So you think you know about RISK

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So you think you know about RISK?

• Ken Darby-Dowman
• School of Information Systems, Computing and
  Mathematics
• and Centre for the Analysis of RISK and
  Optimisation Modelling Applications
• BITLab Colloquium Friday 16th 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

• 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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• To win you have to risk loss
• - Jean Claude Killy
• To win without risk is to triumph without glory
• Pierre Corneille (17th 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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Perceptions of Risk
Human Decision Making Advertising Nuclear
Debate Climate Change Policy Implementation Health
Awareness Campaigns
Psychology Sociology Marketing Politics Health
Risk Assessment
Disaster Planning Treatment Options Risk
Registers Project Management
Business Medicine Social Work
Risk Modelling (Quantitative)
Planning (student numbers!!) Investment
Portfolios Supply Chain Management
Mathematics Operational Research Business
Environmental Risk
Pollution Management Climate Change
Geography Science
Corporate Risk Financial Risk
Bankruptcy (Enron!)
Business Finance
Engineering Risk
Design of structures (cost v safety)
Engineering
Risk Regulation
Legal Framework
Law
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Perceptions of Risk

• The Framing of Decisions and the Psychology of
  Choice
• Amos Tversky and Daniel Kahneman
• Science, Vol 211, pp453-458, 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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Your decision A or B?
Majority Choice A (risk averse)
Your decision C or D?
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
  organisations 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)

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
• Expected Utility Maximisation
• Assumptions
• Return is a random variable with an assumed
  probability distribution
• A rational investor
• Prefers more to less (non-satiation)
  non-decreasing utility function
• Is risk averse non-decreasing, concave utility
  function
• 
  Given the utility function and the
  return
  distribution, we Maximise Expected
  Utility

Utility
Possible returns
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• 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).
• Given assets 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 Markowitzs 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.

Max return / Max risk
E (Return)
Non efficient
Min return / Min risk
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 )

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Cumulative Distribution Function
Probability (Pr (Return x)
0
x
0
Outcome (Portfolio return)
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Summary

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

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References

• Models for Choice under Risk with Applications
  to Optimum Asset Allocation by Diana Roman, PhD
  Thesis, Brunel University (2006).
• (and references therein).
• Roman, D., Darby-Dowman, K. and Mitra, G.,
  Portfolio Construction based on Stochastic and
  Target Return Distributions, Mathematical
  Progamming, Series B, Vol 108, pp541-569, 2006.
• 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, dont have nightmares sleep
  well!

Financial Planning