1. VaR and Changing Volatility Jorion, Chapter 8 VaR and the Unreal World The Pitfalls of VaR estimates

2. Summary Picture of changing volatility Moving averages and rolling VaR’s Riskmetrics and weighted variances GARCH modeling of volatility Correlations and portfolios

3. Picture of Changing Volatility dowvolplt.m

4. Summary Picture of changing volatility Moving averages and rolling VaR’s Riskmetrics and weighted variances GARCH modeling of volatility Correlations and portfolios

5. Moving Average of Volatility Rolling moving average of returns squared madowvar.m

6. Moving Average of Volatility Brooks/Persand and Hoppe papers –Tradeoff between small and large samples –Conditional volatility versus large sample size –Small often looks better –Trickier with weightings Interesting question –Evaluation? (graphical)

7. Summary Picture of changing volatility Moving averages and rolling VaR’s Riskmetrics and weighted variances GARCH modeling of volatility Correlations and portfolios

8. RiskMetrics VaR h(t) = variance at time t Smooth weighting of past volatility

9. Riskmetrics VaR rmdowvar.m hrmdowvar.m

10. Summary Picture of changing volatility Moving averages and rolling VaR’s Riskmetrics and weighted variances GARCH modeling of volatility Correlations and portfolios

11. GARCH Modeling GARCH(1,1): –Complete model for changing variance

12. GARCH Modeling Forecasting Variance h(t)

13. How Does this Differ from Riskmetrics? For 1 horizon, not much Multi-horizon is different h(t+m) is needed

14. GARCH Variance T periods in the future

15. GARCH Variance Forecast Days Ahead Variance Shock Unconditional Variance

16. RiskMetrics VaR Forecasts h(t) = variance at time t

17. Summary Picture of changing volatility Moving averages and rolling VaR’s Riskmetrics and weighted variances GARCH modeling of volatility Correlations and portfolios

18. Correlations Moving averages Riskmetrics (examples) GARCH

19. Riskmetrics Correlation Example (rmcorr.m)

20. Crashes and Correlations Large down moves connected to increases in correlations Implications for risk management and portfolio construction Reliability in the data?

21. Final Suggestions on Volatility Options data and implied volatility High frequency data High/low range data