>hardly in doubt. That doesn't mean that they can be used
>to be predict everything in all situation with certainty,
>but it does mean we should avoid false analogies with other
>kinds of models in other areas when deciding how accurate they
I don't agree. Key parts of the climate models
are empirical (as you in fact discuss above). There is no
essential difference between a climate model which is say 50%
fundamental laws and 50% empirical rules and an economic model
which is 100% empirical rules.
James B. Shearer
Subject: Re: Failure to Predict Blizzard Casts Doubt on Global Warming
Date: Thu, 10 Feb 2000 23:53:21 GMT
In article <38A30AA0.email@example.com>,
on Thu, 10 Feb 2000 12:59:44 -0600,
Leonard Evens <firstname.lastname@example.org> writes:
>Jim Scanlon wrote:
>> To reinforce Len's comments I watched most of an excellent PBS
>> presentation on Nova of the bail out of Long Term Capital Investment
>> firm which used sophisticated mathematical models to remove the risk
>> from investing very large sums of money in global financial markest.
>> They were quite successful returning 43% the first year (minimum
>> investment $10 million). Returns dwindled to 17% as more firms
>> expolited the markets. However when the long term pattern of the global
>> financial system was perturbed by unusual crises in Asia and Russia at
>> the same time the model and reality parted and LTCI started losing $500
>> million a day.
>> Models are very useful tools, but they all have their limits. My
>> understanding of the use of climate models is that they do not "predict"
>> the future but extend,or project various scenarios to give an
>> intelligent estimate of what lies ahead. It's not exactly like
>> predicting the outcome of an elextion based on early returns of reliable
>> voting information--which is pretty good.
>What you say is correct, but I think one should not try to
>draw too many conclusions about models in general from one
>sort of model. About the only thing the economics models
>used by LTCI and climate models have in common is that they
>use computers to do the numerical calculations since exact
>analytic solutions are not possible. But they are based
>on entirely different theoretical analyses in unrelated
>subjects, and the numerical difficulties they deal with are
>of entirely different orders of magnitude and arise for
>entirely different reasons. Projections based on early
>returns are based on statistical models which have even
>less to do with either climate models or those used by
I don't think this is exactly right.
First it is my understanding (which may be wrong) that
LTCM (Long-Term Capital Management, I believe this is the intended
name) was not in fact using sophisticated mathematical models but
instead rather simple minded models based on historical price
relationships between various financial instruments. These
sorts of financial models are somewhat similar to "key precinct"
type electoral models (which are based on historical relationships
between voting results in different precincts). There are also
some climate models based on historical relationships (ie El Nino
vrs La Nina). Such models can fail spectacularly if the system
moves outside the often rather limited domain they are based on.
I also think it is possible to draw general conclusions
from the LTCM fiasco. One is that it is dangerous to rely on
reputations. The people involved in LTCM had glittering
reputations. As a result their investors and creditors failed
to take reasonable precautions which could have averted much of
James B. Shearer
Subject: Re: LTCM, models and experts
Date: Sun, 13 Feb 2000 16:35:12 GMT
In article <38A58C0E.739C88B4@math.nwu.edu>,
on Sat, 12 Feb 2000 10:36:30 -0600,
Leonard Evens <email@example.com> writes (in part):
>I think we have disagreed in the past about climate models
>and will continue to do so. Since neither of us is a
>climatologist, I don't know what difference that makes to
>the science. But I still think that any model has to be
>examined and criticized in its own right, not as part of
>a general criticism of models. For climate models, for example,
>some conclusions may be more valid than others because they
>depend directly on physical principles. In areas where
>empirical data may be used to tweak a model, one should
>have arguments about why such use may lead to inaccuracies
>or the opposite. In other words, it is very important to
>look at details.
I think this is where we disagree. You are saying it is not
reasonable to generalize about models or in other words to construct
models of models (or modeling). On the other hand I think it is useful
to see what can we say about models as a class before examining any
particular model. For example models are all constructed by humans so
if humans are prone to certain types of errors then so will the models
they construct. Also some models depend on complicated computer
calculations. It is well established that large computer programs are
buggy (on the order of one bug per 100 lines of code is typical). This
has to be allowed for in any estimate of model reliability.
It is easy to say that every issue should be carefully
evaluated on its individual merits but no one has the time to do this.
So shortcuts must be found. Relying on reputations is one such
shortcut and I agree it is sensible to do this (to some extent) even
though it is sometimes wrong. I think there are other useful shortcuts
such as people are biased in favor of their interests or complicated
hard to verify models are suspect even though they may be wrong in
a particular case.
James B. Shearer
Subject: Re: Computers and SDI
Date: Mon, 14 Feb 2000 20:46:38 GMT
In article <38A81F0A.589F1CB5@math.nwu.edu>,
on Mon, 14 Feb 2000 09:28:10 -0600,
Leonard Evens <firstname.lastname@example.org> writes:
>On an unrelated matter, I wonder about the state of computer programs
>to handle any of the latest proposed missile defense systems.
>When SDI was first proposed by Reagan, a leading expert on
>military computer systems argued that this was a one time use
>system which could never be tested in the circumstances in which
>it was to be used. (I think his name is David Parnas---sp?)
>It would be interesting to know what the Pentagon has come up
>with for the latest systems. Of course, these are designed
>supposedly only to shoot down a few missiles from a third
>rate poweer like North Korea, so they needn't be as complicated.
>Still many of their proponents have in mind an expansion to
>defend at least against a Chinese missile attack. China if it finds
>it necessary can certainly opt for a large scale attack which
>would bring up the same issues. Perhaps the idea would be to
>use three independent systems and believe two out of the three.
>But since they would necessarily have to share important
>common features, it is not clear how feasible this would be.
>There are of course vast differences between the use of
>complex computer systems for the military and the use of
>climate models to help make policy about fossil fuel use.
>But I suspect there are those who would support the use
>of computers in one of these contexts but not in the other.
>Perhaps it is a matter of whose computer is being in gored.
>(No puns intended!)
One big difference is that nature cannot be bluffed but our
military opponents can be. So it is not necessary for a military
system to actually work to be useful. I think it is doubtful that an
SDI system would actually work very well if put to the test. However I
do not think software is the main problem.
As I recall Parnas' objections it seemed to me that he was
criticizing a strawman rather than a realistic proposal. He was
considering a centralized system in which sensors would observe an
attack and send information back to some central command center which
would assign target lists and distribute them to antimissile satellites
which would then engage and destroy the enemy missiles. I think this is
a poor design. I think a more reasonable design would be distributed
with the antimissile satellites independently selecting and engaging
targets which would considerably simplify the software requirements
(not to mention the communication requirements).
So in this context as well as others I favor keeping things
simple. Particularly since I suspect software is not something the
military does well.
Parnas also seemed to be trying to impose an unreasonable
performance requirement on the system namely that it would reliably
stop all missiles. I think a good chance of stopping most of the
missiles is worthwhile (even ignoring the bluff aspect) especially in
the context of limited attacks. Which is not to say that even this is
presently achievable or is likely to be in the near future.
By the way I don't oppose the use of computers in climate
modeling or the use of climate models in evaluating policy options. I
do oppose relying on them unduly.
James B. Shearer