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## INTRODUCTION TO RISK MANAGEMENT

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**Defense Resources Management Institute**Naval Postgraduate School Monterey, California INTRODUCTIONTORISK MANAGEMENT**Arabic - Fortuitous and favorable.**Greek - Fortuitous and neither favorable nor unfavorable. Latin (risicum) - the challenge that a barrier reef presents to a sailor. French (risque) - mainly negative connotation, but sometimes positive. Oxford Dictionary - “... the chance of hazard, bad consequences, loss, etc....” DEFINITIONS I**Economic risk - the chance of loss due to ….**Business risk - the chance ofloss associated with … Market risk - the chance that a portfolio of investments can lose money because….. Inflation risk - the danger that a general increase in prices ... Interest-rate risk - market risk due to interest rate fluctuations Credit risk - the chance that of a default on a loan ... Liquidity risk - the difficulty in selling a fixed asset ... Derivative risk - the chance of financial loss due to increased volatility …. Cultural risk - the chance of loss because of product market ….. DEFINITIONS II CHANCE Random Occurrence BAD CONSEQUENCE Sense of Loss Hirschey & Pappas, Fundamentals of Managerial Economics Dryden Press, 1998**A**LITTLE BIT OF PROBABILITY**PROBABILITY**• It’s a number – it’s JUST A NUMBER! • It’s a number between 0 and 1 (0 ≤P≤1) • It quantifies the likelihood of an event • It’s a function of experience, judgment, subjective assessment, available data • It’s uses all information you think is relevant to the determination of the likelihood of occurrence of an event**Probability Rules**• Probability = 0 if “never/impossible” • Probability = 1 if “always/certain” • If we are collectively exhaustiveand • mutually exclusive then the probabilities over the outocmes SUM to 1.**If mutually exclusivethen :**P(A or B) = P(A) + P(B) If independent : P(A and B) = P(A) x P(B) Probability Rules**Probability from Data**• Given data we can always derive approximate probabilities using relative frequency. • Relative frequency can be used as an estimate of the probability of the observed value • Taken all together, these can represent the underlying PROBABILITY DISTRUBUTION FUNCTION**Frequency Table**How Big? How Many?**Relative Frequency Table**How Big? How Many?**Relative Frequency Histogram**0.50 0.474 0.45 0.40 0.35 0.30 0.240 0.25 0.20 0.158 0.15 0.10 0.065 0.05 0.038 0.020 0.004 0.001 0.00 [1.5 - 2.5) [2.5 - 3.5) [3.5 - 4.5) [4.5 - 5.5) [5.5 - 6.5) [6.5 - 7.5) [7.5 - 8.5) [8.5 - 9.5)**Prob. of an event = proportion of observations that**corresponds to the event = percent of observations that corresponds to the event = portion of area of histogram that corresponds to the event**AN INVESTMENT DECISION**• Planning for retirement • Two options for investment • Each has a track record, the historical rates-of-return over a specified time period • Each can be used to compute various statistics; e.g., average rate-of-return, etc.**AN INVESTMENT DECISION**Expected Value Std. Dev. Variance A1 5.00% 1.25% 1.5625 A2 5.70% 2.75% 7.5625**r**n n r**What’s the likelihood of**? r < 0 I don’t want a rate of return < 0! I want a rate of return > 0! What’s the likelihood of ? r < 0**The relative frequency histogram over the outcomes contains**allrelevantinformation. This information allows us to quantify risk. This is provides our most powerful tool for risk management. THE FREQUENCY HISTOGRAM( The “KEY to it ALL’’ )**A**QUANTITATIVE DEFINITION OF RISK**A QUANTITATIVE DEFINITION OF RISK**Risk is a COMBINATION of the answers to three questions: (1) “What can go wrong?” (2) “How likely is it to go wrong?” (3) “If it does go wrong, what are the consequences?” Adapted from S. Kaplan and B. John Garrick, “On the Quantitative Definition of Risk”, Risk Analysis, Vol.1, no.1, 1981**EXAMPLE: Hinterland Illegal Immigration**recession; depression; economic collapse What can go wrong? chances are 1 in a 10; a 10% chance; PF = .10 How likely is it to go wrong? large numbers of illegal immigrants ; increasing crime; failing social services; social unrest; If it does go wrong, what happens to Drmecia?**A QUANTITATIVE DEFINITION OF RISK**What can go wrong? Future scenario F How likely is it to go wrong? PF Probability of F If it does go wrong, what are the consequences? Y Result due to F**THE ANSWER TO THE FIRST QUESTION**1. It all starts with the future scenario, F. 2. The F is uncertain so we need probability, PF. 3. F causes a result, an outcome of concern, Y. 4. Y is a function of F. We need to know this relation! The relation between Y and F is uncertain!!!