Behind the Volatility Index Levels : The Paradox of 2016

The low 2016 volatility index levels present a paradox in light of previous research suggesting periods of uncertainty and negative news events should reflect higher VIX levels. This study uses daily data for the VIX, VIX futures and the VVIX, to examine the information content of variations in the natural logarithmic changes in the index levels relative to 12 other parallel time periods encompassing 2004-2016. Straight-forward variation and predictive tests are constructed to determine signs of unusual market volatility behavior. The results reveal strong evidence of unusual volatility behavior during the 2016 election period, pocked by frequent periods of abnormal returns. The 2016 VIX levels alone are shown to be insufficient to draw conclusions regarding investor sentiment.


Background
The impact of negative news is expected to have a negative impact on stock returns and a positive impact on VIX levels as shown by Tetlock (2007), Mamaysky and Glasserman (2017).Their findings demonstrate that increases in VIX are large following the release of negative news events.The more unusual the negative news event, the larger the increase in VIX is.Positive news events are shown to have the reverse effect on VIX levels.
In a perfect world, with no negative news, election periods are expected to have higher volatility levels due to the uncertainty of the outcome.Godell and Vahamaa (2013) study the effects of political uncertainty on implied stock market volatility during five US presidential election cycles.They document increases in VIX with changes in the probability of success of the eventual winner.The association between implied volatility and the probability of electing the eventual winner is positive even after the authors control for changes in overall election uncertainty.The findings indicate that the presidential election process engenders market anxiety as investors form and revise their expectations regarding future macroeconomic policies.VIX decreases as the winner of the US presidential election becomes more certain.
Academic research on VIX and investor sentiment largely confirms the expected relationship between uncertainty and the stock market.Researchers, including Whaley (2000), Traub, Ferreira, McArdle and Antogelli (2000) and Smales (2014), provide evidence in support of high VIX levels during periods of uncertainty, when investors require additional compensation in the form of above-average excess returns for riskier assets.Two studies suggest that VIX levels alone are insufficient to determine the variance premium for stock returns.The first, is a unique study by Dhaene, Dony, Forys, Linders and Shoutens (2012), that proposes a new fear index, with the moniker FIX.The quantification of the FIX takes into account: market risk (VIX), liquidity risk, systemic risk and herd behavior via the concept of comonotonicity.This approach allows the authors to measure an overall level of market uncertainty as well as to identify precisely the individual importance of the distinct risk components.
The second article, by Drechsler (2013), demonstrates that uncertainty is strongly reflected in option prices but the fluctuations in the VIX and implied volatility curve contain an important uncertainty component.The author uses a calibration of the equilibrium model to simultaneously match salient moments of consumption and dividends, the equity premium, risk-free rate, the variance premium and implied volatility skew to document the predictive power of the variance premium for stock returns.Drechsler's results imply that uncertainty and its variation are important for jointly explaining the equity premium, risk-free rate, and the large variance premium embedded in the "high" price of options.The Dhaene, et al. (2012) and the Drechsler (2013) articles indicate the need to look beyond VIX levels to determine underlying uncertainty.

Data
The VIX and VX data series begin on 3/26/2004 with the trade of the first VIX futures contract.The later introduction of the VVIX on 1/3/2007, results in 696 fewer observations for this index than VIX and VX.The last trading day for all data series is 12/30/2016, resulting in a population of 3,214 observations for the VIX, VX indexes and 2,518 for VVIX.
The daily VX data set is constructed by rolling the nearest available contract into the next, one day prior to the delivery of the current contract.Specifically, on the first VX trading day, 3/26/2004, a position is established in the nearest available contract, the May 04.One day prior to the May 04 delivery, 5/19/04, the position is rolled into the Jun 04 contract.On 6/16/04, one day prior to the Jun 04 delivery, the contract is rolled into the Jul 04, and so on.With the exception of the missing Apr 04 contract, there are no further interruptions to the pattern of rolling one-month near futures throughout the 2004-2016 time-period.Testing comparisons of EP 16 are made to all other parallel time periods as well as to the populations.The populations are defined as: 1) Data Period Y (DP Y ).The annual populations begin on the first trading day, through the last in each year Y, resulting in n Y observations.
The DP Y represent a greater barrier to overcome than DP N because annual values are more closely related to disturbances caused by an election period.Table 3 below clarifies the population data periods for DP N and DP Y .

Methodology
This section presents a common application of Variation Test (VT) and Predictive Test (PT) methodologies applied to each X, where X = ln(VIX i,t /VIX i,t-1 ), ln(VX i,t /VX i,t-1 ) and ln(VVIX i,t /VVIX i,t-1 ).

