We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byMaliyah Leyland
Modified about 1 year ago
Copyright © 2010 Lumina Decision Systems, Inc. Measures of Risk and Utility Analytica Users Group Gentle Intro to Modeling Uncertainty Webinar Series Session #4 20 May 2010 Lonnie Chrisman Lumina Decision Systems
Copyright © 2010 Lumina Decision Systems, Inc. Today’s Outline What is risk? (Expected) Utility Risk neutrality, risk aversion Utility of non-monetary outcomes Specific risk measures Uses of risk measures
Copyright © 2010 Lumina Decision Systems, Inc. Course Syllabus (tentative) Over the coming weeks: What is uncertainty? Probability. Probability Distributions Monte Carlo Sampling Measures of Risk and Utility (Today) Risk analysis for portfolios (risk management) Common parametric distributions Assessment of Uncertainty Hypothesis testing
Copyright © 2010 Lumina Decision Systems, Inc. What is Risk? A state of uncertainty where some outcomes are substantially undesirable. Considerations that some (but not everyone) see as inherent in the concept of risk: Involves outcomes that can be avoided or mitigated. Concerns deviation from expected value. Involves harm. Asymmetric – concerns bad outcomes only Concerns events not previously conceptualized as possibilities.
Copyright © 2010 Lumina Decision Systems, Inc. Risk-Return Tradeoffs Decisions often involve tradeoffs between expected benefit and level of risk. This implies a metric for quantifying risk.
Copyright © 2010 Lumina Decision Systems, Inc. Types of things that might be at risk Money Property Lives (risk of death) Shortening of lifespan Physical well-being ( risk of injury, pain ) Emotional well-being Reputation Power or influence Health of the planet (environment) The society’s condition or values Discussion: What units of measurement might be appropriate for each of the above?
Copyright © 2010 Lumina Decision Systems, Inc. Deal or No Deal? You are a contestant on a game show. Hidden in one of two boxes is $1,000,000. The other box is empty. You can open only one box and keep its contents. Or, you receive $400,000 if you leave now without selecting either box. What do you choose? Why? Does this game involve “risk”? How would you quantify the amount of risk? At what threshold amount paid for leaving would you be indifferent?
Copyright © 2010 Lumina Decision Systems, Inc. Regret One metric for risk is minimum regret. Does not use probability of outcome. Outcome Box 1Box 2 Play$1M0 Stop$400K Regret: $600K Regret: $400KRegret: 0 Potential regret $400K $600K At Risk: $400K Decision
Copyright © 2010 Lumina Decision Systems, Inc. Deal or no Deal #2 A friend presents you with two boxes. Hidden in one is $10, the other is empty. You can select one box and keep its contents. Or, you will be given $4 if you stop now. Why is this decision any different than the previous one?
Copyright © 2010 Lumina Decision Systems, Inc. Utility Functions The utility of an outcome reflects a degree of benefit for the decision maker. Twice the money doesn’t usually mean twice the benefit. Daniel Bernoulli: Your utility is proportional to Ln(wealth), the logarithm of your net wealth. Exercise: Estimate your own net wealth. For the $1M deal game: What is your expected utility if you chose a box? What is your utility if you leave with $400K? At what threshold amount with they be the same?
Copyright © 2010 Lumina Decision Systems, Inc. Risk Neutrality & Risk Aversion Most of us Lottery player
Copyright © 2010 Lumina Decision Systems, Inc. Non-Monetary Utility A philanthropic organization must decide between two projects in Africa: Malaria treatments: Will save the lives of X children under the age of 10. AIDS prevention Will prevent Y new cases of AIDS (mostly young adults). Discussion: How could you define utility functions in such a way that these could be meaningfully compared?
