finance: risk management - inriver.bwl.uni-muenchen.de · ordering axiom: the decision maker can...

Institute for Risk Management and Insurance

Part I:

Petra [email protected]

Winter 2010/2011

Finance: Risk Management

mailto:[email protected]


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Course Outline – Block I (Steinorth)

Module I: Introduction and Review

Module II: Optimal Risk Sharing and Diversification

Module III: Reasons for Risk Management

Module IV: Insurance and Incentive Problems

Petra Steinorth Finance: Risk Management


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Course Outline – Block II & III (Rudolph, Elsas)

Block II: Market Risk:

Overview

VaR-Methods I

VaR-Methods II

Hedging

Block III: Credit Risk:

Probability of Default /Rating

Asset-/Default-Correlation

Credit-Portfolio Models

Credit Derivatives / Controlling



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Organizational issues

Contact:

Petra Steinorth [email protected]

Office hours: Tuesday 10:00 a.m. – 12:00 p.m.


mailto:[email protected]


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Course materials

Important information and course materials can be found at

http://www.inriver.bwl.lmu.de

Lehre Winter 2010/2011 Master und Doktorandenveranstaltungen

Finance : Risk Management

The password for protected files will be announced in the lecture.


http://www.inriver.bwl.uni-muenchen.de/

http://www.inriver.bwl.uni-muenchen.de/


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Organizational issues

• Class times

Monday 4 – 8 p.m., HGB E 216

Thursday 12 – 2 p.m., HGB A 016

• Usually (not always) Monday will be the review/exercise/case study

session and Thursday will be the lecture session



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ClassLecture(hours)

Tutorial(hours) ECTS

Cycle

Finance: Risk Management (E) 2 4 9 Summer

Insurance Economics (E) 2 2 6 Winter

Projektkurs Versicherungsmanagement(G)

n.a. n.a. 12 Winter

Versicherungstechnik (G) 2 3 Summer

Reinsurance (E) 2 3 Summer

Introduction to Insurance 2 3 Summer

Other events of interest: INRIVER Brownbag Seminar

http://www.inriver.bwl.lmu.de/forschung/brownbag/index.html

Research Seminar on Management & Microeconomics

http://www.inriver.bwl.lmu.de/forschung/seminar_mm/index.html

Masters level classes offered at the Institute for Risk Management & Insurance

http://www.inriver.bwl.lmu.de/forschung/brownbag/index.html

http://www.inriver.bwl.lmu.de/forschung/seminar_mm/index.html


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M&M seminar

Seminar room 307,

Schackstraße 4 / III. OG

Time: Thursday, 5:00 –

6:30pm



Definition and classifications of risk

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Speculative Risk

describes a situation in which there

is a possibility of loss but also a

possibility of gain.

Examples:

• Gambling

• Stock market investments

• Annual profit or loss of a company

Pure Risk

Describes a situation in which there is

only the possibility of a loss, i.e. the

possible outcomes are either loss or no-

loss.

Examples:

• Personal risks: loss of income or

assets

• Property risk: destruction, stealth

or damage of property

• Liability risk

• Risks arising from failure others

Risk can defined as the possibility of a (positive or negative) deviation from the expected

outcome.

(Ambivalent risk definition)



Risk management

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Risk management instruments

Risk management [in the traditional sense] is a scientific approach to dealing with pure

risk by anticipating possible accidental losses and designing and implementing procedures

that minimize the occurrence of loss or the financial impact of the losses that do occur.

(Vaughan/Vaughan 2003)

Risk control:

• Risk avoidance

• Risk reduction

Risk financing:

• Risk retention(active or passive)

• Risk transfer (e.g. to an insurer



Typology of risks faced by a firm

Market risk: Changes in market prices may reduce the firm's value.

• Components that can be distinguished are interest rate risk, currency risk, commodity risk etc.

Credit risk: A change in the credit quality of a counterparty may affect the value of a firm.

• e.g. default risk: extreme case, where a counterparty is unable or unwilling to fulfill it's

contractual obligations.

Liquidity risk: Typically separated into “funding” and “trading-related” liquidity risk.

• “Funding liquidity risk” relates to the ability of a firm to raise necessary funds.

• “Trading-related liquidity risk” is the risk that a firm can not execute a transaction because of

missing “appetite” on the demand side of the market.

12Petra Steinorth Finance: Risk Management


Typology of risks faced by a firm

Operational risk: Refers to potential losses resulting from e.g. management failure,

fraud, human errors and inadequate systems.

Legal and Regulatory risk:

• Legal risks usually become apparent when a counterpart is sued or sues the firm.

• Regulatory risks are potential changes in law affecting the institution in one way or the other.



(Enterprise) Risk Management as a business function

Risk management as a business function

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Enterprise Risk Management (ERM) brings together all the management of all risks into a

single portfolio. ERM includes managing speculative and pure risks simultaneously.

(Vaughan/Vaughan 2003)

ERM is the discipline by which an organization in any industry assesses, controls, exploits,

finances, and monitors risks from all sources for the purpose of increasing the

organization’s short- and long-term value to its stakeholders.

