1. introduction to risk management
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Risk ManagementTRANSCRIPT
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Risk Management: Introduction
Rangarajan K. Sundaram
Stern School of BusinessNew York University
TRIUM Global EMBA ProgramNew York: January 16-20, 2015
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An Overview
I This is one of two segments in the module on risk management.I Deals mainly with the instruments for managing market risk and credit
risk, in particular, on
I The uses of these instruments.I The risks in these instruments.I The valuation of these instruments.
I Professor Ed Altmans sessions focussing on credit risk complement thismaterial.
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Introduction
I What is Risk?
I Potential that outcomes of an action may differ from those expectedor anticipated.
I Ever-present in all economic activity.I In normal market conditions.
I Changes in input prices, exchange rates, interest rates, etc.
I Unexpected market dislocations:
I Financial bubbles, natural disasters, terrorist attacks, political events,. . .
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The Management of Risk
I From an organizational standpoint, the management of risk requires:
1. Identifying the sources of risks.2. Where possible, measuring/quantifying these risks.3. Managing the risks.
I Eliminating unnecessary risks.I Transferring risk to markets.I Managing the retained risk.
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The Sources of Risk
I Market risk.I Changes in prices in normal market times.
I Credit risk.I Risk that promised payments fail to materialize.
I Liquidity risk.I Difficulty in getting in and out of positions.
I Operational risk.I Lack of proper controls to detect fraudulent activity.
I Others:I Political, terrorist, catastrophe, reputational, . . .
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Our Focus . . .
I . . . is on instruments for managing market and credit risk.
I As noted, Professor Altmans sessions develop the theme of creditrisk further.
I The effects of market risk can be exacerbated by the presence of
I Illiquidity.I Poor operational controls.
I The case studies we examine will look at the interplay of these factors.
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2. Measuring Risks
I Involves specifying a probability distribution over outcomes:
I Set of possible outcomes.I Likelihoods of these outcomes.
I What probability distribution should one use?
I Potential trade-off between using
I distributions that are easy to work with, andI those that fit the data better and/or are more appropriate for the
task at hand.
I Common distribution in financial modeling: the Normal or Gaussian.
I Well understood and easy to work with . . .I . . . but, as we discuss below, some important shortcomings from a
risk-management standpoint.
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3. Managing the Risks
I Involves:
I Eliminating unnecessary risks.
I For example, have minimum creditworthiness standards for advancingcredit.
I Transferring risk to markets.
I Derivatives contracts: Futures/forwards, options, swaps, . . .I Hedging versus insurance.
I Managing the retained risk.
I Capital to be held against retained risk.I Extent of liquid reserves.
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Potential Problems
I Risk-management failures usually because either:
1. Risks are not properly identified.
or
2. Identified risks are inadequately measured.
I Usually mis-specified and/or excessively optimistic models.
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Risk-Management Failures: Famous Examples
I Barings, Sumitomo, Societe Generale.
I Unidentified operational risk: Rogue trading.
I Metallgesellschaft, Aracruz Cellulose.
I Risk of sharp market moves underestimated.
I Amaranth.
I Market and liquidity risks underestimated.I Could not exit positions.
I LTCM, AIG, Fannie Mae, Freddie Mac
I Systemic/correlation risk not captured.
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Comment 1: Unmodeled Features
I Models can only reflect what is put into them.I This can create illusory comfort levels with strategies.I Metallgesellschaft in 1995:
I Hedged long-term forward sales with short-term futures.I Cash flow consequences of sharp oil-price drop ignored.I Bankruptcy resulted.
I AIG in 2008:
I Built sophisticated models to capture default risk.I Ignored collateral requirements from possible
I Market deterioration short of default.I AIGs own credit-rating deterioration.
I Bankruptcy resulted.
