Estimating 90-Day Market Volatility with VIX and VXV

Transcription

1 Estimating 90-Day Market Volatility with VIX and VXV Larissa J. Adamiec, Corresponding Author, Benedictine University, USA Russell Rhoads, Tabb Group, USA ABSTRACT The CBOE Volatility Index (VIX) has historically been a consistent indicator of 30-day or 1-month (21-day actual) realized market volatility. In addition, the Chicago Board Options Exchange also quotes the CBOE 3-Month Volatility Index (VXV) which indicates the 3-month realized market volatility. This study demonstrates both VIX and VXV are still reliable indicators of their respective realized market volatility periods. Both of the indexes consistently overstate realized volatility, indicating market participants often perceive volatility to be much higher than volatility actually is. The overstatement of expected volatility leads to an indicator which is consistently higher. Perceived volatility in the long-run is often lower than volatility in the short-run which is why VXV is often lower than VIX (VIX is usually lower than VXV). However, the accuracy of the VXV is roughly 35% as compared with the accuracy of the VIX at 60.1%. By combining the two indicators to create a third indicator we were able to provide a much better estimate of 64-Day Realized volatility, with an accuracy rate 41%. Due to options often being over-priced, historical volatility is often higher than both realized volatility or the volatility index, either the VIX or the VXV. Even though the historical volatility is higher we find the estimated historical volatility to be more easily estimated than realized volatility. Using the same time period from January 2, 2008 through December 31, 2016 we find the VIX estimates the 21-Day Historical Volatility with 83.70% accuracy. Similarly, we find the VXV estimates the 64-Day Historical Volatility with 84.52% accuracy. Keywords: Options, VIX, Volatility, VXV INTRODUCTION VIX is a consistent measure of expected volatility for the S&P 500 (SPX) as determined by the market prices of SPX Index options. One of the purposes behind the introduction of VIX was to give market participants a guide to the market s expectation for realized volatility over the following 30 calendar days or 21 trading days. VIX has historically been a consistent predictor of realized volatility, but also has been consistently higher than realized market volatility (Blair, Poon &Taylor, 2010). The VIX was initially calculated in 1993 using the CBOE S&P100 Index option prices. During this initial calculation the options used matured within the next 30 calendar days and were all traded at-themoney. The objective was to present a standard market volatility value which demonstrates the expected volatility of the next 30 calendar days or the next 21 trading days. The OEX options were chosen to as those options at the time were some of the most liquid securities traded. The VIX backed-out volatility using the Black-Scholes option pricing formula (Whaley, 1993). In 2003 the VIX was updated to reflect a broader underlying mix with the inclusion of the S&P 500 index, as well as the inclusion of options within the range of moneyness for the options. Strikes are now in-the-money and out-of-the-money. The volatility is again backed-out of the Black-Scholes option 20 The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue

2 pricing formula. However, the strike price now reflects the change in strike prices between the options which are in-the-money and options which are out-of-the-money. The average of the strike prices are taken and inputted into the Black-Scholes model (CBOE White Paper, 2018). The VIX calculation was revised again to reflect the popular weekly options which were introduced by the CBOE in The only difference between weekly options and traditional options is the shorter maturity period of one week as opposed to one month, three months and even longer dated options. The volume for the weekly options grew exponentially and became one of the most popular options products ever introduced. In 2013 the CBOE began to include these options as they are some of the most liquid traded options in the calculation. In addition to VIX, the Chicago Board Options Exchange also calculates and publishes the CBOE 3-Month Volatility Index which is commonly referred to by the ticker VXV. The index was launched in VXV is a consistent measure of the market s expectation for price volatility over the subsequent 93 calendar days or 3 months. On average there are 64 trading days in a 93 calendar day period. Like VIX, the level of VXV is determined through SPX Index option pricing, but the options used to determine VXV expire at a farther date than those contributing to the level of VIX. Practitioners have often compared VXV to VIX and used this relationship as a predictor of future price changes for the S&P 500. There is also a common belief that when VXV is at a significant premium to VIX there is a higher likelihood that VIX will understate the resulting market volatility (Donniger, 2012). This belief stems from VIX moving higher in reaction to market volatility and VXV focusing on a longer time period than VIX. VXV is believed to act as a leading indicator for VIX, although the relationship between VIX and VXV varies over time. Listed options have been historically overpriced relative to the resulting volatility experienced by the underlying market (Chiras & Manaster, 1978). This convention of option pricing is often explained as option sellers receiving extra premium over fair value for taking a short position in an option contract. An unhedged option position exposes a short seller to potentially unlimited losses therefore the seller is compensated with a risk premium for taking on this risk (Hull &White, 1987). The option pricing factor that is associated with the risk premium is implied volatility. Looking back, after realized volatility has been recorded, analysts quantify whether an option was overpriced or underpriced based on the amount of realized volatility that follow a VIX closing price. An example of this risk premium Carr 2006 notes that the average closing price for VIX from January 2, 1990 to October 18, 2005 was while the average realized volatility for the S&P 500 was or a difference of The findings in the Carr study are fairly consistent with the time period covered in this paper. From January 2008 to December 2016 the average close for VIX was and average realized volatility was resulting in an average difference of The average closing price for VIX was higher over the time period than the period in the Carr study and the risk premium was slightly lower. The differences for premiums can be attributed to the Great Financial Crisis which occurred in the latter months of Chart 1 shows the average monthly VIX close versus the following realized market volatility from 2008 to The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue 21

