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How to Manage Risk
(After Risk Management
Has Failed)
FALL 2010 VOL . 52 NO .1
R E P R I N T N U M B E R 5 2 1 0 7
Adam Borison and Gregory Hamm
Please note that gray areas reflect artwork that has been
intentionally removed. The substantive content of the ar-
ticle appears as originally published.
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SLOANREVIEW.MIT.EDU FALL 2010 MITSLOAN MANAGEMENT REVIEW 51
IT IS WELL KNOWNthat over the past decade, and especially over the past few years, a number ofthe worlds most widely respected companies have collapsed. Analysts have cited equally well-known
reasons for these collapses the usual suspects of nonviable business models, greed, incompetent
(and overpaid) management and a lax regulatory environment. Not often mentioned is another key
consideration, something that appears to distinguish collapsed companies strongly from their noncol-
lapsed counterparts. It is the breadth and depth of these companies approach to risk management.
That risk management could be a major (though not sole) cause may seem counterintuitive. The
troubled American International Group Inc., for example, was a leader in risk management and even
R I S K M A N A G E M E N T
How to Manage Risk (AfterRisk ManagementHas Failed)The corporate world has traditionally taken a flawed approachto risk management, but a better alternative is readily available.BY ADAM BORISON AND GREGORY HAMM
THE LEADINGQUESTION
What risk-managementapproachshould com-panies adoptto help themavert futurefailures?
FINDINGSThe traditional fre-quentist approachis based entirely onthe historical record.
The alternativeBayesianapproach incorpo-rates judgmentsto complementhistorical data.
The Bayesian per-spective providesmore powerful andaccurate results.
AIGs former CEO boasted thathis company had the best risk-management [departments] inthe damn industry. In whatways was he wrong?
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52 MITSLOAN MANAGEMENT REVIEW FALL 2010 SLOANREVIEW.MIT.EDU
R I S K M A N A G E M E N T
maintained a risk-management subsidiary. Its former
CEO Maurice R. Hank Greenberg boasted that AIG
had the best risk management [departments] in the
damn industry. Bear Stearns Cos. claimed the best-
in-class processes in analyzing and managing risk;even theNew York Timescited the companys carefully
honed reputation for sound risk management. Fannie
Mae, the Federal National Mortgage Association,
touted its excellent credit culture and risk-manage-
ment capabilities, and Lehman Brothers Holdings Inc.
prided itself on what its leaders called a culture of risk
management at every level of the firm.1
Yet at these companies, and at others with com-
parable cultures, risk management apparently
performed quite dismally. How could this be? We
contend that the answer lies in the concepts andpractices of traditional risk management, which tend
to look for risk in all the wrong places. That is, failure
did not stem from merely paying lip service to risk
management or from applying it poorly, as some
have suggested. Instead, collapse resulted from tak-
ing on overly large risks under the seeming security
of a risk-management approach that was in fact
flawed. The more extensive the reliance on tradi-
tional risk management, we believe, the greater the
risks unknowingly taken on and the higher the
chances of corporate disaster.
This article suggests how the key shortcomings
of traditional risk management can be addressed
by adopting a more sophisticated alternative the
Bayesian approach.
Not By History AloneTwo fundamentally different views have evolved
over the years on how risk should be assessed. The
first view termed the objectivist, or frequentist,
view holds that risk is an objective property ofthe physical world and that associated with each
type and level of risk is a true probability, just as
there is a true atomic number for oxygen. Such
probabilities are obtained from repetitive historical
data, with some of the classic examples (largely for
pedagogic purposes) being coin flips, die rolls and
weather patterns. Based on such data, a frequentist
might say that the probability of flipping a seem-
ingly normal coin and gett ing heads, after having
documented the results of a great many tosses, is
0.5; or that the probability of a high temperature of95 degrees on July 4, 2011, in New York, given the
extensive weather record, is 0.3.
The second view is termed the subjectivist, or
Bayesian, view (named after the Reverend Thomas
Bayes, an English mathematician who made major
contributions to this approach during the 18th cen-
tury). Bayesians consider risk to be in part a
judgment of the observer, or a property of the ob-
servation process, and not solely a function of the
physical world. That is, repetitive historical data are
essentially complemented by other information.
