Common Risk Measures
Descriptions and Comparisons
William C. Wojciechowski
VIGRE Computational Finance Seminar
Rice University
October 15, 2003
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
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
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?
Common Risk Measures
Dispersion Measures
Common Risk Measures
More dispersion does NOT equal more risk
Normal mixture model with possible large win
Normal model without possible large win
Common Risk Measures
More dispersion does NOT equal more risk
Cumulativ e Return Comparison
250
200
Cumulative Return
150
100
50
0
0 50 100 150 200 250
SD(Black) = 3.19 SD(Orange) = 0.96
Common Risk Measures
More dispersion does not equal larger positive
returns
Cumulativ e Return Comparison
0
-50
Cumulative Return
-100
-150
-200
0 50 100 150 200 250
SD(Black) = 2.96 SD(Orange) = 1.02
Common Risk Measures
Dispersion below a target
Fishburn family
Common Risk Measures
VAR (Value at Risk) Measures
Common Risk Measures
Accumulate VAR (AVAR)
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
Simulations
Possibility of large gain
Simulations
Moderate chance of large loss
Simulations
Small chance of catastrophic loss
Conclusions
There are many possible measures of risk
Appears none of the common risk measures
universally applies to all situations
Research opportunities are abundant
Reference
Guy Kaplanski and Yoram Kroll, “VAR risk
measures vs traditional risk measures: an
analysis and survey”, Journal of Risk, 4,
Spring, 2002