Variation Tests (VT)
The variation tests (VT) are straight-forward F-tests comparing the sample variation S(X 16 ), to each other sample election period S(X i ) and to population d = DP Y and DP N .
VT#1 = S(X 2016 )/S(X i ) (1) S(Xi) is the sample variation of Xt during EPi: 1/2 n i = Nov 30 t i = Jun 1 t i = any day t during EP i and i = 6/1 through 11/30 for each year, y = 2004, 2005, … 2016.X ti = the natural logarithmic function of changes in X i : ln(X i,t /X i,t-1 ) .(X d ) is the population standard deviation: for each d = DP Y and DP N .
VT#3 tests the significance of the intraday volatility EP 16 , S(IV 2016 ), relative to the same in other parallel time periods S(IV i ).VT#4 tests the robustness of the results by evaluating each S(X i ) relative to the populations intraday volatility (IV d ).
VT#3 = S(IV 2016 )/S(IV i ) (3) Where: S(IV i ) is the sample volatility of intraday trading values during EPi, or , and the inputs are defined as IV t i = (VX H,t i -VX L,t i )/VX O,t i .IV t i = the Intraday Volatility of VX on day t during EPi, VX H,t i = the Highest value of VX on day t during EPi, VX L,t i = the Lowest value of VX on day t during EPi, VX O,t i = the Opening value of VX on day t during EPi.

Predictive Tests (PT)
The predictive tests are based on the abnormal (AR) and cumulative abnormal returns (CAR) generated from equation 5: where:  4 and 5 show that EP 16 is a period of unprecedented uncertainty as indicated by consistently significant variations across all comparisons.Surprisingly, the results for EP 16 overshadow even those for 2008, a year of significant economic disruption and bank failures.The final volatility measures used to evaluate the volatility during the 2016 election period are based on VIX futures intraday volatility (IV i ).Table 6 shows the level values for S(IV i ) and S(IV Y ) respectively.The results for VT#3 are displayed in column S(IV 16 )/S(IV i ) and show that the intraday volatility during EP16 is significantly greater than all other election periods examined.VT#4, columns S(IV i )/σ(IV N ) and S(IV i )/σ(IV Y ), confirms the unusually high intraday volatility by showing S(IV 16 ) is the only election period with significantly greater volatility compared to both σ(IV N ) and σ(IV Y ).

Variation Test Results
Overall, the four variation tests provide a strong case for significant investor uncertainty during the 2016 election period relative to twelve other parallel time periods.

Predictive Test Results
The Predictive Tests (PTs) are based on the results from 14 regressions; 13 apply DP Y and 1 applies DP N .The regressions establish predictive values for ln(VX d,t /VX d,t-1 ), given contemporaneous values for ln(VIX d,t /VIX d,t-1 ).
The focus of each PT is the significance of the abnormal returns (AR , ) and cumulative abnormal returns (CAR , ) during each election period.The CARs , are cumulated from the first trading day in June to the last trading day in November for each EP i , but the parameters are estimated using DP Y and DP N .The regression statistics are displayed in Table 1, for the interested reader.
Table 7 displays the results for PT#1 and PT#2 as the number of significant , and , days, * , as a proportion of the total number of days in the election period, , * / , using parameters generated from approximately 252 observations per year.Columns AR Y,ti /S(AR Y ) indicate EP 16 has the largest number of significant days at the 90% confidence level and the second the largest at the 95% level.The number of significant , , displayed in columns CAR Y,ti /S(CAR Y ), reveal no interesting results for 2016.This finding suggests that the 2016 election period has a relatively large number of shocks that did not persist over time.The PT results point to a 2016 election period as one pocked by frequent unusual days, more so than other parallel time periods studied, but the shocks are not long-lasting.

Conclusions
The This study provides evidence for significant investor disruption during the 2016 election period.The findings imply that in periods of economic calm, the levels of volatility indexes alone are insufficient and misleading in determining investor sentiment.The byzantine behavior of VIX during the 2016US Presidential election period, provides a unique opportunity to study VIX when economic concerns are not a dominate reason for investor anxiety.Under this scenario, VIX levels can remain low even while investor anxiety is high leading to incorrect conclusions regarding systematic risk levels.
The volatility tests indicate EP 16 as a period of unusually high variations in the volatility indexes compared to other parallel non-election time periods.Similarly, intraday trading values for VIX futures, provides additional evidence in the form of exceptionally high intraday and volume variations.
The predictive tests consider the deviations of actual from predicted values for VIX futures.The results signal EP 16 as a period with a relatively large number of significantly high abnormal return days but a low number of significant cumulative abnormal return days, indicating frequent shocks in EP 16 that do not produce long-lasting results.

Table 1
displays the average levels of VIX i , VX i and VVIX i , where i is equal to each election, and parallel non-election, period (EP i ).The bold values in each column represent the highest values in each election period.The 2016 VIX and VX averages are the lowest since 2006 while VVIX is at its highest level since introduction.

is the highest since the index was introduced in 2007. Similarly, column VX i Premium indicates the 7.56% is also at its highest level since trading began in 2004.
The data is parsed, as shown in Table2, into four actual election periods and nine parallel non-election periods with the corresponding number of observations, n i , shown in the last column.Each election period (EP i ) is defined as the first trading day in June to the last trading day of November.The four years in bold indicate an actual US Presidential election period and the remaining nine years indicate a parallel time period in a non-election year.Both the actual and the parallel non-election periods are referred to as EP i for simplicity.

