A. You believe that the VIX trades in regimes where its average level is significantly different. You define four regimes from 2004 through 2021: June 2008 through October 2011 (financial crisis); February 2020 through March 2021 (the COVID-19 crisis); the 12-month transition periods before and after the financial crisis and the current transition period after the COVID-19 crisis; and the remaining periods of low volatility. In order to test your hypothesis, you examine month-end values of the VIX from January 2004 through October 2021 (214 observations) and conduct the following regression: Dependent variable Y: Month-end value of VIX Dummy variable X1: Financial Crisis: 1 if between June 2008 through Oct 2011, 0 if not Dummy variable X2: COVID-19 crisis: 1 if between Feb 2020 through March 2021, 0 if not Dummy variable X2: Transition period: 1 if in 12 months before or after the financial crisis or the current period since the COVID-19 crisis (June 2007 – May 2008, Nov 2011 – Oct 2012, or April 2021 – Oct 2021) The results for the regression are as follows Coefficients Standard Error Intercept 14.63 0.5226 financial crisis 13.71 1.0610 COVID-19 crisis 15.71 1.6643 transition 5.40 1.1835 How would the introduction of Dummy variable X4: Low volatility period (Jan 2004 – May 2007, or Nov 2012 – Jan 2020) affect the output of this regression? Why? Which of the coefficients are significant at the 0.01 level? According to the regression result, what was the average value of the VIX during the COVID-19 Crisis?
Question 1
A. You believe that the VIX trades in regimes where its average level is significantly different. You define four regimes from 2004 through 2021: June 2008 through October 2011 (financial crisis); February 2020 through March 2021 (the COVID-19 crisis); the 12-month transition periods before and after the financial crisis and the current transition period after the COVID-19 crisis; and the remaining periods of low volatility. In order to test your hypothesis, you examine month-end values of the VIX from January 2004 through October 2021 (214 observations) and conduct the following regression:
Dependent variable Y: Month-end value of VIX
Dummy variable X1: Financial Crisis: 1 if between June 2008 through Oct 2011, 0 if not
Dummy variable X2: COVID-19 crisis: 1 if between Feb 2020 through March 2021, 0 if not
Dummy variable X2: Transition period: 1 if in 12 months before or after the financial crisis or the current period since the COVID-19 crisis
(June 2007 – May 2008, Nov 2011 – Oct 2012, or April 2021 – Oct 2021)
The results for the regression are as follows
|
|
Coefficients |
Standard Error |
|
Intercept |
14.63 |
0.5226 |
|
financial crisis |
13.71 |
1.0610 |
|
COVID-19 crisis |
15.71 |
1.6643 |
|
transition |
5.40 |
1.1835 |
- How would the introduction of Dummy variable X4: Low volatility period (Jan 2004 – May 2007, or Nov 2012 – Jan 2020) affect the output of this regression? Why?
- Which of the coefficients are significant at the 0.01 level?
- According to the regression result, what was the average value of the VIX during the COVID-19 Crisis?
B. In estimating the regression in part A, you are concerned that the t-statistics may be inflated because of serial
4. Based on the DW, what can you say about serial correlation between the residuals? Are they positively or
5. Compute the sample
6. Perform a statistical test at the level to see if there is serial correlation. If you are using the table in the textbook, assume that the critical values of the DW statistic for 214 observations are about 0.11 higher than the critical values for 100 observations.
C. In estimating the regression in part A, you are also concerned that the t-statistics may be inflated because of the presence of conditional heteroscedasticity.
You conduct a regression of the squared residuals against the dummy variables X1, X2, and X3 and find that for the squared residuals regression:
|
|
Multiple R |
0.4145 |
|
|
R Square |
0.1718 |
|
|
Adjusted R Square |
0.1600 |
|
|
SEE |
92.3760 |
7. Conduct a test at the level to see if conditional heteroskedasticity is present
8. In view of your answer for 7), what needs to be done?
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