Although classic cases such as coin flips come up
largely in the frequentist context, they can also be
used to contrast the frequentist and Bayesian views.
For instance, suppose a magician pulls what ap-
pears to be a normal coin out of her pocket, allows
you to flip it 10 times, and it comes up heads five of
those times. She then proposes a wager based on
your flipping the coin one more time and getting
heads. What probability do you assign to that out-
come? A frequentist presumably relies on the
historical data from this coin (as well as from any
other normal coin) and assigns a probability of 0.5.A Bayesian takes not only the data into account but
also his judgment about the cleverness, trustwor-
thiness and financial situation of the magician. He
may thus assign a probability very different from
0.5 perhaps as high as 1.0. Another observer
might assign an altogether different probability,
based on other judgments.
A similar argument can be made with respect to
weather patterns, even where there is a great deal of
DAILY RETURNS DURING THE FIRST THREE QUARTERS
These daily trading results for a financial company exhibited modest variations during
much of 2008. Would the fourth quarter show a similar pattern?
Q1
$75
$50
$25
$0
($25)
($100)
($75)
($50)
Q2 Q4
Daily P & L ($)
Q3
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FALL 2010 MITSLOAN MANAGEMENT REVIEW 53SLOANREVIEW.MIT.EDU
repetitive historical data. For example, while the re-
cord over many decades may indicate to a
frequentist that the probability of a high tempera-
ture of 95 degrees in New York City on July 4, 2011,
is 0.3, a Bayesian taking an analysis of global warm-ing into account may assign a probability that is
greater than 0.3. In both cases, the historical record
of the physical world is the same, but the different
probabilities reflect dissimilar judgments about the
present and future of that world.
Although the Bayesian view is well accepted in
some circles, it has not penetrated the risk-manage-
ment world. Traditional risk management has
instead adopted the frequentist view, despite its
three inherent, and major, shortcomings. First, it
puts excessive reliance on historical data and per-forms poorly when addressing issues where
historical data are lacking or misleading. Second,
the frequentist view provides little room and no
formal and rigorous role for judgment built on
experience and expertise. And third, it produces a
false sense of security indeed, sometimes a sense
of complacency because it encourages practitio-
ners to believe that their actions reflect scientific
truth. Many of a corporations most important and
riskiest decisions which often do not fall into the
narrow frequentist paradigm are made without
the help of the more sophisticated and comprehen-
sive Bayesian approach.
An Exceptional Fourth QuarterValue at Risk (VaR), arguably the centerpiece of
traditional risk management, provides a good ex-
ample of the limitations of the frequentist view,
particularly its overreliance on historical data. The
basic idea behind VaR is to calculate the potential
loss within a specified time period typically, a
day. Controls then can be put in place to limit this
loss to a desired level. In particular, if a companyhas identified a $15 million daily loss as the maxi-
mum it should tolerate, and the fourth quarter is
about to begin, what is the probability of exceeding
such a loss during that period? (See Daily Returns
During the First Three Quarters.)
Using data from approximately 200 daily trials
during the first three quarters of 2008, a frequentist
represents the range of daily returns as a normal
distribution with a mean of $1 million and a stan-
dard deviation (or volatility) of $5 million. Based
on this, the probability of a daily loss of more than
$15 million is extremely small, well under 0.1%.
(See Probabilities of Daily Returns, Based on the
Record Alone.) It is a less-than-one-in-1,000 event.
And the probability of a daily loss of more than $25
million is infinitesimal.
The Bayesian approach, in contrast, is to look at
the daily return, like all risks, as a matter of judgment
that is informed by but not limited to the repetitive
historical data. A Bayesian explicitly recognizes that
despite three quarters (or more) of data exhibiting a
volatility of $5 million, the future will not necessarily
replicate the past with certainty. For example, there
could be an unusual end-of-year effect or other
(much larger) socioeconomic forces at work.
Although little, if any, repetitive historical data
underlying these broader phenomena may be avail-
able, a Bayesian can quantify his judgment. For
example, the analyst might see two competing phe-
nomena: Deteriorating market conditions could
cause volatility in the fourth quarter to increase, per-
haps double, while newly imposed regulatory policiesmight cause volatility to decrease. Let us say that the
Bayesian assigns a 30% chance that the volatility will
remain unchanged during the fourth quarter, a 30%
chance that it will double to $10 million and a 40%
chance that it will be halved to $2.5 million.