3 Chart 1: VIX Overstates / Understates Realized Volatility Note in Chart 1 the majority of months where VIX under stated the following market volatility occurred in In the last three years of this study s time frame VIX was higher than realized volatility during only three monthly observations and in two of those the difference was miniscule. Table 1 demonstrates the descriptive statistics of both the VIX and the 21-day realized volatility. Notice the VIX mean is higher than the 21-Day Realized Volatility by The standard deviation is higher for the 21-Day Realized Volatility by The difference of the skew was much smaller indicating the distribution a similarly shaped. The 21-Day Realized Volatility is much more peaked than the VIX. The minimum is significantly lower for the 21-Day Realized Volatility (4.6298) compared to the minimum of the VIX ( ). The maximum for the VIX and the 21-Day Realized Volatility are similar of and respectively. Table 1: VIX & 21-Day Realized Volatility Descriptive Statistics VIX 21-Day Realized Volatility Mean Standard Deviation Skew Kurtosis Minimum Maximum Table 2 evaluates the differences between the VIX and the 21-Day Realized Volatility. The descriptive statistics look at either only the days which overstate the 21-Day Realized Volatility or the days which understate the 21-Day Realized Volatility. The standard deviation for the understates is which is much higher than the for the overstates. The VIX often overstates the 21-Day Realized Volatility causing the expectation that the overstated value will often be more in-line with the correct value. Table 2: Over/Understates 21-Day Realized Volatility Descriptive Statistics Understates Overstates Mean Standard Deviation Skew Kurtosis Minimum Maximum There are several studies exploring the relationship between VIX and the amount of price volatility in the S&P 500 that follows a closing level for VIX. A study that is parallel to this paper, Karagiannis 22 The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue

4 2014, takes into account the relative level of VIX futures versus the spot VIX index as a predictor of market volatility that follows. The basis of the Karagiannis study has merit as VIX futures are a good predictor of VIX index price movement. However, as expiration approaches this usefulness has not historically held up. A weakness of the Karagiannis study is that the time to expiration for a VIX futures contract is constantly changing and this will have an impact on the price difference between VIX futures and the spot VIX index regardless of the market s outlook for volatility. The study that resulted in this paper focuses on the VXV VIX relationship and VXV is a measure that consistently targets a 64-day time frame. The hypothesis is using two measures that both have a consistent time frame will improve on the results of the Karagiannis study. Currently there is no peer reviewed research that takes VXV into account as a predictor of future market volatility or subsequent stock market price behavior. In fact, there is no published peer reviewed research that uses VXV in existence. There are some practitioner uses of the relationship between VXV and VIX as a prediction of directional stock market price behavior, but again no studies that the author is aware of where VXV is used as a factor to predict 30 calendar day realized volatility for the S&P 500. The relationship between VXV and VIX that has been used to attempt to time trend changes in the S&P 500 was one of the factors that resulted in considering VXV as a compliment to VIX in attempting to predict realized market volatility. Chart 2: VXV Overstates / Understates Realized Volatility Note in Chart 2 the majority of months where VXV under stated the following market volatility occurred in In the last three years of this study s time frame VXV was higher than realized volatility during only three monthly observations and in two of those the difference was miniscule. Table 3 demonstrates the descriptive statistics of both the VXV and the 64-day realized volatility. Notice the VXV mean is higher than the 64-Day Realized Volatility by The standard deviation is higher for the 64-Day Realized Volatility by The difference of the skew was much smaller indicating the distribution a similarly shaped. The 64-Day Realized Volatility is much more peaked than the VXV. The minimum is significantly lower for the 64-Day Realized Volatility (6.2837) compared to the minimum of the VIX ( ). The maximum for the VXV and the 64-Day Realized Volatility are similar of and respectively. Table 3: VXV & 64-Day Realized Volatility Descriptive Statistics VXV 64-Day Realized Volatility Mean Standard Deviation Skew Kurtosis Minimum Maximum The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue 23