Table 3 (
continued).Population N and Y 1 * ln(VIX d,t /VIX d,t-1 ) + AR d,t (5) where: ln(VX d,t /VX d,t-1 ) = the lognormal of the near VIX futures contract on day t, for population d = DP Y and DP N , ln(VIX d,t /VIX d,t-1 ) = the lognormal of the VIX spot index on day t for population d.  d,o and  d,1 = regression coefficients for population d.AR d,t = the abnormal return prediction of ln(VX d,t /VX d,t-1 ) for parameters based on d, i.e., AR d,t = ln(VX d,t /VX d,t-1 ) -( d,o +  d,1 * ln(VIX d,t /VIX d,t-1 ).PT#1 and PT#2 apply t-tests to determine if AR d,t i and CAR d,t i are insignificantly different from zero at each point in time based on population d: and PT#4 apply F-tests to determine the significance of S(AR d,16 ) and S(CAR d,16 ) relative to each S(AR d,i ) and S(CAR d,i ) respectively, to test the hypotheses:

Table 4
Table5displays level values for (VIX Y ), (VX Y ) and (VVIX Y ) respectively.The results of the F-tests are revealed in columns S(VIX i )/σ(VIX N )-S(VVIX i )/σ(VVIX Y ) using volatility results from both DPY and DPN.Columns S(VIX i )/σ(VIX N ) and S(VX i )/σ(VX N ) show that S(VIX i ) and S(VX i ) are significantly greater than (VIX N ) and (VX N ) only for the 2011 and 2016 election periods.When the sample variances are compared to (VIX Y ) and (VX Y ) in columns S(VIX i )/σ(VIX Y ) and S(VX i )/σ(VX Y ), respectively, the single significant variable relative to (VIX Y ) is the volatility of VIX during EP 16 , S(VIX 16 ).The volatility of VVIX, columns S(VVIX i )/σ(VVIX N ) and S(VVIX i )/σ(VVIX Y ), identifies the 2016 election period as the only one significantly greater than both σ(VVIX N ) and σ(VVIX Y ).Tables displays the level values for S(VIX i ), S(VX i ) and S(VVIX i ) with the corresponding F-test results for VT#1 in columns S(VIX 16 )/S(VIX i ), S(VX 16 )/S(VX i ) and S(VVIX 16 )/S(VVIX i ).The findings show that S(VIX 16 ) and S(VX 16 ) are significantly higher than S(VIX i ) and S(VX i ) in seven of thirteen EP i s.Further, the level values of S(VIX 16 ) and S(VX 16 ) are exceeded by only one other year, 2011.The VVIX results indicating that the variation in the VVIX index during EP 16 , S(VVIX 16 ), is higher than all other S(VVIX i ) since introduction, and significantly so in seven of nine EP i s.

Table 7 .
Proportion of significant AR Y,ti and CAR Y,ti Days

Table 8
displays the results from repeating the first two PTs using DPN, rather than DPY.The results indicate the election period of 2008 has the highest number of significant AR N,ti days at the 90% significance level and 2016 has the highest at the 95% level.The significance of the number of CAR N,ti days remains unremarkable in 2016, providing further support for frequent shocks that do not persist.

Table 9
depicts the results of PT#3 and PT#4, constructed to show the volatility of abnormal and cumulative abnormal returns during EP 16 relative to the variabilities of each other election period based on annual parameters.Columns S(AR Y,i ) and S(AR Y,16 )/S(AR Y,i ) reveal the S(AR Y,16 ) is exceeded only by S(AR Y,08 ), however, significance is established in only five time periods.Columns S(CAR Y,i ) and S(CAR Y,16 )/S(CAR Y,i ), confirm the lack of a significant or notable cumulative effect for EP 16 based on annual parameters.The tests are repeated using DP N parameters with similar results.
2016 Paradox: a strong economy, strong stock market, low inflation, low unemployment and low VIX levels combined with high levels of anxiety, uncertainty and fear of the future.Incorrect conclusions regarding the state of investor sentiment were made because the focus was on a single parameter of risk-VIX levels.Using volatility tests and predictive test, this study demonstrates that VIX levels alone are insufficient, and at times misleading, in determining investor sentiment.The volatility tests showEP 16 as a period of unusually high variations in VIX compared to other parallel non-election time periods.Similarly, intraday trading variations for VIX futures are exceptionally high during the 2016 election period.The predictive tests signal EP 16 as a period with frequent abnormal shocks, without persistent echo.Together, the tests show that investor sentiment is better described by the distribution of VIX than the level.