bepp 305 805 lecture 1

BEPP 305/805:

Risk Management, Lecture 1 Professor Jeremy Tobacman

January 16, 2014

Goals

• Individuals and firms face risks in nearly all decisions that they make.

• Provide an introduction to decision making in a world with uncertainty. ▫ How should individuals, and managers of firms, make

decisions involving risk?

▫ What are the typical mistakes made in decisions involving risk?

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Why study risk management?

• As an individual, you face risks in many aspects of your life.

• Managers of firms make many decisions that involve risks, and the consequences can be large.

• A lesson from the recent financial crisis: the failure to properly manage risk can result in disaster.

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Lessons from the financial crisis

“The crisis spurred a remarkable degree of reflection and activity throughout the community. The unifying theme is a focus on risk management: the risks of a particular product or financial service, the risks to a firm, and the systemic risks to society as a whole.” - Retiring HBS Dean Jay Light on the recent developments in the curriculum

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“I believe that a CEO must not delegate risk control. It’s simply too important… ”

– Warren Buffet

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"Named must your fear be before banish it you can.“

– Yoda

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Structure of the course

1. Optimal decision making under risk (Tobacman)

2. Barriers to risk management (Wang)

3. Corporate risk management (Nini)

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Module I in one slide

• Why is it important to account for risks?

• How is risk measured in practice?

• What is the optimal way to make decisions under risk?

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Module II in one slide

• Barriers to risk management

• Market impediments

▫ Information and incentive problems

• Psychological impediments

▫ People don’t always behave optimally

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Module III in one slide

• Corporate risk management

▫ When firms SHOULD NOT manage risk

▫ When firms SHOULD manage risk

▫ Strategies for corporate RM

▫ Managing liability risk

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Overview of the syllabus

• Course structure and requirements

• Prerequisites

• Course grading

• Policies for dropping/withdrawing

• Expectations

• Policies for exams

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Grading

• Three exams, one for each module.

• Problem sets, posted on Canvas

▫ Work in teams but write your own solutions ▫ Graded on a complete/incomplete system ▫ You can skip turning in one problem set with no penalty ▫ Module I due dates: 1/24, 1/31, 2/7 at 5:00pm

• Survey questions will also be posted on Canvas

• Problem sets and survey answers are worth 10% of your

grade

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Slides and notes

• Slides will be posted on Canvas

• Notes summarizing certain aspects of the course material will be posted on Canvas periodically, generally after the material is covered in class

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One slide study guide

• Primary resources:

▫ Lectures

▫ Notes posted to Canvas

▫ Problem sets

• Readings are intended to be references

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About me

• Assistant Professor in BEPP since 2008

• Ph.D. in Economics from Harvard

• Research on household finance for the poor

▫ Consumer credit in the US

▫ Microinsurance against rainfall risk in India

▫ Behavioral economics

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My info

• Office: 1409 SH-DH

• Email: tobacman@wharton.upenn.edu

• Office hours: Tuesdays 4:30-5:30pm or by appt

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TAs for the course

• Banruo (Rock) Zhou

▫ banruo@wharton.upenn.edu

• Ella Zhang

▫ zhq@sas.upenn.edu

• Neil Iyer

▫ neiliyer@wharton.upenn.edu

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Practice Sessions

• Neil (1/21 & 2/4) - 4:30pm

• Rock (1/21 & 2/4) - 7:30pm

• Ella (1/22 & 2/5) - 4:30pm

• Attend the most convenient one

• Optional but awesome

• Rooms TBA

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Probability Theory

Rest of the lecture

1. Define what we mean by risk

2. Build up concepts of probability theory

3. Some methods for measuring risk

a. Variance as a measure of risk

b. Value at Risk

c. Mean-variance criterion

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An example

• A person retires at age 70, with a total of $1 million

• She expects to live for another 25 years

• How much can this person consume per year?

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An example

• A person retires at age 70, with a total of $1 million

• She expects to live for another 25 years

• How much can this person consume per year?