Copyright © 2010 Lumina Decision Systems, Inc. Exercise (financial risk) Build a model of a potential 5 yr rental property investment. Purchase price: $250K $50K down payment (Mortgage: $200K at 5.5% 30yr fixed) – not needed for model Total net income over 5 yrs: Normal($-25K,$10K) Appreciation in 5 yrs: Normal(12%,10%) To be sold after 5 years. Mortgage balance at that time: $185K Compute Profit, Return-on-investment View Mean, CDF results
Copyright © 2010 Lumina Decision Systems, Inc. Some possible (single-number) risk measures for previous example Expected profit (?) Does this capture “risk”? Mean(profit) Expected change in log-wealth utility. Mean( Ln(profit+wealth) – Ln(wealth) ) Probability of losing money Probability(profit<0) Standard deviation (of profit) – aka “volatility” SDeviation(Profit) 5% fractile (of profit) GetFract(profit,5%) Exercise: Encode each of these in the Rental Investment model.
Copyright © 2010 Lumina Decision Systems, Inc. Value at Risk (VaR) Definition: The 5% five-year VaR is the 5% percentile for the loss at the 5 year mark (relative to the value now). Note: Also called the 95% five-year VaR. In Analytica example: GetFract( -Profit, 95% ) Will be a positive number (the amount of loss) if Probability(Profit 5%. 1% VaR is also commonly used.
Copyright © 2010 Lumina Decision Systems, Inc. ChanceDist Given: Index Outcome (possible outcomes) Array P indexed by Outcome (probabilities) ChanceDist(Probs,Outcome) Encodes the discrete distribution.
Copyright © 2010 Lumina Decision Systems, Inc. Exercise Model the above transitions & price changes over 100 days/transitions. Compute the 100-day 5% VaR. (Use SampleSize=1000 and Random Latin Hypercube) Compute the worst loss among 1000 sampled runs. Bear +0.3% Bull -0.2% Crash -10% Start ($1)
Copyright © 2010 Lumina Decision Systems, Inc. Expected Shortfall Also known as: Conditional value at risk (CVaR) Expected tail loss Definition: The expected loss when the loss exceeds the VaR. Exercise: Compute the 100-day 5% expected shortfall for the previous example. Mean(loss, w:loss>=value_at_risk)
Copyright © 2010 Lumina Decision Systems, Inc. Uses for a risk measure Decision making As an objective. As a constraint. Explicit risk/reward trade-offs. Reporting / monitoring Communicating level of risk being incurred (in a portfolio, or by an organization). Regulation (Basel II & Sarbanes-Oxley) Explaining Behavior analysis
Copyright © 2010 Lumina Decision Systems, Inc. Summary Several conceptions of “risk” exist. Utility allows: Direct incorporation of risk attitudes into decision making Incorporation of non-monetary considerations. Some possible measures of risk: Standard deviation (volatility) Minimum regret Probability of loss Fractile levels Value at risk (VaR) Expected shortfall
Copyright © 2010 Lumina Decision Systems, Inc. Monte Carlo Simulation Analytica User Group Modeling Uncertainty Series #3 13 May 2010 Lonnie Chrisman,
Copyright © 2010 Lumina Decision Systems, Inc. Risk Analysis for Portfolios Analytica Users Group Modeling Uncertainty Webinar Series, #5 3 June 2010 Lonnie.
Chapter McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Risk and Capital Budgeting 13.
Copyright © 2010 Lumina Decision Systems, Inc. Common Parametric Distributions Gentle Introduction to Modeling Uncertainty Series #6 Lonnie Chrisman, Ph.D.
Copyright © 2004 South-Western 27 The Basic Tools of Finance.
Copyright ©2004 Pearson Education, Inc. All rights reserved. Chapter 13 Investing Fundamentals.
Money and Banking Lecture 11. Review of the Previous Lecture Application of Present Value Concept Internal Rate of Return Bond Pricing Real Vs Nominal.
Chapter 15: Decisions Under Risk and Uncertainty McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
Copyright © 2010 Lumina Decision Systems, Inc. Statistical Hypothesis Testing (8 th Session in “Gentle Introduction to Modeling Uncertainty”) Lonnie Chrisman,
McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 15 Decisions under Risk and Uncertainty.
How to Build an Investment Portfolio The Determinants of Portfolio Choice The determinants of portfolio choice, sometimes referred to as determinants of.
Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Managerial Economics Thomas Maurice eighth edition Chapter 15.
Risk and Capital Budgeting 13 Chapter Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin.
