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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].

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    Marzol to Lead Companys Strategy and Competitive

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    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

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