▫ Assume a real interest rate of 2% per year:

Approximately $50.22k per year

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Dollars remaining (in thousands)

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But, there is uncertainty!

• What if the person lives longer than 25 years?

• What if the interest rate falls?

• Calculations based on averages can be misleading

▫ Need to account for risk

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Another example

• A manager wants to estimate inventory costs for the business, based on inventory amount.

▫ If demand is lower than inventory: Unsold units spoil, entailing a $50 cost per unit.

▫ If demand exceeds inventory: Extra units must be air-freighted in, at a cost of $150 per unit.

• Monthly demand is, on average, 5,000 units per month.

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Understanding probabilities is crucial

• Given average monthly sales of 5,000, what are expected inventory costs if the manager decides to have monthly inventory of 5,000? • Zero?

• More than Zero?

• Cannot be determined? Source of this example: Harvard Business Review

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Understanding probabilities is crucial

• Expected inventory costs are greater than zero, if there is any variation in demand from month to month.

• Using averages can be very misleading!

• The appropriate method is to consider the whole probability distribution for demand, not just the average of the distribution.

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The “flaw of averages”

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One of many other examples

• In 1997, the U.S. Weather Service forecast that North Dakota’s rising Red River would crest at 49 feet.

• Official in Grand Forks made flood management plans using this single number, an average….

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One of many other examples

• In 1997, the U.S. Weather Service forecast that North Dakota’s rising Red River would crest at 49 feet.

• Official in Grand Forks made flood management plans using this single number, an average….

• The river crested above 50 feet, breaching the dikes.

• 50,000 people were forced from their homes, and there was $2 billion in property damage.

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What is risk?

• Very broadly, risk involves uncertainty

▫ Many possible outcomes

• Most decisions involve some degree of uncertainty

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Examples of risk

• Individuals

▫ Labor income, mortality, injuries, asset returns

• Firms

▫ Input costs, borrowing costs, demand, regulation

• Governments

▫ Unemployment, social security costs, business cycles, wars, commodity prices

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How can we model risk?

• Answer: Probability theory

• Provides us a way to think about what the most likely outcome is

• … and gives us a way to model the range of possible outcomes

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Some concepts

• Sample space

▫ Set of all possible things that can happen

• Probability distribution

▫ Relative chance that each state can occur

• Random variable

▫ Function that assigns outcomes to each state

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A simple example: a coin flip

• Sample space ▫ {H,T}

• Probability distribution

▫ {½, ½}

• Random variable, some examples ▫ X = Number of heads

X(H)=1. X(T) = 0

▫ Y = Number of tails Y(H)=0, Y(T) = 1

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Another example: two coin flips

• Sample space ▫ {HH, HT, TH, TT}

• Probability distribution

▫ {¼, ¼, ¼, ¼}

• Random variables ▫ X = number of heads

X(HH) =2, X(HT) = 1, X(TH) = 1, X(TT) = 0

▫ Y = proportion of heads Y(HH) = 1, Y(HT)= ½, Y(TH) = ½, Y(TT) = 0

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Probability distribution

Outcomes x1 x2 x3 x4 x5 x6

Pro

ba

bil

ity

p1

p2 p3

p4

p5

p6

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Properties of random variables

• Expected value

▫ Measure of the central tendency

• Variance and standard deviation

▫ Measures of dispersion

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Expected value (mean)

• Weighted average of outcomes

E X p1x1 p2x2 ... p

nxn

n

ii

xi

p

1

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Variance

• Expected squared deviation from the mean

2

222...

2211

XEXE

XEn

xn

pXExpXExpXVar

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Standard deviation

• Square root of the variance

▫ Same units as X  

SD X( ) = Var X( )

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Variance and SD as measures of risk

• Var and SD measure the expected dispersion

between outcomes and the average outcome

• Higher when ▫ Outcomes can deviate a lot from expected value ▫ Probability of extreme deviations is high

• Let’s think about whether these are good measures of risk

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Example

• Investment A

▫ $0 with probability 2/3

▫ $9M with probability 1/3

• Investment B

▫ $-5M with probability 0.2

▫ $5M with probability 0.8

• Which is the riskier investment?