● Uncertainties abound in life. (e.g. What's the gas price going to be next week? Is your lottery ticket going to win the jackpot? What's the presidential.
Basic Tools of Finance Finance is the field that studies how people make decisions regarding the allocation of resources over time and the handling of.
VAR. Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull The Question Being Asked in VaR “What loss level is such.
© Harry Campbell & Richard Brown School of Economics The University of Queensland BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets.
Stephen G. CECCHETTI Kermit L. SCHOENHOLTZ Understanding Risk Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin.
Investment and portfolio management MGT 531. Lecture #31.
Goals-Based Investing: Integrating Traditional and Behavioral Finance Jakub Karnowski, CFA Portfolio Management for Financial Advisers.
Investment Analysis and Portfolio Management Lecture 5 Gareth Myles.
Chapter 7 Dividend Policy Meaning of Dividend Dividend refers to the business concerns net profits distributed among the shareholders. It may also be termed.
IIASA Yuri Ermoliev International Institute for Applied Systems Analysis Mathematical methods for robust solutions.
Investments Lecture 4 Risk and Return. Introduction to investments §Investing l Definition of an investment: The current commitment of dollars for a period.
Options, Futures, and Other Derivatives 6 th Edition, Copyright © John C. Hull Chapter 18 Value at Risk.
Value at Risk Chapter 20 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull
LECTURE 22 VAR 1. Methods of calculating VAR (Cont.) Correlation method is conceptually simple and easy to apply; it only requires the mean returns and.
Value of information Marko Tainio Decision analysis and Risk Management course in Kuopio
TK 6413 / TK 5413 : ISLAMIC RISK MANAGEMENT TOPIC 6: VALUE AT RISK (VaR) 1.
CDU – School of Information Technology Risk Management - Slide 1 HIT241 - RISK MANAGEMENT Introduction Project risk management is the art and science of.
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Managerial Economics, 9e Managerial Economics Thomas Maurice.
Copyright ©2004 Pearson Education, Inc. All rights reserved. Chapter 18 Asset Allocation.
Sports and Entertainment Marketing © Thomson/South-Western ChapterChapter Sports and Entertainment Means Business 2.1 Sports and Entertainment Economics.
Chapter 2 Risk Measurement and Metrics. Measuring the Outcomes of Uncertainty and Risk Risk is a consequence of uncertainty. Although they are connected,
PowerPoint Slides by Robert F. BrookerCopyright (c) 2001 by Harcourt, Inc. All rights reserved. Managerial Economics in a Global Economy Chapter 13 Risk.
1 Market Risk Cheryl J. Rathbun Citigroup Chief Operating Officer U.S. Basel II Implementation Director rights reserved November 2008.
RISK VALUATION. Risk can be valued using : Derivatives Valuation –Using valuation method –Value the gain Risk Management Valuation –Using statistical.
Chapter 13 Risk Analysis Dr Loizos Christou. Risk and Uncertainty Risk –Situation where there is more than one possible outcome to a decision and the.
DECISION MODELS. Decision models The types of decision models: – Decision making under certainty The future state of nature is assumed known. – Decision.
Lecture 4 Environmental Cost - Benefit - Analysis under risk and uncertainty.
Portfolio Management Unit – 1 Session No.4 Topic: Investment Objectives Unit – 1 Session No.4 Topic: Investment Objectives.
Decision Making Under Uncertainty and Risk 1 By Isuru Manawadu B.Sc in Accounting Sp. (USJP), ACA, AFM
Sensitivity and Scenario Analysis. Financial Modeling Any model we use has the potential to have error How do we account for the uncertainty associated.
Known dividend to be paid before option expiration ◦ Dividend has already been announced or stock pays regular dividends ◦ Option should be priced on.
Chapter 4 Measurement PowerPoint Presentation by Matthew Tilling ©2012 John Wiley & Sons Australia Ltd.
Lotter Actuarial Partners 1 Pricing and Managing Derivative Risk Risk Measurement and Modeling Howard Zail, Partner AVW
© 2007 Thomson South-Western. The Basic Tools of Finance Finance is the field that studies how people make decisions regarding the allocation of resources.
© 2017 SlidePlayer.com Inc. All rights reserved.