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So you think you know about RISK? Ken Darby-Dowman School of Information Systems, Computing and Mathematics and C entre for the A nalysis of RIS K and Optimisation M odelling A pplications BITLab Colloquium – Friday 16 th February 2007

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Structure What is Risk? Risk – Research Opportunities Perceptions of Risk Risk Assessment (in brief) Quantitative Modelling – Investment Decisions Summary References The last word!

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A few of the many quotes on Risk: 1.‘There are risks and costs to a program of action, but they are far less than the long- range risks and costs of comfortable inaction’ - John F. Kennedy ‘Only those who risk going too far can possibly find out how far they can go’ - T. S. Eliot

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4.‘To win you have to risk loss’ - Jean Claude Killy 5.‘To win without risk is to triumph without glory’ -Pierre Corneille (17 th Century Dramatist) Attitude to risk: Where do YOU sit? Risk Averse Risk Neutral Risk Seeking

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Definitions Uncertainty arises when a state is ‘not able to be accurately known or predicted’ (O.E.D) Risk: The possibility of incurring misfortune or loss (O.E.D) Uncertainty is not risk Uncertainty may lead to risk Uncertainty + Action Risk Generally Uncontrollable Generally Controllable Can be reduced by change of action

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Risk TopicExample ApplicationsAcademic Disciplines Perceptions of Risk Risk Assessment Risk Modelling (Quantitative) Environmental Risk Corporate Risk Financial Risk Engineering Risk Risk Regulation Human Decision Making Advertising Nuclear Debate Climate Change Policy Implementation Health Awareness Campaigns Psychology Sociology Marketing Politics Health Disaster Planning Treatment Options Risk Registers Project Management Business Medicine Social Work Planning (student numbers!!) Investment Portfolios Supply Chain Management Mathematics Operational Research Business Pollution Management Climate Change Geography Science Bankruptcy (Enron!) Business Finance Design of structures (cost v safety) Engineering Legal FrameworkLaw

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Perceptions of Risk ‘ The Framing of Decisions and the Psychology of Choice’ -Amos Tversky and Daniel Kahneman Science, Vol 211, pp , January 1981 Problem: The UK is preparing for an outbreak of Bird Flu in humans which will kill 6000 people if no action is taken. Two alternative programmes to combat the disease have been proposed. Which of the two programmes would you favour?

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If Programme A is adopted:2000 people will be saved If Programme B is adopted:⅓ probability that 6000 people will be saved ⅔ probability that no people will be saved If Programme C is adopted:4000 people will die If Programme D is adopted:⅓ probability that nobody will die ⅔ probability that 6000 people will die Your decision: A or B? Your decision: C or D? Majority Choice: A (risk averse) Majority Choice: D (risk taking)

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Risk Assessment Probability –Impact (P-I) Table Risk Identification: Identify all risks, each of which threatens the achievement of the organisation’s goals. Risk Assessment: Qualitatively assess the probability, P, of a risk event (a possible event that would produce a negative impact on the organisation) (Nil, V.Low, Low, Medium, High, V.High) Impact Assessment: Qualitatively assess the Impact, I, inflicted on the organisation if the risk event occurred. (Nil, V.Low, Low, Medium, High, V.High) Probability NilV. LowLowMediumHighV. High IMPACT V. High High Medium Low V. Low High Severity Medium Severity Low Severity Major Benefit: Forces through planning!

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Quantitative Modelling of RISK in Investment (Portfolio Selection) What makes one portfolio ‘better’ than another? Balance Risk and Return A.Expected Utility Maximisation Assumptions 1)‘Return’ is a random variable with an assumed probability distribution 2)A rational investor: a)Prefers ‘more’ to ‘less’ (non-satiation) non-decreasing utility function b)Is risk aversenon-decreasing, concave utility function Given the utility function and the return distribution, we Maximise Expected Utility Practical Difficulty: How to chose an appropriate utility function? Not Favoured Utility Possible returns

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B.Mean - Risk Models Harry Markowitz (The Father of Modern Portfolio Theory), Nobel Prize Winner in 1990 proposed the Mean-Variance (E-V) Model for portfolio selection (1959). Givenassets: 1,2,… Let= covariance between returns of asset and asset = the expected rate of return of asset = desired level of return for the portfolio (chosen by the decision maker) Let= fraction of capital to be invested in asset Min- Min (Variance of portfolio return) Subject to- Achieve a return of - and invest all capital

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Solve Markowitz’s model for different values of to obtain a series of ‘optimal’ portfolios that form the ‘efficient frontier’ Each portfolio on the efficient frontier has a claim to be the ‘best’. Choice depends on your risk/return attitude. E (Return) Risk Max return / Max risk Non efficient Min return / Min risk

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Choice of risk measure Markowitz model : Variance of portfolio return (Volatility) Pro: - Model is a Quadratic Program – Computationally tractable - Clear attempt to address the risk / return paradigm Con: - Symmetric measure for risk – Penalises ‘upside risk’ as well as ‘downside risk’ – OK if returns are symmetric around mean return (Normality) – but, in practice this is not generally the case – the return distribution is skewed. -Can be overcome by using one-sided risk measures (eg. Semi-variance) Variance is a ‘risk measure of the first kind’ – it measures the magnitude of deviations from a target.

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Risk Measures of the Second Kind (Favoured by regulators) 1.Value at Risk (VaR) 2.Conditional Value at Risk (CVaR) CVar is the average loss below VaR E (Loss / Loss ≤ VaR ) 1 0 x Probability (Pr (Return ≤ x) Outcome (Portfolio return) Cumulative Distribution Function 0

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Summary 1.Risk has something for everybody to get their teeth into! 2.We looked at perceptions of risk and discovered surprising results 3.We scratched the surface of mathematical modelling of portfolio selection and reviewed the basis of professional investment management

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References 1.‘Models for Choice under Risk with Applications to Optimum Asset Allocation’ by Diana Roman, PhD Thesis, Brunel University (2006). (and references therein). 2.Roman, D., Darby-Dowman, K. and Mitra, G., ‘Portfolio Construction based on Stochastic and Target Return Distributions’, Mathematical Progamming, Series B, Vol 108, pp , Roman, D., Darby-Dowman, K. and Mitra, G., ‘Mean- Risk Models using Two Risk Measures: A Multi- Objective Approach’, to appear in Quantitative Finance (2007).

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And, remember, don’t have nightmares – sleep well! Financial Planning

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