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Comment 2: Unmodelable Features
I Operational risk:
I Nick Leeson and Barings: > $1 billion in losses.I Yasuo Hamanaka and Sumitomo: > $2.5 billion losses.I Jerome Kerviel and Soc Gen: e5 billion losses.I Kweku Adoboli and UBS: $2 billion losses
I Of course, not just a trading/financial markets issue:
I Enron.
I Incentives matter! Where does Harvard Universitys $1 billion+ inswap-related losses in 2009 fit in?
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Comment 3: The Normal Distribution
I Key issue: Choosing a distribution that best represents the uncertaintyconcerning future prices.
I What is meant by best?I The most common starting point: Normal (a.k.a. Gaussian).I Instructive to understand the pros and cons of this choice.I Defined by two parameters:
I The mean : centers the distribution.I The standard deviation : measures dispersion around .
I Distribution has the familiar bell-shape (hence bell curve).
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The Normal Distribution
-5 -4 -3 -2 -1 0 1 2 3 4 5
x Xc
x
Probability of observa7on < x
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The Normal DistributionThe Mean: Centering the Distribution
-6 -4 -2 0 2 4 6 8
MEAN = 0 STD DEV = 1
MEAN = 2 STD DEV = 1
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The Normal DistributionThe Standard Deviation: Dispersion Around the Mean
-6 -4 -2 0 2 4 6
MEAN = 0 STD DEV = 1.50
MEAN = 0 STD DEV = 1.0
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The Normal Distribution: Properties
I Distribution is symmetric around the mean.I Likelihood of an observation depends solely on its distance from the mean
(measured in standard deviations):
Distance from mean % of all observations
1 standard deviation 68% 1.96 standard deviations 95% 2.58 standard deviation 99% 3 standard deviation 99.73%
I Thus, for example, if observations are normally distributed only around 1in 370 observations should be more than three standard deviations fromthe mean.
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The Normal Distribution: PropertiesOne Standard Deviation from the Mean
-5 -4 -3 -2 -1 0 1 2 3 4 5 m - s m+s
16% 16%
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The Normal Distribution: Properties1.96 Standard Deviations from the Mean
-5 -4 -3 -2 -1 0 1 2 3 4 5
2.5% 2.5%
m - 1.96s m + 1.96 s m
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Are Financial Markets Normal?
I Normal distributions have found widespread applications in the physicaland natural sciences.
I How well do they fit financial market data?I The main problem: In virtually every financial market, they underestimate
significantly the likelihood of extreme or tail observations.
I Example Observations more than 3 standard deviations from the meanshould occur only about 0.27% of the time (roughly once every 370observations).
I In practice, they occur far more frequently (see the next severalslides).
I Normality is of limited use in estimating tail risk.
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S&P 500 Returns: 1950-2015
No of Observations: 16,360 Period: 3-Jan-1950 to 8-Jan-20153 Std Dev 4 Std Dev 5 Std Dev 6 Std Dev
Actual No. Beyond 225 93 44 26 Theoretical No. Beyond 44.2 1.04 0.009 0.00003 Actual/Theoretical 5.09 89.74 4,691.2 805,424
No of Observations: 16,360 Period: 3-Jan-1950 to 8-Jan-20153 Std Dev 4 Std Dev 5 Std Dev 6 Std Dev
Actual Freq (Days) 73 176 372 629 Theoretical Freq (Days) 370.4 15,787.2 1,744,278 506,797,317 Theoretical/Actual 5.09 89.74 4,691.2 805,424
I Thus, for example, observations 4 standard deviations from the mean occurredroughly once every seven months, 89.7 times more frequently than predicted bynormality of once every 62.6 years.