5 Table 4 evaluates the differences between the VXV and the 64-Day Realized Volatility. The descriptive statistics look at either only the days which overstate the 64-Day Realized Volatility or the days which understate the 64-Day Realized Volatility. The standard deviation for the understates is which is much higher than the for the overstates. The VXV often overstates the 64-Day Realized Volatility causing the expectation that the overstated value will often be more in-line with the correct value. Table 4: Over/Understates 64-Day Realized Volatility Descriptive Statistics Understates Overstates Mean Standard Deviation Skew Kurtosis Minimum Maximum The VIX and VXV often move in-line with each other (Rhoads 2011). The VIX is often more reactionary than the VXV, which is seen when comparing Chart 1 and Chart 2. Chart 3 looks at both the VIX and the VXV together. The VIX consistently has higher spikes than the VXV. Conversely, the VIX also has lower lows than the VXV. The reduction in higher highs and lowers lows demonstrates the VXV having a lower volatility than the VIX. The standard deviation for the VIX during the sample time period is compared with a standard deviation of 8.55 for the VXV. Surprisingly, the average for the VXV is slightly higher than the average of the VIX at and respectively. Since both the VIX and VXV overstate volatility the VXV seems to overstate volatility even higher than the VIX. However, the VXV has a lower reaction to market events than the VIX. Chart 3: VIX vs. VXV HYPOTHESIS Many studies (Christofferson, Jacobs & Mimouni, 2010) have demonstrated the differences in realized volatility from VIX. However, the relationship has not been analyzed incorporating the Great Financial Crisis of During the 2008 crisis the VIX increased to almost a level of 90. The volatility of VIX increased causing larger discrepancies between predicted volatility and realized volatility. Hypothesis 1: The VIX remains a good 21-Day Realized Volatility estimator. This is tested by linear regression modeling. Hypothesis 2: The VXV remains a good estimator of realized 64-Day Realized Volatility. This is tested by linear regression modeling. 24 The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue

