Volatility - Volatility Modeling Copyright 2000 2006...

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1 Volatility Modeling Copyright © 2000 – 2006 Investment Analytics
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Copyright 2001-2006 Investment Analytics Volatility Slide: 2 Asset Return Characteristics ± The Standard Gaussian Model ± Thick Tails ± Non-Normal Distribution ± Volatility Clustering ± Leverage ± Volatility & Correlation
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Copyright 2001-2006 Investment Analytics Volatility Slide: 3 Standard Gaussian Model ± Asset returns follow random walk ± Return this period independent of past return ± Asset returns are normally distributed ± These assumptions underlie all major financial theories ± CAPM ± Black-Scholes model
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Copyright 2001-2006 Investment Analytics Volatility Slide: 4 Thick Tails, Non-Normal Distribution ± Mandelbrot (1963), Fama (1963, 1965) Skewness = -0.6 Kurtosis = 5.7
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Copyright 2001-2006 Investment Analytics Volatility Slide: 5 Tests for Normality ± Error Distribution Moments ± Skewness: should be ~ 0 ± Kurtosis: should be ~ 3 ± Statistical Tests ± Lilliefors Kolmagorov-Smirnov nonparametric test ± Shapiro-Wilk test ± More powerful ± Jarque-Bera Test ± n[Skewness / 6 + (Kurtosis – 3)2 / 24] ~ χ 2 (2)
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Copyright 2001-2006 Investment Analytics Volatility Slide: 6 Volatility is Stochastic Volatility - DOW Stocks 0% 20% 40% 60% 80% 100% 120% 140% 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 DJIA IBM INTC IP JNJ
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Copyright 2001-2006 Investment Analytics Volatility Slide: 7 Volatility Clustering ± High vol. followed by high vol. ± Decay back to normal levels SP500 Index Volatility 0% 20% 40% 60% 80% 100% 120% 140% 160% Jan- 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00
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Copyright 2001-2006 Investment Analytics Volatility Slide: 8 The Volatility Cone V o l at i t y ( % ) Maximum Minimum A v e r a g Days 0 60 03
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Copyright 2001-2006 Investment Analytics Volatility Slide: 9 Leverage Effect ± Black (1976) ± Stock price changes negatively correlated with volatility ± Fixed costs provide a partial explanation ± Firm with equity and debt becomes more leveraged as stock falls ± Raises equity returns risk/volatility ± Correlation too large to be explained by leverage alone ± Christe (1982), Schwert (1989)
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Copyright 2001-2006 Investment Analytics Volatility Slide: 10 Volatility Seasonality DOW Volatility Seasonality 40% 60% 80% 100% 120% 140% 160% JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
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Copyright 2001-2006 Investment Analytics Volatility Slide: 11 Volatility Correlation ± Volatilities tend to change together ± Stocks: Black (1976) ± FX: Diebold & Nerlove (1989) ± Also across markets ± Stock & bond volatilities move together (Schwert, 1989)
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Copyright 2001-2006 Investment Analytics Volatility Slide: 12 Volatility Correlation Correlation: IBM vs JNJ Volatility -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 May-85 May-88 May-91 May-94 May-97 May-00
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Copyright 2001-2006 Investment Analytics Volatility Slide: 13 Asset Characteristics – Conclusions ± The Bad News ± iid Gaussian model inappropriate ± The Good News ± Correlation suggests few common factors may explain variation ± Volatility models (GARCH, etc.)
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Copyright 2001-2006 Investment Analytics Volatility Slide: 14 Volatility Metrics ± Consider statistic f of log asset price s iH,(i+1)H ± If f is homogeneous in some power γ of volatility,then ± and ±
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Volatility - Volatility Modeling Copyright 2000 2006...

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