**BEGINNING – MIDDLE – END**F→ X → Y F1 F2 F3 … FK Y1 Y2 Y3 … YN THE “SYSTEM” X1 then X2 then….. XM F1, F2,… → X1 thenX2 then… → Y1, Y2,…**F**= EXAMPLE: Hinterland Illegal Immigration Illegal immigration is proportional to the ratio of per capita GDP. GDPD/popD GDPH/popH Y illegal immigration = G. H. Hanson (2009), “The Economics and Policy of Illegal Immigration in the U.S.”, Washington, D.C.: Migration Policy Institute**THE ANSWER TO THE SECOND QUESTION**PF PY THE “SYSTEM” X1 then X2 then….. XM Probability Distribution for Outcomes of Interest Probability Distribution for Future Scenarios → Math Model→ SIMULATION MODELING**THE ANSWER TO THE THIRD QUESTION**What number of illegal immigrants do you most want to avoid? 10000; 100000; 1000000; 10000000; 20000000. HOW YOU FEEL (about the possible Y) = PREFERENCE What outcome do you most prefer to avoid: minor economic strain; substantial strain; or collapse of government social/educational services?**THE ANSWER TO THE THIRD QUESTION**1. It all starts with the future scenario, F. 2. The F is uncertain so we need probability, PF. 3. F causes a result, an outcome of concern, Y. 4. Y is a function of F. GivenPFwe can derivePY 5. How do you feel about the probable outcomes? Do you prefer to avoid some Y more than other Y?**Preferences < = > value function< = > v(Y)**(1) v(Y) > 0 if Y is “good” (2) v(Y) < 0 if Y is “bad” Value Function Charcteristics reference point [defining GAINS from LOSSES] (2) loss aversion [losses MORE IMPORTANT than GAINS] (3) decreasing marginal values THE ANSWER TO THE THIRD QUESTION**Reference Point**v(Y) Gains ( +) concave Illegal Immigration Losses ( - ) convex**A QUANTITATIVE DEFINITION OF RISK**1. It all starts with the future scenario, F. 2. The F is uncertain so we need probability, PF. 3. F causes a result, an outcome of concern, Y. 4. Y is a function of F. Given PF we can derivePY 5. Your preference info, v(Y), is the LAST PIECE! defines the consequences!**Probability**Distribution (Outcome) Decision Maker Preferences AND PY v(Y) AND AND**PF**F g(F) g(F) PY Y v(Y) Risk Hinterland Economy Collapse Prob. of Economic Collapse Prob. Dist. Illegal Immigrants Number of Illegal Immigrants How does Drmecia “feel” about the Y?**SPECIAL CASE OF PREFERENCE**v(Y) Y**SPECIAL CASE OF PREFERENCE**v(Y) Y “I can’t bear the thought of experiencing loss! “ In the limit the weight we assign to all outcomes <=> a loss tends to -∞. In this case risk is very simple to quantify risk. “Experiencing loss would be a catastrophe!”**ASSESSING THE RISK**PY 0.1 0.3 0.9 0.4 0.5 1.0 0.8 0.6 0.7 0.2 - + v(Y)**ASSESSING THE RISK**PY 0.1 0.3 0.9 0.4 0.5 1.0 0.8 0.6 0.7 0.2 v(Y)**ASSESSING THE RISK (SPECIAL CASE)**RISK = P{ Y correspond to loss } RISK = P{ Y ≥ reference point } RISK = P{ unacceptable Y } RISK = P{ Y you prefer to avoid }**Who uses this stuff?.......**OVERALL C-RATING System for Readiness: C-1 = MAE > 89% P{not capable} ≤ 0.11 C-2 = MAE 80-89% 0.11 ≤ P{not capable} ≤ 0.20 C-3 = MAE 70-79% 0.21 ≤ P{not capable} ≤ 0.30 C-4 = MAE 50-69% 0.31 ≤ P{not capable} ≤ 0.50 C-5 = MAE < 50% 0.50 ≤ P{not capable} Senate Armed Services Committee, terminology used in arguments before the committee, Feb. 1997 AR 220 – 1 (2010), AFI 10-201 (2006), SORTS (US Department of Defense)**A**QUANTITATIVE APPROACH TO RISK MANAGEMENT**1950 B.C. – Code of Hamurabi – formalization of bottomry**contracts containing a risk premium for chance of loss of ships and cargo. 750 B.C. – Greece – the use of bottomry contracts. 1285 A.D. – King Edward - forbids use of soft coal in kilns to manage air pollution in London. 1583 A.D. – 1st life insurance policy issued in England. 19th and 20th century – water and garbage sanitation, building codes, fire codes, boiler inspections, railroads, steamboats, autos. 1959 A.D. – H. Markowitz, stock portfolio diversification. The History of Risk Management**RISK MANAGEMENT PROCESS**What can go wrong F? What is F and PF? Identify Risks Assess Risks What are the outcomes [Y, and PY]? What are the consequences, v(Y)? What is the risk [quantified]? Prevent Mitigate Negotiate Implement Monitor Management Action**Prevention.**Mitigation. Hedging. Diversification. Tools of Risk Management**ASSESSING THE RISK**Definition depends on a reference point. National policy often specifies a reference point. Not everyone has the same reference point. THE RISK CURVE Why not plot P{ Y ≥ y* } versus y*, for any y* ?**theoretical derivation**direct assessment simulation Determining theOutcomeDistribution Generating your own data**Number of**earthquakes Size of earthquake Earthquake cost VARIABLE Cost per Total cost earthquake Program Cost FIXED Earthquake policy EARTHQUAKES