Complexity theory is designed to bring order out of a rough-and- tumble world, something close to every insurance professional's or actuary's heart. Whether applied in the laboratory or as part of a mathematical model, it can do wonderful things . But in the real world it's just what its name says-a theory. It may help us understand why things go one way or another, but it can't foretell those things with such certainty that an insurance company could, say, set its rates based on the knowledge that only one hurricane will strike Florida during the coming year...Complexity theory; risk; risk management; managing risk; climate change; global warming; chaotic systems; weather; hedging; hedge

Chichilnisky, Graciela

English

Research Papers in Economics

B Y
￿
G R A C I E L A
C H I C H I L N I S K Y
YOU CAN'T USE
COMPLEXITY THEORY TO
PREDICT HURRICANES OR
OTHER CLIMATIC EVENTS, BUT
IF YOU'RE SMART YOU CAN USE IT
TO HEDGE YOUR BETS ON THE FUTURE .
28
￿
Contingencies JANUARY/ FEBRUARY 1998
omplexity theory is designed to bringorder out of a rough-and-
tumble world, something close to every insurance profession-
al's or actuary's heart. Whether applied in the laboratory or as
part of a mathematical model, it can do wonderful things. But
in the real world it's just what its name says-a theory. It may
help us understand why things go one way or another, but it
can't foretell those things with such certainty that an insurance
company could, say, set its rates based on the knowledge that
only one hurricane will strike Florida during the coming year.
-------------------------
GRACIELA CHICHILNISKY IS
UNESCO PROFESSOR OF
MATHEMATICS AND ECONOMICS
AND DIRECTOR, PROGRAM ON
INFORMATION AND RESOURCES,
COLUMBIA UNIVERSITY,
NEW YORK CITY.
WEATHER MAP COURTESY OF THE NATIONAL
OCEANIC AND ATMOSPHERIC ADMINISTRATIONYet I see a connectionbetween complexity theory and risk management, which is the essence of insurance. In particular,
I've focused on the risk management of complex systems.
Admittedly, the prediction of complex systems is inherently difficult, even impossible, according to some prominent
writers (see sidebar on p. 30). But I want to take a position closer to analysts who say that, if you're smart enough, you
can sometimes discern patterns, even in chaos. There are situations when you can actually make predictions, provid-
ing you have the right instruments. So what's needed for better risk management is something in the nature ofa gestalt
shift and, in particular, financial innovation.
In short, what's needed is a new method of predicting. And here the function is not to know the future (though
people may tell you it is). In finance, analysts are not trying to predict the future (nobody can really do that); in-
stead, they hedge against the risk of a downside future event. Whether we can predict the future is beside the
point-it's a misunderstanding of the true nature of the problem. The real challenge is knowing how to hedge
effectively against an adverse event. After all, if the future were predictable, there'd be no need for insurance in
the first place . All that would be required is a steady accumulation of funds sufficient to pay the resulting loss-
es when a predicted event occurred.
Given that we can't predict events, we must rely on financial innovation. In particular, we must focus on
complex systems. They're the most difficult, but they're frequently the best representation of how the world
works today. With a bit more sophistication and financial innovation, we can deal with these systems fairly eas
ily. The scheme suggested here won't do a perfect job-nothing can-but it provides a new way of managing
and accounting for risk, and of dealing with apparent chaos.
Order from Chaos
The key observation behind all my work comes from mathematics and chaotic systems: Most chaotic systems
exhibit order, and that order is given by what are called "chaotic attractors." This means even systems that are
difficult to make predictions about, and difficult to observe, will eventually settle into patterns.
Think, for instance, about the weather. Perhaps you've been told that, as a result of the chaotic attractors,
there are two possible patterns into which the weather may settle . In one, there will be a high probability of 10 in-
tense and destructive tornadoes. Conversely, in the other pattern, there are clear skies and an absence of intense
storms.
In essence, there are two corresponding actuarial tables for
catastrophic storms, one with 10 such events and another with
one. You're not predicting which will come to pass, only that
one of two will happen, and that they're equally likely.
Given that you don't' know which pattern will occur, the
standard principles of insurance aren't really of any help in de-
ciding what steps to take, based on the actuarial tables for the
two scenarios. In one case, you decide to be very cautious and
assume that 10 storms will occur. Then you have to consider
how much capital you'll need to reserve given that assump-
tion. If each of the events eventually costs $1 billion, then you
know you'll need $10 billion. Of course, if there's only one cat-
astrophic event, the cost of carrying that collateral has been
enormous, since you've been carrying 10 times the amount
you needed and the opportunity cost of that capital is not in-
consequential.
On the other hand, if you decide there will be only one
storm, you'll be under protected. In that situation, the risk you
face is financial catastrophe .
