Interactions between United States (VIX) and United Kingdom (VFTSE) Market Volatility: A Time Series Study

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1 Sacred Heart University WCOB Student Papers Jack Welch College of Business Interactions between United States (VIX) and United Kingdom (VFTSE) Market Volatility: A Time Series Study Jacob Friar friarj@mail.sacredheart.edu Follow this and additional works at: Part of the Economics Commons Recommended Citation Friar, Jacob, "Interactions between United States (VIX) and United Kingdom (VFTSE) Market Volatility: A Time Series Study" (2017). WCOB Student Papers This Essay is brought to you for free and open access by the Jack Welch College of Business at DigitalCommons@SHU. It has been accepted for inclusion in WCOB Student Papers by an authorized administrator of DigitalCommons@SHU. For more information, please contact ferribyp@sacredheart.edu, lysobeyb@sacredheart.edu.

2 1 Interactions between United States (VIX) and United Kingdom (VFTSE) Market Volatility: A Time Series Study Jacob Friar EC-491 Jack Welch School of Business Sacred Heart University 5151 Park Avenue Bridgeport, CT Phone: friarj@mail.sacredheart.edu Abstract Financial markets have become increasingly more dependent on calculated measures of volatility. Many of the leading economies have developed their own indices that reflect the expectations of market volatility, including the United States (VIX) and the United Kingdom (VFTSE). This study uses these two indices in particular to conduct a time series analysis as a means to identifying potential relationships between the value of the VIX and VFTSE, over time. The analysis concludes that there is a two-way relationship between the indices, and therefore the VAR Model was implemented. Further evaluation of the impulses reveals that while values of each index affect the other, past values of a given index also affects itself. These results could have implications on the direction of expected volatility in the US and UK markets following dramatic changes to the VIX and VFTSE indices.

3 2 1. Introduction Volatility indices are a relatively new development, but have risen to prominence because of their usefulness in analyzing the financial markets and making investment decisions. Periods of high volatility cater toward one type of investment strategy, while low volatility markets favor a different tactic. In addition to aiding investors due to their real-time fluctuations, this paper examines whether interactions between volatility in the US and UK financial markets could aid in forecasting the volatility of one another, and therefore create even more of an edge for investors. Additionally, this could help government policy makers as they can warn people of impending dangers, if in fact a relationship between the indices exist. Section 2 of this paper includes an overview of literature relating to this study. The research includes descriptions of the VFTSE and VIX indices, as well as a discussion of various relationships between the US and UK markets. I did not come across any prior studies on this exact material, therefore there is no inclusion of prior studies on this precise topic. The timeseries analysis was completed using EViews software. The description of the data is in Section 3 of this document, the process of this analysis is detailed in full in Section 4, and the corresponding results are in Section 6, the appendix. The conclusions of my findings are summarized in Section 5. The analysis displays empirical evidence of the VIX and VFTSE granger causing one another, as well their own past shocks affecting their future results. Examination of the impulse graphs generated from EViews in appendix 6 displays the typical responses to past shocks. Out-

4 3 of-sample analysis and forecasting future period would enhance this study, and are anticipated to be done and added to this paper in the near future. 2. Literature Overview This time-series analysis has the purpose of analyzing the relationship between the volatility indexes of the United States (VIX) and United Kingdom (VFTSE). First, it is imperative to garner a complete understanding for what the indexes represent, and the implications they have on the economy. Following the synopsis of foundational information, a description of the data, model, and findings will be fully explained. The FTSE 100 Volatility Index (VFTSE) represents the volatility implied by the options prices of the UK benchmark equity index. It is calculated using the VIX model-free methodology, and reflects the expectation of market participants for the future volatility of the underlying index during the next thirty calendar days and thus, is considered to be the market forecast of the future realized volatility of the UK stock market 1. The VFTSE was originally constructed and launched in 2008 by NYSE Euronext, but historical values dating back to January of 2000 using end-of-day values were recorded for comparison to other indices. The FTSE 100 Index consists of the 100 largest companies (measured by market capitalization) in the UK market, which accounts for 81% of their market. Therefore, the VFTSE calculated off of this index utilizes an optimal sample from the marketplace in the UK. Upon examining a graph of the index, it is evident 1

