1. introduction to risk management

Risk Management: Introduction

Rangarajan K. Sundaram

Stern School of BusinessNew York University

TRIUM Global EMBA ProgramNew York: January 16-20, 2015

Risk & its Management 1 cRangarajan K. Sundaram

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.


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,. . .


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.


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, . . .


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.


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.


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.


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.


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.


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.


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?


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).


The Normal Distribution

-5 -4 -3 -2 -1 0 1 2 3 4 5

x Xc

x

Probability of observa7on < x


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


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


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.


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%


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


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.


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.


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







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 30-Jun-2007



I Even before 2007, changes of more than 4 standard deviations from the meanwere 45 times more likely in reality than predicted by normality.


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


Actual Number Beyond 1 0 0Theo Number Beyond 2.8 0.07 0.0006Actual/Theoretical 0.36 0 0






I Changes of > 4 standard deviations from the mean are 30 times more likely thanpredicted by normality.

I But . . .


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


Others

I Copper: 2008-13

No of Observations: 15153 Std Dev 4 Std Dev 5 Std Dev





Period: 1-Jan-2011 to 31-Dec-2013I Brent crude: 2006-2012


Actual no beyond 17 7 1Theoretical no beyond 4.9 0.114 0.001Actual/Theoretical 3.5 61.5 970.1



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.


Comment 4: Historical Behavior

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50.00

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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


The Material to Follow

I Derivatives and their role in risk-management:

I Futures & Forwards.I Options.I Swaps.I Credit derivatives.


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.


Introduction

1. introduction to risk management

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