What do insurers do in this case? They have several options;
all, however, have accompanying downsides. One is to settle
on something between the extremes of $1 billion and $10 bil-
lion. If both patterns are equally likely, it could seem perfect-
ly logical to divide the difference and choose $5 .5 billion as
the target. But by doing that you're guaranteed to be wrong
100 percent ofthe time-50 percent ofthe time you'll be over-
insured and 50 percent of the time you'll be under-insured, by
several billion dollars in both cases. If you're too low, and in-
suring yourself, you're making yourself liable for risks you can't
cover. But if you set the target too high, you're forced to set
unattractively high rates. You'll likely end up losing your cus-
tomers. In many instances, that's happening right now.
If you want to insure property in the Caribbean, for exam-
ple, you must pay a premium that's roughly 33 percent of the
Contingencies JANUARY/ FEBRUARY 1998
￿
2930
￿
Contingencies JANUARY/ FEBRUARY 1998value of the property. You know there isn't really a one-in-three
chance of a catastrophic event. But because the possibility may,
in fact, be one in 10, or one in two, insurers have to take some-
thing like an average. So we end up with 33 percent. As a re-
sult, most of the properties in the Caribbean are uninsured.
Another option is self-insurance. Stanford University, for
example, purchases no earthquake insurance. For many years,
the university covered itself. Some may think of that as a so-
lution, but it isn't. In the end, regulators still look at Stanford
and say, "Okay-you're selling insurance to yourself. So all the
usual state regulations about insurance apply to the universi-
ty." Stanford, as a result, has the same burden of accumulating
data, record-keeping, and reserves as any insurance company.
Back to the Weather
Let's think again about those two weather patterns. What do
they really mean? They qualify as chaotic attractors-complex
systems. As complex as they are, most of them tend to settle
into patterns . The problem is that, using the example I gave,
the chaotic behavior could settle into two patterns. One is as-
sociated with a certain type of weather; the other is associated
with another type . Still, there's a lot of uncertainty with these
two patterns; you can'tmake exact predictions-we're talking
about averages here . One pattern is associated with just one
catastrophic storm, and the other with 10 storms.
With chaotic systems, although you've identified the at-
tractors, you can't predict whether you're going in one direc-
tion or another. So in some sense, although chaotic systems
are not as chaotic as they appear to be-there's a method in
their madness-you don't know in which direction they'll go.
The solution is to change our way of looking at them.
The Securities Component
The securitiesindustry has a different approach to this dilem-
ma than the insurance industry. The insurance industry knows
that you can'tpredict when and where a specific event will hit,
so it relies instead on actuarial tables to provide broader (sta-
tistically based) predictions inherent in the law of large num-
bers. This is the principle behind insurance-safety in num-
bers. You can't predict precisely who will be hit, but you can
predict how many people, overall, will be hit.
Even if a given system is chaotic, you still have enough in-
formation to allow you to say something about it. What you
say takes the form of one, two, or three possible scenarios and,
with them, one, two, or three actuarial tables. Selecting from
among them is the problem.
The remedy is to use principles from securities markets.
These markets don't rely on the sort of statistically based in-
formation the insurance industry uses. What they do is hedge.
They operate by seeking patterns and, armed with that, hedge
against probable downside risks. They hedge, for instance, when
they use bonds and equities to provide a cushion against in-
terest-rate changes-without looking for the statistical safety in
numbers that characterizes insurance procedures. They search
for factors that are correlated. Securities houses, then, hedge
against correlated events, not by using the law of large num-
bers or insurance principles, but by usinginverse correlation.
The obvious question arises: "What I've got isn't stocks and
bonds; it's two equally probable actuarial tables. What am I sup-
posed to use as a hedge?" The answer is-use the same princi-
ples that have proved so successful in the securitiesmarkets.
You have to hedge the risks in one of your actuarial tables
ALTHOUGH CHAOTIC SYSTEMS ARE NOT AS CHAOTIC
AS THEY APPEAR TO BE-THERE`S A METHOD IN THEIR
MADNESS-YOU DON'T KNOW IN WHICH DIRECTION
THEY'LL GO. THE SOLUTION IS TO CHANGE OUR WAY
OF LOOKING AT THEM.
against the risks in the other. You need to look at the risk not
as something you're trying to predict statistically, but as the de-
velopment of different scenarios. Then you have to, in effect,
insure yourself by usinginsurance policies within each of the
scenarios. In each case you assume the scenario that's going to
occur. Insurance goes as far as possible-because it's a very ef-
ficient method-in dealing with one of the scenarios. But when
dealing with multiple scenarios, where you have no way of de-
ciding between them, you have to use a different financial in-
strument. This instrument is a security contract, one that's con-
tingent not on interest rates but on actuarial tables instead.
