1. Portfolio VaR Jorion, chapter 7

2. Goals Portfolio VaR definitions Portfolio VaR global equity example –Delta normal –Historical –Bootstrap Incremental VaR

3. Portfolio VaR VaR on portfolio of assets Similar to standard VaR with new complications –Covariance –Dependence –Portfolio weights

4. Global Portfolio Example Data – wldeqp.dat, wldeqp.info –Column 1: date (mm/dd/yy) 92-2002 –Column 2-6, MSCI equity indices (US $) World Japan US Germany UK

5. Historical VaR Matlab – gport.m Notes: –Portfolio weights: Equal weighted over US, Japan, Germany, UK –Compares delta normal with historical

6. Monte-Carlo VaR Matlab – mcgport.m Critical issue: –Variance covariance matrix –See revised normal.m Similar patterns to univariate VaR

7. Bootstrap VaR Matlab: – bgport.m Note: –Bootstrap modeling of dependence – Importance of getting this right

8. Correlations and Portfolio VaR

11. Extremes VaR on portfolio is max for correlation of 1 Portfolio VaR is the sum of VaR’s

12. Component Issues Sensitivity to portfolio changes –Analytic tools (in Jorion) Bootstrap and monte-carlo methods –Try sweeping through different portfolios –Applications – US to Global change bsensgport.m – US to Japan change bsensgport2.m

13. Adding Options to Equity Portfolios Problem: –50/50 US/UK equity portfolio –Cover the US position only by purchasing a put Do this at the money first 20 day (1 month European option) –First, what does the eventual portfolio distribution look like?

14. Part 1 What does an option do to the distribution? optdist.m

15. Part 2 Evaluating option purchases – usoptchoice.m

16. Summary Portfolio choice adds different dimensions –Covariances –Joint bootstrapping Often critical May be most important part of modeling risk factors