VaR and Changing Volatility

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VaR and Changing Volatility

• Jorion, Chapter 8
• VaR and the Unreal World
• The Pitfalls of VaR estimates

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Summary

• Picture of changing volatility
• Moving averages and rolling VaRs
• Riskmetrics and weighted variances
• GARCH modeling of volatility
• Correlations and portfolios

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Picture of Changing Volatility

• dowvolplt.m

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Summary

• Picture of changing volatility
• Moving averages and rolling VaRs
• Riskmetrics and weighted variances
• GARCH modeling of volatility
• Correlations and portfolios

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Moving Average of Volatility

• Rolling moving average of returns squared
• madowvar.m

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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)

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Summary

• Picture of changing volatility
• Moving averages and rolling VaRs
• Riskmetrics and weighted variances
• GARCH modeling of volatility
• Correlations and portfolios

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RiskMetrics VaR

• h(t) variance at time t
• Smooth weighting of past volatility

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Riskmetrics VaR

• rmdowvar.m
• hrmdowvar.m

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Summary

• Picture of changing volatility
• Moving averages and rolling VaRs
• Riskmetrics and weighted variances
• GARCH modeling of volatility
• Correlations and portfolios

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GARCH Modeling

• GARCH(1,1)
• Complete model for changing variance

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GARCH Modeling

• Forecasting Variance h(t)

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How Does this Differ from Riskmetrics?

• For 1 horizon, not much
• Multi-horizon is different
• h(tm) is needed

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GARCH Variance T periods in the future
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GARCH Variance Forecast
Variance
Shock
Unconditional Variance
Days Ahead
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RiskMetrics VaRForecasts

• h(t) variance at time t

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Summary

• Picture of changing volatility
• Moving averages and rolling VaRs
• Riskmetrics and weighted variances
• GARCH modeling of volatility
• Correlations and portfolios

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Correlations

• Moving averages
• Riskmetrics (examples)
• GARCH

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Riskmetrics Correlation Example(rmcorr.m)
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Crashes and Correlations

• Large down moves connected to increases in
  correlations
• Implications for risk management and portfolio
  construction
• Reliability in the data?

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Final Suggestions on Volatility

• Options data and implied volatility
• High frequency data
• High/low range data