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Case 4 - Sample Answers

APS 425 - Advanced Managerial Data Analysis

APS 425 Case 4 – Winter 2008
Sample A S l Answers 3/11/2008

Instructor: G Willi Schwert I G. William S h
585-275-2470 schwert@schwert.ssb.rochester.edu

GARCH(1,1) Model for S&P500

Typical GARCH(1,1) Lots of persistence

.07 .06 .05 .04 .03 .02 .01 .00 1000 2000 3000 4000 5000

Conditional standard deviation

(c) Prof. G. William Schwert, 2003-2008

1

Case 4 - Sample Answers

APS 425 - Advanced Managerial Data Analysis

EGARCH(1,1) Model for S&P500
Asymmetric coefficient, c(4) is negative, so crashes => more volatility
.06 .05 .04 04 .03 .02 .01 .00 1000 2000 3000 4000 5000

Conditional standard deviation

EGARCH(1,1) Model for S&P500 2000-2008
Results are certainly y affected by 87 crash, but general tenor is similar
.030 .025 .020 .015 .010 .005 .000 3750 4000 4250 4500 4750 5000 5250 5500 Conditional standard deviation

(c) Prof. G. William Schwert, 2003-2008

2

Case 4 - Sample Answers

APS 425 - Advanced Managerial Data Analysis

Plot EGARCH(1,1) Estimate of Conditional SD vs VIX
sd01 = sqr(253*GARCH01), where GARCH01 is the estimate of the variance of the daily stock return Note that VIX looks generally higher than EGARCH for most of these periods
.5 5

.4

.3

.2

.1

.0 3750 4000 4250 4500 4750 5000 5250 5500 SD01 VIX

Combine VIX with EGARCH (1,1) Model for S&P500
Include yesterday’s VIX y y (squared, divided by 253) in the equation to predict today’s variance of returns Coefficient is ..29, and tstat is 4.1 Suggests that VIX contains information beyond the EGARCH model

(c) Prof. G. William Schwert, 2003-2008

3

Case 4 - Sample Answers

APS 425 - Advanced Managerial Data Analysis

Combine VIX with EGARCH (1,1) Model for S&P500 - Diagnostics
Residual diagnostics look good g g

Combine VIX with EGARCH (1,1) Model for S&P500 - Diagnostics
Residual diagnostics look good
500 Series: Standardized Residuals Sample...

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