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S&P 500 Returns: 1950-2015
No of Observations: 16,360 Period: 3-Jan-1950 to 8-Jan-20153 Std Dev 4 Std Dev 5 Std Dev 6 Std Dev
Actual No. Beyond 225 93 44 26 Theoretical No. Beyond 44.2 1.04 0.009 0.00003 Actual/Theoretical 5.09 89.74 4,691.2 805,424
No of Observations: 16,360 Period: 3-Jan-1950 to 8-Jan-20153 Std Dev 4 Std Dev 5 Std Dev 6 Std Dev
Actual Freq (Days) 73 176 372 629 Theoretical Freq (Days) 370.4 15,787.2 1,744,278 506,797,317 Theoretical/Actual 5.09 89.74 4,691.2 805,424
I Thus, for example, observations 4 standard deviations from the mean occurredroughly once every seven months, 89.7 times more frequently than predicted bynormality of once every 62.6 years.
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S&P 500 Returns: 1950-2007No. of Observations: 16,081
3 Std Devs 4 Std Devs 5 Std Devs 6 Std DevsActual No. Beyond 223 90 43 26 Theoretical No. Beyond 43.4 1.02 0.009 0.00003 Actual/Theoretical 5.14 88.3 4,664 819,397
No. of Observations: 14,4633 Std Devs 4 Std Devs 5 Std Devs 6 Std Devs
Actual No. Beyond 129 41 19 10 Theoretical No. Beyond 39.0 0.92 0.008 0.00003 Actual/Theoretical 3.30 44.8 2,291 350,410
No. of Observations: 16,081Frequency (Days) 3 Std Devs 4 Std Devs 5 Std Devs 6 Std DevsActual frequency (days) 72.11 178.68 373.98 618.50 Theoretical frequency (days) 370.4 15,787.19 1,744,278 506,797,332 Theoretical/Actual 5.14 88.4 4,664 819,397
No. of Observations: 14,463Frequency (Days) 3 Std Devs 4 Std Devs 5 Std Devs 6 Std DevsActual frequency (days) 112.12 352.76 761.21 1,446.30 Theoretical frequency (days) 370.4 15,787.19 1,744,278 506,797,332 Theoretical/Actual 3.30 44.8 2,291 350,410
Period: 3-Jan-1950 to 3-Dec-2013
Period: 3-Jan-1950 to 30-Jun-2007
Period: 3-Jan-1950 to 3-Dec-2013
Period: 3-Jan-1950 to 3-Dec-2013
No. of Observations: 16,0813 Std Devs 4 Std Devs 5 Std Devs 6 Std Devs
Actual No. Beyond 223 90 43 26 Theoretical No. Beyond 43.4 1.02 0.009 0.00003 Actual/Theoretical 5.14 88.3 4,664 819,397
No. of Observations: 14,4633 Std Devs 4 Std Devs 5 Std Devs 6 Std Devs
Actual No. Beyond 129 41 19 10 Theoretical No. Beyond 39.0 0.92 0.008 0.00003 Actual/Theoretical 3.30 44.8 2,291 350,410
No. of Observations: 16,081Frequency (Days) 3 Std Devs 4 Std Devs 5 Std Devs 6 Std DevsActual frequency (days) 72.11 178.68 373.98 618.50 Theoretical frequency (days) 370.4 15,787.19 1,744,278 506,797,332 Theoretical/Actual 5.14 88.4 4,664 819,397
No. of Observations: 14,463Frequency (Days) 3 Std Devs 4 Std Devs 5 Std Devs 6 Std DevsActual frequency (days) 112.12 352.76 761.21 1,446.30 Theoretical frequency (days) 370.4 15,787.19 1,744,278 506,797,332 Theoretical/Actual 3.30 44.8 2,291 350,410
Period: 3-Jan-1950 to 3-Dec-2013
Period: 3-Jan-1950 to 30-Jun-2007
Period: 3-Jan-1950 to 3-Dec-2013
Period: 3-Jan-1950 to 3-Dec-2013
I Even before 2007, changes of more than 4 standard deviations from the meanwere 45 times more likely in reality than predicted by normality.