5 4 that the VFTSE fluctuates daily, but, the mean of its daily change is virtually zero, thus there is no visible trend in the data. The CBOE s Market Volatility Index (VIX) is based on options of the S&P 500, and was instituted in 1993, well before the VFTSE. The purpose of its creation was multifaceted: the CBOE desired a benchmark of expected short-term market volatility and economists desired a volatility metric that would be useful for comparing market fluctuations in then-current times to stock market crashes like October Like the VFTSE, the VIX is forward looking, quantifying what is expected to happen. Originally based on the S&P 100, it was then switched to the S&P 500. The focus under both circumstances was to use the index with the most actively traded index options in the United States. The more active the index options, the more integrated, influential, and useful the volatility index is. The VIX has no visible trend, and the mean of its daily changes is virtually zero. The purpose of this study is to analyze the relationship between these indices. The potential for a relationship like that is high, as there are various other ways in which the economies of the UK and US are intertwined. For instance, unexpected economic shocks in each country create similar results in volatility. Also, volatility often has its highest spikes following unexpected, or uncertain events. A study conducted by the International Monetary Fund examined four specific factors of shocks within an economy: uncertainty, the unemployment rate, the policy rate and industrial production 2. The United States and United Kingdom respond to these shocks similarly, relative to each of these four categories. According to the study, all four categories, but in particular industrial production, have strikingly similar responses of volatility in the US as it does in the UK. This data indicates a potential relationship between 2

6 5 past shock effects on volatility indexes. The magnitude of the reaction to the shocks differs in some circumstances, but the direction of the responses is nearly synced 3. Additionally, more similarities between the UK and US economies exist due to political allegiances. Foreign policy between the two countries is closely tied together, which has resulted in a strong economic bond. The US-UK bilateral investment relationship was the largest in the world as of US foreign direct investment in the UK was $571 billion, and UK foreign direct investment in the US was $518 billion. Additionally, UK affiliates employ approximately 987,000 US workers, and US firms employ approximately 1.27 million people in the UK. As one can see, the economies of the two nations are closely integrated 4. Thus, the impact the UK has on the US, and vice a versa, is significant in a multitude of ways. This study will use empirical evidence to show that this trend continues into their volatility indexes. Additionally, it will look to quantify the time-series relationship, so as to aid with potential forecasting. 3. Data Description The first data set is titled p_vftse. This data set represents all of the closing prices of the VFTSE index since Various days do not trade, such as weekends and holidays, therefore there are only closing prices for actual trading days. The first day used is January 4th, 2000, and the last one is October 3 rd, The mean of the data points is 20.21, and the standard deviation is The mean of daily change is nearly zero, though, as this is stationary data. The

7 6 higher the value along the vertical axis, the more volatility it displays. There are a total of 4140 p_vftse observations. P_VFTSE Table 1 Summary Statistics Variable Name Observations Mean Std. Dev. Max Min P_VFTSE The second data set is titled p_vix. This data set consists of all the prices of the VIX index in the United States. Just like the p_vftse data, the prices listed are for trading days, which do not include weekends and holidays. All of the dates between both data sets were made to match, and only those data points were used. The mean of this data set is 20.45, and the median is The higher the value along the vertical axis, the more volatility it displays. There are a total of 4140 p_vix observations.

8 7 P_VIX Table 2 Summary Statistics Variable Name Observations Mean Std. Dev. Max Min P_VIX Steps of Time Series Analysis The time-series analysis was conducted using EViews technology, and the data was imported from a Microsoft Excel file. The first step when performing a time-series analysis is to create a line graph displaying both data sets (See Appendix 1). The graph contains overlapping scales, with p_vftse being displayed on the left vertical axis in blue, and p_vix being displayed on the right vertical axis in red. The horizontal axis along the bottom is labeled using years in the format of the last two numbers of the year being portrayed (ie: "00 is 2000). The purpose of this step is to visually examine the likelihood of the data being stationary (I(0)) or nonstationary (I(1)). In this case, the visual test would suggest that the data is stationary.