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Example

• Profit from Investment A

▫ $0 with probability 2/3

▫ $9M with probability 1/3

• Profit from Investment B

▫ $-5M with probability 0.2

▫ $5M with probability 0.8

Mean = 3M Variance = 18𝑀2 Mean = 3M Variance = 16𝑀2

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Asymmetry

• Var and SD potentially measure risk, but they miss something:

• Large losses are “more risky” than large gains

• Extreme example

▫ Worst case scenario

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Another way to quantify risk

• Value at Risk (VaR)

• Question:

▫ What is the minimum loss under exceptionally bad outcomes?

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Value at Risk (VaR)

• Minimum loss in the bottom p% of outcomes

▫ Focus on the left tail of the distribution

▫ Usually 1% or 5% for a given time interval

Pro

ba

bil

ity

1%

2% 3%

5%

VaR at 10% is -4

7.5%

VaR at 1% is -10 VaR at 5% is -6

Profit -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20

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Example

• Profit from Investment A: ▫ -$1M with probability 0.1% ▫ $0 with probability 49.9% ▫ $2 with probability 50%

• Profit from Investment B:

▫ -$1 with probability 20% ▫ $1 with probability 80%

• Which investment is riskier?

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Example

• Profit from Investment A: ▫ -$1M with probability 0.1% ▫ $0 with probability 49.9% ▫ $2 with probability 50%

• Profit from Investment B:

▫ -$1 with probability 20% ▫ $1 with probability 80%

• Which investment is riskier?

VaR at 1% = $0 VaR at 5% = $0 VaR at 10%= $0 VaR at 1% = -$1 VaR at 5% = -$1 VaR at 10%= -$1

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Mean-Variance Criterion

• Balancing expected tendency and variance

• aE(X)-bVar(X)

▫ a>0, b>0

• An investment in X might be preferred to Y if:

▫ a[E(X)]-b[Var(X)] > a[E(Y)]-b[Var(Y)]

▫ What does this say?

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Mean-Variance Criterion

• Basis of Markowitz’s (1950) portfolio theory ▫ 1990 Nobel Prize ▫ Often used in practical applications

• Prior to Markowitz, portfolios were chosen on the basis of E(X) alone, without regard for Var(X)!

• We will study the properties of the mean-variance criterion later in the course

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Review of concepts: An example

• Random variable: damages from an automobile accident

Possible Outcomes for Damages Probability

$0 0.50

$200 0.30

$1,000 0.10

$5,000 0.06

$10,000 0.04

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Expected value

Possible Outcomes for Damages Probability

$0 0.50

$200 0.30

$1,000 0.10

$5,000 0.06

$10,000 0.04

EV = .5(0) + .3(200) + .1(1,000) + .06(5,000) + .04(10,000) = $860

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Variance

Possible Outcomes for Damages Probability

$0 0.50

$200 0.30

$1,000 0.10

$5,000 0.06

$10,000 0.04

Variance = .5(0-860)2 + .3(200-860)2 + .1(1,000-860)2

+ .06(5,000-860)2 + .04(10,000-860)2 = 4,872,400 ($2)

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Standard deviation

Possible Outcomes for Damages Probability

$0 0.50

$200 0.30

$1,000 0.10

$5,000 0.06

$10,000 0.04

SD = (Variance) 1/2 = (4,872,400)1/2 = 2,207 ($)

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Practical concerns

• Where do these probabilities come from?

• We need a way to translate past observations into probabilities

▫ Statistics

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Summary of today’s class

• Inference based on samples averages can be quite misleading

▫ Need to account for risk

• Probability theory allows us to model risks A measure of a typical observation (mean)

Measures of expected dispersion (variance and SD)

(Imperfect) measures of risk

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