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USD-EUR Exchange Rates: 2004-2011
No of observations: 20853 Std Dev 4 Std Dev 5 Std Dev
Actual Number Beyond 24 4 1Theo Number Beyond 5.6 0.13 0.0012Actual/Theoretical 4.3 30.3 836.6
No of observations: 10423 Std Dev 4 Std Dev 5 Std Dev
Actual Number Beyond 1 0 0Theo Number Beyond 2.8 0.07 0.0006Actual/Theoretical 0.36 0 0
No of observations: 10433 Std Dev 4 Std Dev 5 Std Dev
Actual Number Beyond 23 4 1Theo Number Beyond 2.8 0.07 0.0006Actual/Theoretical 8.17 60.5 1672.4
Period: 1-Jan-2008 to 31-Dec-2011
Period: 1-Jan-2004 to 31-Dec-2007
Period: 1-Jan-2004 to 31-Dec-2011
I Changes of > 4 standard deviations from the mean are 30 times more likely thanpredicted by normality.
I But . . .
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Crude Oil Changes: WTI
I WTI crude: 2005-2015
No of observations: 2,518 Period: Jan 3, 2005 to Jan 5, 20153 Std Dev 4 Std Dev 5 Std Dev
Actual No. Outside 43 22 7 Theoretical No. Outside 6.80 0.16 0.001 Actual/Theoretical 6.32 137.5 4,861
I WTI crude: 2012-15
No of observations: 757 Period: Jan 3, 2012 to Jan 5, 20153 Std Dev 4 Std Dev 5 Std Dev
Actual No. Outside 11 2 2 Theoretical No. Outside 2.04 0.05 0.0004 Actual/Theoretical 5.39 41.7 4,608
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Others
I Copper: 2008-13
No of Observations: 15153 Std Dev 4 Std Dev 5 Std Dev
Actual Number Beyond 17 4 1Theo Number Beyond 4.09 0.1 0.0009Actual/Theoretical 4.2 41.7 1151.3
No of Observations: 7563 Std Dev 4 Std Dev 5 Std Dev
Actual Number Beyond 3 0 0Theo Number Beyond 2.04 0.1 0.0004Actual/Theoretical 1.5 0.0 0.0
Period: 1-Jan-2008 to 31-Dec-2013
Period: 1-Jan-2011 to 31-Dec-2013I Brent crude: 2006-2012
No of Observations: 17983 Std Dev 4 Std Dev 5 Std Dev
Actual no beyond 17 7 1Theoretical no beyond 4.9 0.114 0.001Actual/Theoretical 3.5 61.5 970.1
Period: 1-Jan-2006 to 18-Dec-2012
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Non-Normality
I The non-normality of equity returns has been documented at least since1965.
I Non-normality is also reflected in implied volatilities obtained from optionprices.
I Normality is mainly useful as a benchmark; other distributions maycapture tail-risk better:
I Students t.I Jump-diffusions.I Cornish-Fisher.I Others.
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Comment 4: Historical Behavior
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50.00
100.00
150.00
200.00
250.00
300.00
350.00
400.00
450.00
500.00
1/2/98 1/2/01 1/3/04 1/3/07 1/3/10 1/3/13
Tech Stocks
Fin Stocks
Tech: CSCO + INTC + MSFT Fin: C + JPM + MS
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The Material to Follow
I Derivatives and their role in risk-management:
I Futures & Forwards.I Options.I Swaps.I Credit derivatives.
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Si tacuisses, philosophus mansissesor: Beware of geeks bearing formulae. (Warren Buffet, 2009)
I Alan Greenspan, Federal Reserve Chairman, in 2004:
Not only have individual financial institutions become lessvulnerable to shocks from underlying risk factors, but also thefinancial system as a whole has become more resilient.
I Joseph Cassano of AIG Financial Products in August 2007:
It is hard for us, without being flippant, to even see a scenariowithin any kind of realm of reason that would see us losing $1in any of those transactions,
I Robert Lucas, Nobel Laureate in Economics, in 2003:The central problem of depression-prevention has been solved.
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Introduction