9 8 Following the construction of a graph, the next step is to complete the Augmented Dickey Fuller (ADF) test. This test determines whether the data is stationary or not by testing for a unit root. The null hypothesis states that there is a unit root, thus the data would be nonstationary. After conducting an ADF test for both p_vftse and p_vix independently, it is confirmed that both data sets are stationary because the probability from the ADF test is below 0.10, thus, we reject the null hypothesis that a unit root exists at a significance level of 1% (See Appendix 2). Due to the fact that both data sets are I(0), the next step in the time-series process is to determine the Lag Length for the Granger Causality Test. By running the data through the Estimate VAR function, and then utilizing the Lag Length Criteria option, the proper Lag Length can be attained. Using the Schwarz Criterion, we have identified that the proper lag length for this analysis is 6 (See Appendix 3). Now that the Lag Length of 6 (using SC) has been determined, the next step is to perform the Granger Causality Test. For the Granger Causality Test, the lag is entered as n-1, therefore the lag entered is 5. There are two null hypotheses in this test: p_vix does not Granger Cause p_vftse, and p_vftse does not Granger Cause p_vix. Both probabilities are below 0.01, therefore we reject the null hypothesis at a 1% significance level on both occasions (See Appendix 4). Therefore, there is a two-way relationship between the p_vftse and p_vix, and so we elected to use the Vector Autoregressions Model (VAR). When estimating the VAR model, we input 6 lags as required by the Schwarz Criterion. Additionally, the stationary data values of

10 9 p_vftse and p_vix are entered into the Endogenous Variables field (See Appendix 5). The models derived are as follows: P_VFTSEt = t t t t t t t t t t t t-6 P_VIXt = t t t t t t t t t t t t-6 Using t-statistics, one can analyze the significance of each coefficient. In the P_VFTSE model, all coefficients are significant at a 1% level except for fourth lag of the VFTSE (where the coefficient is 0.033), which is insignificant. In the P_VIX model, there is a more variability in the significance of coefficients. The first and fifth lags of the VIX are significant at 1%, and the fourth is significant at 5%. The remaining lags are all insignificant. The VFTSE first lag is significant at 5%, the second is significant at 10%, and the third, fifth and sixth are significant at 1%. The fourth lag of the VFTSE is insignificant (See Appendix 5). The final step of the time-series analysis is to examine the impulse graphs of the VAR model (See Appendix 6). Each graph represents a different scenario, but all are displayed over a 30-day time horizon (x-axis). The vertical axis could be viewed in dollars because these indices move like stocks, but would be more accurately labeled as points. Every single graph is portraying significant data because the x-axis never intersects the 95% confidence interval represented by the orange dotted-lines.

11 10 The top-left graph displays the response of the VFTSE to a shock in the VFTSE. Initially, there is an increase in the VFTSE following its past shock, but over the next 30 days it slowly, albeit steadily deteriorates. Top-right displays the response of the VFTSE to a shock in the VIX. This graph shows that on the first day, there is no reaction, but on the second day there is a spike upward in the VFTSE. This is likely due to the fact that the UK market closes before the US markets, so there is no reaction on day one. Following the initial spike, the response flattens out and slowly descends toward zero except for a shock on days 5 and 6. Bottom-left reveals the reaction of the VIX to a shock in the VFTSE. This graph displays the shock in UK volatility results in an immediate increase in the VIX, but that spike slowly diminishes over the time horizon. Lastly, the bottom-right graph displays the response of the VIX to a shock in the VIX. A shock to US volatility is followed by a significant spike, and then it slowly recedes over time. The response of past shocks on a given index effecting itself are the most dramatic, and the spike is as high as 1.4 in the US and 1.6 in the UK, initially (See Appendix 6). 5. Conclusion Based on the time-series analysis, the VFTSE and VIX granger cause one another at a significance level of 1%. The interactions between each index can be investigated through analysis of their impulse charts. While the indices have the most dramatic spikes from past shocks of itself, there is a relationship between past shocks of one index affecting the other. All of the observable results falls within a 95% confidence interval, as indicated by the orange dotted lines, and therefore are significant.

