1. Common Risk Measures Descriptions and Comparisons William C. Wojciechowski VIGRE Computational Finance Seminar Rice University October 15, 2003

2. 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

3. Defining Risk Risk - chance that an investment’s 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

4. 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?

5. Common Risk Measures Dispersion Measures

6. Common Risk Measures More dispersion does NOT equal more risk Normal mixture model with possible large win Normal model without possible large win

7. Common Risk Measures More dispersion does NOT equal more risk

8. Common Risk Measures More dispersion does not equal larger positive returns

9. Common Risk Measures Dispersion below a target Fishburn family

10. Common Risk Measures VAR (Value at Risk) Measures

11. Common Risk Measures Accumulate VAR (AVAR)

12. 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

13. Simulations Possibility of large gain

14. Simulations Moderate chance of large loss

15. Simulations Small chance of catastrophic loss

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

17. Reference Guy Kaplanski and Yoram Kroll, “VAR risk measures vs traditional risk measures: an analysis and survey”, Journal of Risk, 4, Spring, 2002