MFE 230H Section 1

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MFE 230HSection 1

• Bradyn Breon-Drishbreon_at_haas.berkeley.edu
• Aug. 14, 2007

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Administrative details

• Office hours
• Tentatively
• Tue. 530pm-730pm, Room F689
• Sections
• Tentatively
• Tue. 4pm-530pm, Room TBA

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Assignment 1

• Volatilities
• VAR (relative to the mean)
• Parametric
• Empirical (nonparametric)
• Confidence intervals

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Simplified example

• Daily SP close 12/29/1995-12/2/03
• Follow-up period (part (d)) 12/2/03-12/31/03
• Long position of 1 billion
• For returns, VAR, etc. will compute daily values
  only

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The Tasks

• Compute daily volatilities
• First-order serial correlation and test if
  significantly different from zero
• Compute parametric VAR
• Standard error and 95 confidence interval
• Compute empirical VAR
• Plus skewness and kurtosis

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Volatilities and correlation

• Daily volatility

• Or, more conveniently STDEV(Data)

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Volatilities and correlation - 2

• Correlation
• CORREL(Data1,Data2)
• Use series and lagged series as inputs
• Standard error?
• For large T, under null hypothesis of zero
  correlation

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Parametric VAR

• General formula (eq. 5.10, p.111)

• -a is 1-c quantile of a standard normal
  distribution, where c confidence level
• The time scaling depends on the period for the
  estimated volatility

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Parametric VAR Standard Error

• SE(VAR) depends on SE(s)
• From eq. 5.15 (p.124)

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Parametric VAR Standard Error - 2

• Given VAR formula, we then have

• So that 95 c.i. for VAR is

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Empirical VAR

• General formula (eq. 5.2, p.108)

• R 0.05 quantile of the empirical distribution
• Percentile(Data,0.05)

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Skewness Kurtosis

• Skewness (?)
• SKEW(Data)
• SE Sqrt(6/T)
• Kurtosis (d)
• KURT(Data)
• SE Sqrt(24/T)

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Questions?