As might be expected, combining this subjective
information with frequency data in a seamless fash-
ion results in an augmented distribution that is
wider than the one based on the data alone. (See
PROBABILITIES OF DAILY RETURNS,
BASED ON THE RECORD ALONE
The first three quarters results are reflected by this normal distribution.
Given the periods record, the probabilities of large losses are very small.
-20
10%
6%
5%
4%
9%
8%
7%
3%
0%
1%
2%
-15 25
Daily Return
-10 -5 20151050
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54 MITSLOAN MANAGEMENT REVIEW FALL 2010 SLOANREVIEW.MIT.EDU
R I S K M A N A G E M E N T
Modified Probabilities of Daily Returns.) From
this distribution, the Bayesian determines that the
probability of a daily loss of more than $15 million
is roughly 2.0% over 20 times that of the frequen-
tist approach and that the probability of a daily
loss of more than $25 million is small but noninfi-
nitesmal. (The idea of a Bayesian approach to VaR
was originally suggested in 1997 and followed up in
2000 and 2004.2It has so far gained little traction,
however. Financial analyst Riccardo Rebonatos
2007 book Plight of the Fortune Tellers: Why We Need
to Manage Financial Risk Differently3is one of the
few risk-management volumes that counsel greater
emphasis on a Bayesian approach.)
It is worth noting that the increase in the loss
probability with the Bayesian approach is notbe-
cause the Bayesian thinks that things will get worse.
The increase comes because this approach formally
and precisely reflects a recognition that we have lim-
ited understanding of the world and the important
but nonexclusive role that frequency data play in
that world. The Bayesian view makes room for judg-ment, quantifies that judgment in order to integrate
it with data on an equal footing and acknowledges
the uncertainty that inevitably remains.
The actual daily losses for the fourth quarter of
2008, together with the 99.9% loss limits for the
two approaches, would be $15 million for the fre-
quentist approach and $27 million for the Bayesian
approach. (See Daily Returns During the Full
Year.) If such a limit is accurate, there should be
only a one-in-1,000 chance that it will be exceeded
in any one day. With roughly 50 trials in the
fourth quarter, we expect that this limit should not
be exceeded during that per iod at all. But as we
now know, the fourth quarter of 2008 turned outto be a very turbulent period. Losses grew dramati-
cally and were much more consistent with the
Bayesian than the frequentist view. The frequentist
limit was exceeded 15 times, while even the larger
Bayesian limit was exceeded six t imes. Of course,
this example was developed to make the point that
the Bayesian view is more comprehensive and real-
istic. But despite the artificial construct, we believe
that the broader conclusion holds. Risk manage-
ment built around the reality of judgment
(supported by available data) is superior to r iskmanagement built around the fantasy of fact.
Altered Rainfall Patterns?Weather provides another example for contrasting
the frequentist and Bayesian approaches to risk as-
sessment and for highlighting Bayesian integration
of data and judgment. Consider a company whose
success, and possibly even existence, depends on
rainfall. Such a company could be a supplier of
drinking water, a hydroelectric-based energy utility,
an agricultural operation or a financial enterprise
with rainfall -dependent investments. Suppose
1,000 millimeters is a critical level of rainfall for the
company; that is, it needs a 1,000-millimeter year at
regular intervals ideally, at least every five to 10
years. How can we assess the risk of not receiving
this level of rainfall in the future?
The frequentist approach focuses entirely on the
data, typically applying well-accepted statistical
constructs. In this example, the rainfall pattern can
be matched by a normal distribution with a mean
of 880 millimeters and a standard deviation of 166
millimeters. With this distribution, the probabilityof rainfall of more than 1,000 millimeters in any
one year is about 23%. The probability of going
withouta 1,000-millimeter rainfall level for five
years is then (1.0 0.23)5or about 27%; for 10
years, about 7%; and for the 30 years between 1976
to 2005, less than 0.04%, or one in 2,500. Based on
this frequentist risk assessment, one can say that the
rainfall risk is extremely low.