(Casualty Actuarial Society 2003)

General Management

Enterprise Risk Management

Risk Management (traditional sense)

Insurance Management



Risk management process

1. Determination of objectives

“The primary objective of risk management is to prevent the operating effectiveness of the

organization, […]” (Vaughan/Vaughan 2003)

2. Identification of all significant risks

3. Evaluation of potential frequency and severity of risks

Getting information on the probability distribution of risks

4. Development and selection of methods for managing risks

5. Implementing the risk managements methods chosen

6. Monitoring performance and suitability of risk management methods and strategies on an

ongoing basis



Components:

• Action space /

Decision space : Set of all risky alternatives

• State space : Set of all potential and relevant

states

• Outcome space : Set of all possible outcomes

• Outcome function : maps every possible combination

to an outcome f(a,s)=z

},{ 1 naaA

),,( 1 mssS

},,{ ,1,1 mnzzZ

ZSAf →:

SsAasa ∈∈ , ),,(

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Expected utility theory – A basic model


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Expected utility principle


A decision maker has a strictly increasing, bounded utility function u, defined on

the set of possible outcomes Z (Bernoulli utility function).

The decision maker’s preferences over probability distributions with values in Z

are represented by the expected value of the outcomes’ utility (expected utility).

In other words: The decision maker chooses the action that

maximizes expected utility


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i. Ordering Axiom:

The decision maker can order all possible actions, i.e. a complete weak

preference relation exists over A. For any three random variables

it holds that

(Comparability, Completeness)

(Transitivity)

212121~~~~~~~a) zzzzzz

313221~~~~~~b) zzzzzz ⇒

321~,~,~ zzz

ii. Continuity Axiom:

For any set of outcomes with , there is a

probability such that z2 ~ }{ 31 zpzp

321 zzz

Expected utility axioms

321 ,, zzz


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Expected utility axioms

iii. Independence Axiom:

Given two random variables and such that

Let be another random variable and let p be an arbitrary probability

with

Then it holds that

.~)(~21 z z

)1,0(p

3231~~)(~~ z pzz p z

1~z 2

~z

3~z



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Expected utility theorem

Note

• The expected utility theorem (among other things) provides the existence of

the utility function.

• Obtaining a Bernoulli’s utility function can be a challenging task in a real life

situation.


Suppose a preference relation satisfies axioms i), ii) and iii). Then a utility

function u exists such that the preference relation has a representation of the

expected utility form (in particular this implies the decision rule: maximize the

expected utility).

The so called Bernoulli utility function u is unique except for positive linear

transformations.


• A risk-averse decision maker prefers a certain payment to a (non-trivial) lottery with an

expected value equal to the certain payment, i.e.

(Note: Risk aversion does not mean that a decision maker avoids every risk)

• In the expected utility context this translates to

From the Jensen Inequality we know:

If and only if u(·) is a strictly concave function, for any (non-trivial)

random variable .

A decision maker is risk-loving if and only if

risk-neutral if and only if

for every random result .


Bernoulli utility functions and risk attitudes

zzE ~)~(

))~(())~(( zuEzEu

))~(())~(( zuEzEu

z~

))~(())~(( zuEzEu

))~(())~(( zuEzEu

z~


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• Linear utility functions imply risk-neutrality

for instance

• (Strictly) convex utility functions imply a risk-loving attitude

for instance

• (Strictly) concave utility functions imply risk-aversion

for instance


zzu 5.210)(1

0z ,)( 2

2 zzu

0z ,)(3 zzu



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u(z)

z

u2(z)

u3(z)

u1(z)

strictly convex

linear

strictly concave

0u

0u

0u

0u


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Certainty equivalent and risk premium

• The certainty equivalent c of a lottery is the amount of money for

which the individual is indifferent between the lottery and the certain

amount.

i.e.

• The risk premium rp is defined as the difference between the

expectation and the certainty equivalent of a lottery.

i.e.

))~(()( zuECu

Risk-aversion implies:

)]~[( zEu


)))~((())~(()( 1 zuEuCzuECu

CzErp )~(

)~(zEC 0 rp


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State-by-state dominance

s1 s2 s3

A 10 4 7

B 7 1 6


Lottery A is state-by-state dominant over lottery B, if A yields a better outcome

than B in every possible state of nature.

Example:


First-order stochastic dominance (i)

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Lottery A first-order stochastically dominates B, if for any outcome z the likelihood

of receiving an outcome equal to or better than z is greater under A than under B.


Distribution function FA(·) has first-order stochastic dominance over

distribution function FB(·) ( ) if and only if

for all with for some)z(F)z(F BA ].,[z 10

)z(F)z(F BA

],[z 10

)(F)(F BFSDA


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First-order stochastic dominance (II)

z

)z(F

maxz

1

BF

AF

)(F)(F BFSDA



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Example

First-order stochastic dominance (III)

EUR

50

40

30

20

10

Likelihood

(Lottery B)

0

0.5

0

0

0.5

Likelihood

(Lottery A)

0.5

0

0.25

0.25

0

10 20 30 40 50

F(z)

1

0,75

0,5

0,25

0

EUR



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First-order stochastic dominance (IV)

• If distribution A first-order stochastically dominates B, any expected utility

maximizing individual with positive marginal utility will prefer A to B.

First-order stochastic dominance theorem:

and )()( BFSDA FF .0 uEuEu BA



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Second-order stochastic dominance (I)

Distribution function FA(·) second-order stochastically dominates

FB(·) ( ) if FB(·) is a mean-preserving spread of FA(·).)(F)(F BSSDA

Example

EUR

40

30

20

10

Likelihood

(Lottery A)

0

0.5

0.5

0

Likelihood

(Lottery B)

0.25

0.25

0.25

0.25

F(z)

1

0,75

0,5

0,25

020 30 40 EUR10 30 40 EUR



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Second-order stochastic dominance (II)

• Any risk averse individual prefers A to B, if B is a mean-preserving spread of A.

Second-order stochastic dominance theorem:

and )()( BSSDA FF .0,0 uEuEuu BA


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