1 Background
The purpose of this project is to analyze the predictability of the realized variance of natural gas. The project would be easier to handle in EViews, as it involves importing and manipulating the data.
The Excel spreadsheet volatility contains the time-series of (i) the 1-month realized variance (RV t) of the natural gas market and (ii) the 1-month implied variance (IV t), which is the market expectation of the future realized variance. In order to make things easy, the two series are synchronized. To be speci c, the implied variance observed on October 29, 1992, is the market expectation recorded on October 29, 1992 of the realized variance for the 1-month period beginning on October 29, 1992. The realized variance observed on that day is the variance of natural gas futures recorded over the 1-month period starting on October 29, 1992.
1. Plot the time-series of the realized variance:
(a) Comment on the main feature(s) of this time-series?
(b) What is the intuition/economic rationale behind these features?
(c) Formally test the hypothesis that the realized variance follows a normal dis-
tribution.
(d) If the realized variance is not normally distributed, what are the implications of this non-normality for models that use the realized variance as dependent variable? What potential remedy can you suggest to tackle this issue?
2. De ne the variance risk premium (VRPt) as the di erence between the realized variance and the implied variance:
VRPt = log(RV t) − log(IV t) (1)
(a) Compute and interpret the summary statistics of the variance risk premium.
(b) Formally test the null hypothesis that the average variance risk premium is equal to 0.
Explain how you would carry out the test.
Discuss the test statistic and the critical value.
Explain the economic importance of testing this null hypothesis. In other words, why is this an interesting hypothesis and what do we learn from
this test?
3. Analyze the information content of the implied variance. Speci cally, estimate the regression model below:
(2)
(a) Explain why it might be desirable to model log(RV ) rather than RV .
(b) Formally test the assumptions that the residuals () are (i) independent in the time-series dimension and (ii) homoskedastic.
Present the null and the alternative hypotheses.
Present and interpret the results of the test: What is your conclusion?
If the null hypotheses are rejected, take the necessary steps to address the associated issues.
(c) Test the hypothesis that the implied variance is an unbiased predictor of the realized variance.
Clearly spell out the null and the alternative hypotheses.
Present and interpret the results of the test: What is your conclusion?
(d) A colleague points out that the test of the unbiasedness of the implied variance is related to testing that the average variance risk premium is equal to zero.
Discuss this statement.
(e) Consider the alternative model:
(3)
Formally compare the performance of the models in Equations (2) and
(3).
What do you conclude about the incremental information content of the lagged value of the dependent variable?
(f) A colleague points out that this predictability exercise is in-sample. However, there is no guarantee that the in-sample evidence might hold going forward.
Discuss how you would modify the research design to address this concern.