Testing VaR IEF 217a: Lecture Section 7 Fall 2002 Jorion, Chapter 6

Testing Issues Portfolio construction Statistical tests –Exceptions –Dependence

Initial Question Which return? Problem with dynamic strategies Example: –VaR target set at t for t+10 –Someone changes portfolio at t+3 –Violation of target no longer relevant –VaR assumes constant portfolios

Solutions (cleaned portfolios) Freeze portfolios Eliminate nonmarket flows –Funding costs –Fee income

Testing Frameworks Exceptions –Find actual times VaR returns exceeded Clustering –Look at time series properties of exceptions –Do they clump together

Exceptions Count number of returns < alpha VaR level Should be alpha fraction

Bernoulli Test Find fraction outside at the alpha level

For 0.01 VaR

Matlab Example Testing delta normal VaR and Dow dowexceptions.m varconf.m

Conditional Exceptions Prob(exception tomorrow: exception today) Estimate this and compare dowcond.m

Summary For Dow At 5% level –Too few exceptions At 1% level –Too many exceptions At both –Too much persistence