Advanced Risk Management

Transcription

1 Winter 2012/2013 Advanced Risk Management Part I: Decision Theory & Risk Management Motives Lecture 1: Introduction & Review

2 Teaching Staff for Part I : Dr. Yunjie (Winnie) Sun sun@bwl.lmu.de Office hour: Tuesday 10am-12pm and by appointment Time & Location: Thursday 12-2pm, Professor-Huber-Platz 2, Lehrturm U104. Monday 4-8pm, Professor-Huber-Platz 2, Lehrturm U104. 1

3 Course Outline Part I (Sun) Part I Decision Theory and Risk Management Motives: Review of Decision Theory Optimal Risk Sharing and Diversification Reasons for Risk Management Insurance and Incentive Problems 2

4 Course Outline Part II & III (Glaser, Elsas) Part II: Part III: Market Risk: Overview VaR-Methods I VaR-Methods II Hedging Credit Risk: Overview/Introduction Probability of Default /Rating Asset-/Default-Correlation Credit-Portfolio Models Backup/Review Session 3

5 Course Outline Part I: Da te L/T Conte nt Re a dings Thu, pm L Introduction & Review GRAVELLE / REES (2004), Chap.17; EECKHOUDT / SCHLESINGER (2006); DOHERTY (2000) Chap. 2 Mon, pm L T Decision Theory Proofs and examples EECKHOUDT / SCHLESINGER (2006); KIMBALL (1990); PRATT (1964) Thu, pm L Optimal Risk Sharing & Diversification Arrow- Lind Theorem GRAVELLE / REES (2004), Chap. 19; FOLDES / REES (1977) Mon, pm L T Risk Management Motives Examples and applications STULTZ (2003), Chap. 2; DOHERTY (2000) Chap. 7, DOHERTY (2000), Chap. 7, STULTZ (2003), Chap. 3 Mon, pm Thu, pm L T L Insurance and Incentive Problems Case Study: "Ca ta strophe Risk Ma na ge me nt " Guest Lecture "S e c uritiza tion of Insura nc e Risk " DOHERTY(2000), Chap. 3 Uni Credit (2007); DOHERTY (2000), Chap.16; DOHERTY / RICHTER (2002) Mon, pm T Case Study: "Unite d Gra in Growe rs Ltd." Thu, pm T Case Study: "Insura nc e a nd Re pa ir Ma rke ts " NELL, RICHTER and SCHILLER (2009) Mon, pm T Review Assignment Questions & Answers 4

6 Course materials are available at Alternatively, Lehre Winter 2012/2013 Masterveranstaltungen Advanced Risk Management The password for protected files will be announced in the lecture. 5

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8 Institute for Risk Management and Insurance 7 7

9 Masters level classes offered at the Institute for Risk Management & Insurance Class Lecture (hours) Tutorial (hours) ECTS Cycle Advanced Risk Management (E) Winter Insurance Economics (E) Summer Projektkurs Versicherungsmanagement (G) n.a. n.a. 12 Winter Versicherungstechnik (G) 2 3 Summer Reinsurance (E) 2 3 Summer Principles of Risk Management and Insurance 2 3 Proseminar Aktuelle Entwicklungen in der Altervorsorge 2 3 Winter Other events of interest: MRIC Brownbag Seminar Research Seminar on Management & Microeconomics 8

10 Management & Microeconomics (M&M) Seminar Institute for Risk Management and Insurance Time & Venue: see Date Presenter (Affiliation) Title Wanda Mimra (ETH Zürich) "Reputation in Credence Goods Markets: Experimental Evidence" Ronald Klingebiel (Warwick Business School) "Anticipation or Agility? Creating Hits and Preventing Flops in Mobile Handset Innovation" Klaus Meyer (China Europe International Business School) "Multinational Enterprises from Emerging Economies" Kevin Boudreau (London Business School) tba Harris Schlesinger (University of Alabama) tba Andrei Hagiu (Harvard Business School) tba Pavlos Symeou (Cyprus University of Technology) tba Tyler Leverty (University of Iowa) tba Anna Krzeminska (Leuphana Universität Lüneburg) tba 9

11 Definition and classifications of risk Risk can be defined as the possibility of a (positive or negative) deviation from the expected outcome. (Ambivalent risk definition) 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 noloss. Examples: Personal risks: loss of income or assets Property risk: destruction, theft or damage of property Liability risk Risks arising from failure others 10

12 Risk management 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 management instruments Risk control: Risk avoidance Risk reduction Risk financing: Risk retention(active or passive) Risk transfer (e.g. to an insurer 11

13 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. 12

14 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. 13

15 (Enterprise) Risk Management as a business function Institute for Risk Management and Insurance 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) Risk management as a business function General Management Enterprise Risk Management Risk Management (traditional sense) Insurance Management 14

16 Risk management process 1. Determination of objectives The primary objective of risk management is to preserve the operating effectiveness of the organization, [ ] (Vaughan/Vaughan 2003) 2. Identification of all significant risks 3. Evaluation of potential frequency and severity of risks Gathering 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 15

17 Expected utility theory A basic model Components: Action space A a,, a ) : Set of all risky alternatives ( 1 m State space S { s1,1,, s n, m} : Set of all potential and relevant states Outcome space Z : Set of all possible outcomes Outcome function f : A S Z : maps every possible combination to an outcome f(a,s)=z 16

18 Decision matrix s 1 s 2 s m a 1 z 11 z 12 z 1. z 1m a 2 z 21 z 22 z 2. z 2m z.1 z.2 z.. z.m a n z n1 z n2 z n. z nm In this setup an action a j is represented by the associated outcome random ~ variable (or lottery ) z j (often also written as {(z j1, p 1 ),, (z jm, p m )} ) 17

19 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 18

20 Expected utility axioms 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 z ~ 1, z ~ 2, z~ it holds that 3 a) z~ z~ z~ ~ z ~ z~ z~ b) z~ z~ z~ z~ z~ z~ (Comparability, Completeness) (Transitivity) ii. Continuity Axiom: For any set of outcomes z with z1 z2 z 1, z2, z3 3, there is a probability p such that z 2 ~ z p } { 1 z3 19

21 Expected utility axioms iii. Independence Axiom: Given two random variables ~z and ~z 2 such that 1 z~ ( ) ~. 1 z 2 Let ~z 3 be another random variable and let p be an arbitrary probability with p (0,1) Then it holds that z ~ p z~ ( ) z~ p z ~

22 Expected utility theorem 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. 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. 21

23 Bernoulli utility functions and risk attitudes 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. E ( z ~ ) z~ (Note: Risk aversion does not mean that a decision maker avoids every risk) In the expected utility context this translates to u( E( z ~ )) E( u( z ~ )) From the Jensen Inequality we know: If and only if u( ) is a strictly concave function, random variable z ~. u( E( z ~ )) E( u( z ~ )) for any (non-trivial) A decision maker is risk-loving if and only if risk-neutral if and only if u( E( z ~ )) E( u( z ~ )) u( E( z ~ )) E( u( z ~ )) for every random result z ~. 22

24 Bernoulli utility functions and risk attitudes Institute for Risk Management and Insurance Linear utility functions imply risk-neutrality for instance u1( z) z (Strictly) convex utility functions imply a risk-loving attitude for instance 2 u2( z) z, z 0 (Strictly) concave utility functions imply risk-aversion for instance u3( z) z, z 0 23

25 Bernoulli utility functions and risk attitudes u 0 strictly convex u 0 linear u 0 strictly concave u 0 u(z) u 2 (z) u 1 (z) u 3 (z) z 24