The Bayesian approach to this issue combines,
MODIFIED PROBABILITIES OF DAILY RETURNS
This distribution reflects both the historical record (the first three quarters results)
together with the observers judgments on how the fourth quarter could differ.
-50
24%
8%
4%
20%
16%
12%
0%-40 50
Daily Return
-30 -20 -10 30 4020100
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FALL 2010 MITSLOAN MANAGEMENT REVIEW 55SLOANREVIEW.MIT.EDU
as always, the available data with judgments about
the broader issues at hand. In this example, the
most important broader issue is the potential effect
of climate change on rainfall a topic of consider-
able controversy and discussion and a Bayesianmight begin with a formal assessment of expert
judgment regarding this effect.
Reflecting a great deal of uncertainty, our expert
estimates that the effect of climate on rainfall ranges
from a decrease of 200 millimeters per year to an
increase of 100 millimeters per year. Combining
this expert assessment with the historical data, we
obtain a distribution for annual rainfall that is
wider and shifted lower than that of the historical
data alone. Specifically, the mean is 830 millimeters,
and the standard deviation is 200 millimeters.Under these conditions, the probability of total
rainfall greater than 1,000 millimeters in any one
year is reduced to about 16%, which means that the
probabilities of going withouta 1,000-millimeter
rainfall year during any particular time interval are
quite different from those of the frequentist case:
about 42% for five years, 17% for 10 years and 0.5%
for all 30 years between 1976 and 2005. The latter
rainfall risk indicated by the Bayesian approach is
low, but not as low as the one-in-2,500 figure based
on the historical data alone. In fact, this probability
is more than 10 times higher.
As it turned out, the actual yearly rainfalls over
the 1976 to 2005 interval were substantially lower
than those of the previous 100 years. There was not
a single year with rainfall over 1,000 millimeters
during that 30-year period. Admittedly, this exam-
ple was chosen, as the first example, to make a
point. Not surprisingly, the Bayesian assessment
appears to be more comprehensive and realistic.
Nevertheless, we believe, as before, that a broad
conclusion holds. Assessing risk by formally inte-
grating both data and judgment leads to moreuseful results.
Learning, and Then Adjusting,ContinuouslyAnother limitation of traditional risk management
that is, of the frequentist approach involves not so
much how risk is defined or measured but how it is
prevented or mitigated. Because risk is assessed solely
by means of the historical record, and this record
changes gradually and subtly, management activity
in the traditional context is largely fixed or static. It
adjusts very slowly and modestly, if at all. Historical
frequency data are collected to establish the facts.
With the facts in hand, extensive rules are estab-lished and controls put in place. These controls
remain essentially undisturbed until there is a seri-
ous failure or disaster, although by then it is too late.
This is a rigid process, and there is no natural sys-
tem for monitoring a wide range of potentially
relevant events, developing insights from those
events and adapting in response.
By contrast, the Bayesian perspective leads natu-
rally to adjustments in the risk-management
activity itself. Because Bayesian risk assessment
combines both data and judgments, its underlyinglogic provides a built-in and rigorous way of updat-
ing assessments as new data arrive or new judgments
emerge. Equally importantly, it provides a natural
way to adjust risk-management activity in response
to this learning.
Commodity prices, such as those involving oil,
provide a good example of the contrast between
these two perspectives with respect to the actual
managementpart of risk management. (See Oil-
Market Prices Over the Past 20 Years, p. 56.) The
pattern has been volatile, particularly in the most
recent years. Consider a company that is interested
in reducing its exposure to this volatility. The typi-
cal frequentist approach is to collect as much of the
oil-price data as possible and parameterize a model
of the pr ice behavior. The model can be simple,
such as classic Brownian motion, or sophisticated,
DAILY RETURNS DURING THE FULL YEAR
With actual results of the fourth quarter of 2008 showing that it was more
turbulent than the first three quarters, the Bayesian approach would have
been particularly useful to risk managers.
Q1
$75
$50
$25
$0
($25)
($100)
($75)
($50)
Q2 Q4
Daily P & L ($)
Q3
99.9% loss limit for frequentist approach
99.9% loss limit for Bayesian approach
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56 MITSLOAN MANAGEMENT REVIEW FALL 2010 SLOANREVIEW.MIT.EDU
R I S K M A N A G E M E N T
such as a mean-reverting Ornstein-Uhlenbeck pro-
cess. Based on the model chosen, the company
estimates future volatility and exposure, and it then
implements an appropriate hedging strategy.