In risk management, the key is to think of the future as a
combination oftwo factors. The first is a statistical factor, which
is what you're familiar with-the actuarial table. But if you're
insecure, as you should be, aboutwhat triggers insurable events,
your only option is to betjust like in a casino. If there's one
sort of outcome, and you're protected for that, you'll have a
shortfall, and if the other scenario happens, and you're pro-
tected for that, you'll have too much insurance and the carry-
ing cost will be too high. So what you do is buy securities that
pay more in one weather pattern and less in another. Thus, by
transferring moneybetween the two possible states, you're pro-
tected. In more concrete tenns, it's a combination of a modified
reinsurance package, which diversifies the risk and protects the
insurer against unknown financial risks, and a security, which
captures correlated risks that can't be diversified in any way.
So the fact that you can't make predictions becomes irrele-
vant-as long as you have chaotic attractors, which give rise
Contingencies JANUARY/FEBRUARY 1998 3 1SCOTT&WHITE
TEMPLE, TEXAS
Scott & White, one of the nation's largest medical
centers, including a 492 physician clinic with 17
locations, a top rated 139,500 member HMO and a 486
bed teaching hospital affiliated with Texas A&M
University Health Science Center College of Medicine
located in Central Texas is actively recruiting for an
Actuary. Candidatesmust have a Bachelors degree in
Actuarial Science, Math or Statistics and ASA with 2
years experience in managed care. Responsibilities
include developing rates and capitation, rating policies
andmethodologies, and budget preparation for consulting
actuarial review.
Scott & Whiteprovides an outstanding career opportunity
for professional growth along with excellent benefits,
relocation assistance and ideal living conditions in the
sunbelt ( 1 hour North ofAustin and 2'l, hoursSouth of
Dallas on 1-35). Qualified candidates send resume with
salaryhistory to: GRACE COLE, Scott & White Human
Resources, 2401 S. 31st Street, Temple, Texas 76508;
Fax (254)724-1631; http://sw.org EOE.
07&
0
Would Like To
B o u nC e
a few ideas off you!
Specializing in the placement of
Actuaries & Benefit Consultants
CAROL ZADEK, M.B .A., C.A.C.
Managing Director
19762 MacArthur Blvd ., Suite 321 . Irvine. CA 92612
714-253-3444 - Fax: 714-253-4011
E-Mail: HdHntrCZ4aol .com
32
￿
contingencies JANUARY/ FEBRUARY 199 8
to patterns. While the patterns are not predictable, ifyou can
distinguish a finite number of patterns you're positioned to
take effective action and hedge the risk inherent in each pat-
tern by reverse correlation.
So chaotic systems can be used for practical purposes. We
live in a world where we need to know what could happen, hav-
ing used a rational approach to classifying risks. And the risk
may well take the form of one of several patterns, with corre-
spondingly different actuarial tables. Once you've understood
that risk, take action. Take out a hedge against the risk.
Some Pieces in Place
While this concept has yet to be implemented totally, some
pieces of it, interestingly enough, have been coming onto the
market. The Chicago Board of Trade is now selling catastrophe
futures, for example . They're a piece of the totalpuzzle I've de-
scribed here, since they help you protect against different ac-
tuarial tables governing a given segment of time . But the mar-
ket for these instruments to date has been very thin, because
the same people who buy them-insurers-are the people who
report how much a given instrument should pay, thus poten-
tially creating a conflict of interest.
Meanwhile, during the summer of 1996, Merrill Lynch and
Morgan Stanley floated new instruments, such as environmental
bonds, with exactly the same structure. This is a bond with a
coupon that,in addition to the standard terms, includes a fac-
tor that pays differently depending on the frequency of cata-
strophic events.
In addition, there have been attempts to adapt the funda-
mentals of securities to fit the insurance industry-in a word,
securitization. There are companies that carry insurance con-
tracts as their main asset (but of course, there are also liabili-
ties); they sell shares in the company, thereby accessing the
capital market. Much like Ginnie Mae, you take a large num-
ber of risks, pool them, cut the pool into small portions (shares)
that are put on the market, and let people invest in the com-
pany. This procedure lets companies access capital markets
from an insurance base, and that's good, given the potential for
losses from a major catastrophe. It's nearly impossible to put
aside enough reserves for a "Big One," and the associated cost
of doing so is tremendous.
So different pieces of the theory I've advanced here have
been implemented, but not the whole thing. The bottom line,
then: You can't predict one particular outcome using com-
plexity theory, but you can look for the relevant chaotic at-
tractors. Then, if there turns out to be more than one of these,
you can use securities as hedges between them. The actual fi-
nancial instrument has been created and developed at the Pro-
gram on Information and Resources at Columbia University,
and is in the process of beingimplemented . It protects against
financial as well as natural catastrophes in the most cost-effi-
cient way.

A Radical Shift in Managing Risks: Practical Applications of Complexity Theory

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics