Common Risk Measures Descriptions and Comparisons

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Common Risk MeasuresDescriptions and Comparisons

• William C. Wojciechowski
• VIGRE Computational Finance Seminar
• Rice University
• October 15, 2003

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Defining Risk

• What is risk?
• How is risk measured?
• Types of risk market, credit, liquidity, etc.
• Finance is one area of risk management
• Against The Gods The Remarkable Story of Risk -
  Peter L. Bernstein

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Defining Risk

• Risk - chance that an investments return will
  be less than expected.
• Market Risk loss in value due to decline in
  price
• Event Risk catastrophic actions cause decrease
  in value
• Liquidity Risk lose value by not being able to
  transact

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Measuring Risk

• X - a random variable representing the value of
  an investment at some future time t
• Scalar, such as volatility of X?
• Vector, such as a value and probability?
• Consider the whole distribution of X?

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Common Risk Measures

• Dispersion Measures

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Common Risk Measures

• More dispersion does NOT equal more risk
• Normal mixture model with possible large win
• Normal model without possible large win

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Common Risk Measures

• More dispersion does NOT equal more risk

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Common Risk Measures

• More dispersion does not equal larger positive
  returns

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Common Risk Measures

• Dispersion below a target
• Fishburn family

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Common Risk Measures

• VAR (Value at Risk) Measures

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Common Risk Measures

• Accumulate VAR (AVAR)

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Common Risk Measures

• Simulations
• Generate random return streams X and Y
• For each risk measure, calculate the risk of X
  and Y
• Count the number of times the risk measure makes
  the correct decision

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Simulations

• Possibility of large gain

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Simulations

• Moderate chance of large loss

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Simulations

• Small chance of catastrophic loss

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Conclusions

• There are many possible measures of risk
• Appears none of the common risk measures
  universally applies to all situations
• Research opportunities are abundant

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Reference

• Guy Kaplanski and Yoram Kroll, VAR risk measures
  vs traditional risk measures an analysis and
  survey, Journal of Risk, 4, Spring, 2002