The Bayesian approach uses not only the histori-cal data on oil prices but also accommodates
judgments about the underlying factors that drive
them. In particular, a Bayesian might believe that
prices are influenced over the long term by two key
structural drivers global economic conditions
and climate policies. As information is gained about
these drivers, judgments regarding oil-price risk will
change, which then leads automatically to a modi-
fied hedging strategy. (See Learning from Recent
Experience.) The company begins with a hedging
strategy for 2010 based on historical data and itsjudgments about the future situation. Some of the
future judgments, namely, 2010 economic condi-
tions, climate policies and oil price, are then revealed.
This 2010 information serves to update judgments
regarding 2011 about economic conditions, climate
policies and oil price. The company then adjusts its
hedging strategy for 2011 based on the revealed 2010
situation and the updated 2011 judgment. The ac-
tual 2011 situation will later be revealed too, and the
hedging strategy for 2012 can similarly be adjusted
in response. This updating and adjustment process
continues to 2013 and beyond.
Once again, the frequentist and Bayesian ap-
proaches show themselves to be substantially
different. The frequentist approach relies on a great
deal of historical data. It adjusts only slowly to
changing conditions, and these adjustments, such
as they are, must essentially be imposed on the
risk-management process. On the other hand, the
Bayesian approach captures both data and judg-ments. It adjusts quickly to changing conditions, as
well as to evolving judgments. And it is inherently
dynamic learning and adjustment are internal
and automatic.
Make Room for BayesiansThe frequentist view that decisions should be based
solely on facts drawn from repetitive historical data
rather than on data complementedby judgments
derived from experience and expertise can be linked
to failed companies errors and subsequent collapse.Why is this distinction between fact alone and
fact-plus-judgment so important? First, because
the fact-alone perspective provides no effective
guidance on issues often those with greatest im-
pact where there are little or no frequency data.
Its a classic case of losing ones keys where it is dark
but looking for them under the street lamp because
the light there is so much better. Second, because
unlimited faith in historical data even large
amounts of it leads to overconfidence and ex-
cessive risk taking. And finally, because a system
based solely on historical fact inevitably lurches
from crisis to crisis.
The Bayesian perspective provides more accu-
rate and powerful results. It recognizes that risk is a
matter of bothdata and judgment, and it uses the
combination in a rigorous manner for identifying,
assessing and managing risk. Where there is a great
deal of relevant data, this information plays a dom-
inant role, with the integration of judgment making
a substantial improvement over the traditional ap-
proach. Where there is little or no relevant data,
judgment plays a dominant role, prov iding valueunder conditions beyond the scope of the tradi-
tional approach.
With the Bayesian approach, risk can be mea-
sured quantitatively, whatever the amount and
quality of the data. And rather than focusing entirely
on the observed world, Bayesian risk assessment
also reflects the consistency, reliability and precision
of the observer. Recognizing the important, some-
times central, role of judgment can lead to more
OIL-MARKET PRICES OVER THE PAST 20 YEARS
The volatility of recent years challenges the frequentist approach, based as that is
on the historical record alone. But the Bayesian approach incorporates the learning
acquired from newly emerging patterns.
1987 1989
$160
$140
$120
$100
$80
$0
$40
$60
$20
1991 1995
Price per Barrel ($)
1993 20071997 1999 20032001 2005
Year
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SLOANREVIEW.MIT.EDU FALL 2010 MITSLOAN MANAGEMENT REVIEW 57
reasonable and realistic behavior in large part be-
cause we realize that judgment is not perfect and
can be refined as more experience is acquired.
Admittedly, obtaining probabilities from subjec-
tive judgments rather than frequency data requiresa great deal of care. The cognitive (unintentional)
and motivational (intentional) biases underlying
probability judgment are well known.4For example,
individuals typically exhibit considerable overcon-
fidence in their probability assessments that is,
the distributions are too narrow. There also are well-
documented biases involving the overweighting of
information that is readily available and easily re-
membered. Fortunately, established and emerging
techniques for probability encoding, such as those
based on expert interviews
5
and prediction mar-kets,6can reduce these biases.