12 11 This paper would be enhanced if more volatility indices were computed and analyzed relative to the VFTSE and the VIX. Additionally, forecasting future periods would have enhanced analysis, as well as out-of-sample analyses. All of these steps would provide evidence potentially useful in forecasting financial market volatility. The potential implications of this paper could aid in analyzing financial market volatility in the US and UK, and the interactions between the nations. As a disclaimer, investment firms that choose to use this research do so at their own risk, as there are no suggestions to choose investment practices based on these findings. 6. Time-Series Graphs (Appendices) Appendix P_VFTSE P_VIX

13 12 Appendix 2 Null Hypothesis: P_VFTSE has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=30) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(P_VFTSE) Method: Least Squares Date: 12/07/16 Time: 12:56 Sample (adjusted): 1/05/ /03/2016 Included observations: 4139 after adjustments Variable Coefficient Std. Error t-statistic Prob. P_VFTSE(-1) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Null Hypothesis: P_VIX has a unit root Exogenous: Constant Lag Length: 4 (Automatic - based on SIC, maxlag=30) t-statistic Prob.* Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided p-values.

14 13 Augmented Dickey-Fuller Test Equation Dependent Variable: D(P_VIX) Method: Least Squares Date: 12/07/16 Time: 12:57 Sample (adjusted): 1/11/ /03/2016 Included observations: 4135 after adjustments Variable Coefficient Std. Error t-statistic Prob. P_VIX(-1) D(P_VIX(-1)) D(P_VIX(-2)) D(P_VIX(-3)) D(P_VIX(-4)) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) Appendix 3 VAR Lag Order Selection Criteria Endogenous variables: P_VFTSE P_VIX Exogenous variables: C Date: 12/07/16 Time: 13:04 Sample: 1/04/ /03/2016 Included observations: 4128 Lag LogL LR FPE AIC SC HQ NA * * * * * * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error

15 14 AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion Appendix 4 Pairwise Granger Causality Tests Date: 12/07/16 Time: 13:08 Sample: 1/04/ /03/2016 Lags: 5 Null Hypothesis: Obs F-Statistic Prob. P_VIX does not Granger Cause P_VFTSE E-136 P_VFTSE does not Granger Cause P_VIX Appendix 5 Vector Autoregression Estimates Date: 12/10/16 Time: 20:29 Sample (adjusted): 1/12/ /03/2016 Included observations: 4134 after adjustments Standard errors in ( ) & t-statistics in [ ] P_VFTSE P_VIX P_VFTSE(-1) ( ) ( ) [ ] [ ] P_VFTSE(-2) ( ) ( ) [ ] [ ] P_VFTSE(-3) ( ) ( ) [ ] [ ] P_VFTSE(-4) ( ) ( ) [ ] [ ] P_VFTSE(-5) ( ) ( ) [ ] [ ] P_VFTSE(-6) ( ) ( )

16 15 [ ] [ ] P_VIX(-1) ( ) ( ) [ ] [ ] P_VIX(-2) ( ) ( ) [ ] [ ] P_VIX(-3) ( ) ( ) [ ] [ ] P_VIX(-4) ( ) ( ) [ ] [ ] P_VIX(-5) ( ) ( ) [ ] [ ] P_VIX(-6) ( ) ( ) [ ] [ ] C ( ) ( ) [ ] [ ] R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent Determinant resid covariance (dof adj.) Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion

17 16 Appendix 6 Response to Cholesky One S.D. Innovations ± 2 S.E. Response of P_VFTSE to P_VFTSE Response of P_VFTSE to P_VIX Response of P_VIX to P_VFTSE Response of P_VIX to P_VIX

18 17 7. Bibliography Abiola Ayopo, B., Adedoyin Isola, L., & Russel Olukayode, S. (2016). Stock Market Volatility: Does our Fundamental's Matter? Economic Studies. Denis, Stephanie and Kannan, Prakash, The Impact of Uncertainty Shocks on the UK Economy (March 2013). IMF Working Paper No. 13/66. Available at SSRN: Fernandez-Villaverde, J., Guerron-Quintana, P., Kuester, K., & Rubio-Ramirez, J. (2015). Fiscal Volatility Shocks and Economic Activity. American Economic Review. Giot, Pierre, The Information Content of Implied Volatility Indexes for Forecasting Volatility and Market Risk (December 13, 2002). Available at SSRN: Mix, Derek E. "The United Kingdom: Background and Relations with the United State." Congressional Research Service (2015): Print. Siriopoulos, Costas and Fassas, Athanasios, The Information Content of VFTSE (November 30, 2008). Available at SSRN: Whaley, Robert E., Understanding VIX (November 6, 2008). Available at SSRN: