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Institute for Risk Management and Insurance
Part I:
Petra [email protected]
Winter 2010/2011
Finance: Risk Management
Institute for Risk Management and Insurance
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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
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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.
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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.
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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
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M&M seminar
Seminar room 307,
Schackstraße 4 / III. OG
Time: Thursday, 5:00 –
6:30pm
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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)
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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
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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.
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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.
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(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
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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
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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
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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.
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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.
Institute for Risk Management and Insurance
• 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 .
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Bernoulli utility functions and risk attitudes
zzE ~)~(
))~(())~(( zuEzEu
))~(())~(( zuEzEu
z~
))~(())~(( zuEzEu
))~(())~(( zuEzEu
z~
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Bernoulli utility functions and risk attitudes
• 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
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zzu 5.210)(1
0z ,)( 2
2 zzu
0z ,)(3 zzu
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Bernoulli utility functions and risk attitudes
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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
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)))~((())~(()( 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
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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:
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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.
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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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