The shortcomings of the frequentist view nar-
rowness of thinking, unwillingness to accept the
possibility of error and the inability to adapt to
changing circumstances clearly played a signifi-
cant role in the recent financial collapses. Companies
such as Citigroup Inc. and Merrill Lynch & Co. con-
tinued to increase their exposure to subprime
mortgages even as evidence regarding deterioration
in the housing market accumulated: During the
early years of the housing boom, default rates on all
mortgages were unusually low. That led bankers
and, more important, rating agencies to build
unrealistic assumptions about future default rates
into their valuation models.7At these companies,
early warning signs were ignored and unrealistic de-
fault rates were not adjusted until it was too late.
With a Bayesian view, such problems may not
have been eliminated altogether, but they could
have been substantially reduced through more
comprehensive and realistic risk assessment and
more dynamic and adaptive risk management.
Many measures are being deployed to recover fromthe collapses and to build a more robust system that
prevents future crises a shift from traditional
risk management to Bayesian risk management
should be a part of this effort.
Adam Borisonis a senior vice president and Greg-
ory Hammis a senior economist at NERA Economic
Consulting in San Francisco. Comment on this arti-
cle at http://sloanreview.mit.edu/x/52107, or contact
the authors at [email protected].
REFERENCES
1.A. Gomstyn, Former AIG CEO Greenberg Defends
Reputation, March 16, 2009, http://blogs/abcnews.com;
Bear Stearns Names Michael Alix Chief Risk Officer and
Robert Neff Deputy Chief Risk Officer, Business Wire,
February 3, 2006; L. Thomas Jr. Bear Stearns Chief
Weathers the Storm, New York Times, June 29, 2007;
Federal National Mortgage Association, Fannie Maes
Marzol to Lead Companys Strategy and Competitive
Analysis Group, press release, August 26, 2004; and
Lehman Brothers, Annual Report, 2.
2.G.A. Holton, Subjective Value at Risk, Financial Engi-
neering News 1 (August 1997): 1, 8-9, 11; K. Dowd,
Estimating Value at Risk: A Subjective Approach, Jour-
nal of Risk Finance 1, no. 4 (2000): 43-46; and T.K. Siu, H.
Tong and H. Yang, On Bayesian Value at Risk: From Lin-
ear to Nonlinear Portfolios, Asia-Pacific Financial
Markets 11, no. 2 (2004): 161-184.
3.R. Rebonato, Plight of the Fortune Tellers: Why We
Need to Manage Risk Differently (Princeton, New Jer-
sey: Princeton University Press, 2007).
4.A. Tversky and D. Kahneman, Judgment Under
Uncertainty: Heuristics and Biases, Science 185, no.
4157 (September 27, 1974): 1124-1131.
5.See, for example, C.S. Spetzler and C.-A.S. Stael Von
Holstein, Probability Encoding in Decision Analysis, Man-
agement Science 22, no. 3 (November 1975): 340-358.
6.See, for example, J. Wolfers and E. Zitzewitz, Predic-
tion Markets, Journal of Economic Perspectives 18, no.
2 (spring 2004): 107-126.
7.S. Tully, Wall Streets Money Machine Breaks Down,
Fortune, Nov. 26, 2007, 64.
Reprint 52107.
Copyright Massachusetts Institute of Technology, 2010.
All rights reserved.
LEARNING FROM RECENT EXPERIENCE
By identifying the drivers of oil price and by incorporating their revealed
values over time into the risk-management model, the Bayesian approach
enables a more effective hedging strategy year after year.
HedgingStrategy
2010
HedgingStrategy
2011
HedgingStrategy
2012
Oil Price2010
EconomicConditions
2010
ClimatePolicies
2010
Oil Price2011
EconomicConditions
2011
ClimatePolicies
2011
Oil Price2012
EconomicConditions
2012
ClimatePolicies
2012
http://www.sloanreview.mit.edu/http://blogs/abcnews.comhttp://blogs/abcnews.comhttp://blogs/abcnews.comhttp://blogs/abcnews.comhttp://blogs/abcnews.comhttp://www.sloanreview.mit.edu/8/14/2019 how to manage risk (after risk failed).pdf
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