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Portfolio VaR

Portfolio VaR. Jorion, chapter 7. Goals. Portfolio VaR definitions Portfolio VaR global equity example Delta normal Historical Bootstrap Incremental VaR. Portfolio VaR. VaR on portfolio of assets Similar to standard VaR with new complications Covariance Dependence Portfolio weights.

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Portfolio VaR

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  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

  9. Correlations and Portfolio VaR

  10. 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

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