Common Risk MeasuresDescriptions 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

Cu

mu

lativ

e R

etu

rn

0 50 100 150 200 250

05

01

00

15

02

00

25

0

Cumulative Return Comparison

SD(Black) = 3.19 SD(Orange) = 0.96

Common Risk Measures

More dispersion does not equal larger positive returns

Cu

mu

lativ

e R

etu

rn

0 50 100 150 200 250

-20

0-1

50

-10

0-5

00

Cumulative Return Comparison

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