6 The introduction of the VXV has given practitioners an easy way to quickly estimate the 3-month volatility. The VXV was launched in January 2002, with limited attention by academics. This is the first study demonstrating VXV as a good estimator for the 3-month volatility. Hypothesis 3: VIX estimates the 21-Day Historical Volatility better than 21-Day Realized Volatility. A regression is done with the VIX and realized volatility and historical volatility and realized volatility. Hypothesis 4: VXV estimates the 64-Day Historical Volatility better than 64-Day Realized Volatility. A regression is performed with the VXV and 64-day realized volatility and historical volatility with 64-day realized volatility. Hypothesis 5: The new model combing VIX and VXV proves to be a better estimator of the 3-month or 64-Day Realized Volatility. The new model combines VIX and VXV, thus creating a new indicator. The model is formed using two different techniques equally weighted VIX and VXV as well as multiple regression. The combination of the two indexes combines the market sentiment of both the short-term and long-term, providing more information than either index individually. The combination of the two generates better accuracy for the 64-day realized volatility. DATA The data used in this study were acquired from three different sources. VIX and VXV daily closing prices from January 2, 2008 through December 31, 2016 were obtained from the Chicago Board Options Exchange website. The daily closing prices for the S&P 500 were downloaded from Yahoo Finance. In order to assure data integrity VIX, VXV, and S&P 500 data was downloaded from Bloomberg and compared to the CBOE and Yahoo Finance data for accuracy. There were no discrepancies found among the various data sources. This data represents daily closing market pricing for 1763 days from January 2, 2008 through December 30, Volatility indexes are created to depict standard measures of implied volatility as indicated by option pricing. When implied volatility is determined from option pricing the result is stated as a percent. The standard method of quoting an implied volatility index is to take the volatility measure and multiply it times 100 with the result being a non-percent quote. For example, implied volatility of 0.20 or 20% would be depicted by a volatility index as For easy comparison during testing, realized volatility was converted to a non-percent whole number. Realized volatility was calculated from daily returns of the S&P 500. The goal of this study is to create a model that predicts realized volatility over a 30 calendar day period. VIX is a measure based on 30 calendar days and does not differentiate between days when the markets are open or closed. On average there are 21 trading days over a 30 calendar day period so realized volatility for this study is based on 21 trading days. Also, on average there are 252 trading days in a year in the United States. The results is that this is an industry standard and 252 trading days was used in order to annualize realized volatility over a 21 day period for a direct comparison with VIX. Microsoft Excel was used to complete the creation of the realized volatility data for this study. The realized data was calculated using S&P 500 closing prices. The method behind creating realized volatility involves determining a 21-Day standard deviation of daily returns as measured in percent. In Excel the =stdevep() function was utilized for this calculation. This 21-Day standard deviation was then multiplied times the square root of 252. The result is an annualized volatility measure which is the measure that the model is being created to predict. Finally, in order for the realized volatility measure to be directly comparable to VIX the result was multiplied by 100. The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue 25

7 RESULTS In the early stages of this study the average difference between VIX and realized volatility from January 2, 2008 and December 31, 2016 was analyzed. The result was an average difference between VIX and realized volatility that was in line with studies that were conducted in the past. Another outcome of this study was showing that, although VIX consistently understates realized volatility, VIX continues to be a useful tool to estimate realized volatility. VXV and 21-Day Realized Volatility were also compared and despite a different time frame, VXV has historically had a good ability to accurately estimate the 21-day Realized Volatility. The primary goal of this study was to improve on using VIX as a predictor of future market volatility by incorporating VXV into a model. The first part of the study was to run two regression analyses comparing VIX and VXV with realized volatility individually. Then the two factors were combined with the hope of developing a model that is a better predictor. Finally, VIX and VXV were compared as a predictive indicator with their respective historical counter-parts. Hypothesis 1: The VIX is still a good way to estimate the 21-Day Realized Volatility. The VIX was used to estimate today s 21-Day Realized Volatility. This was done using a regression with the VIX as the independent variable and the 21-Day Realized Volatility as the dependent variable. The R-squared value for the time frame is The F score is and the p-value is almost zero, 1.1E-305. Table 5 has the statistical output. Table 5: Hypothesis 1 Regression Output SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 2267 ANOVA df SS MS F Significance F Regression Residual Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 21 Day Realized E VIX The statistical output demonstrates the daily VIX does an adequate job predicting the daily 21-Day Realized Volatility. The VIX does not perfectly generate the day s volatility but gives the market an estimate roughly 60% of the time. This result is consistent with the VIX s tendency to over-state volatility or over-react to volatility. Table 6 demonstrates the descriptive statistics of both the VIX and the 21-Day Realized Volatility. The average VIX ( ) is higher than the average 21-Day Realized Volatility ( ). The 26 The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue

8 standard deviation for both the VIX ( ) and 21-Day Realized Volatility ( ) are similar as are the skew of (VIX) and (21-Day Realized Volatility). Similarly, the kurtosis of the VIX (6.6362) and 21-Day Realized Volatility (9.3863) are similar. The maximum values are also similar VIX ( ) and 21-Day Realized Volatility ( ). The minimum values are different with the VIX ( ) being higher than the 21-Day Realized Volatility (4.6298). Table 6: VIX and 21-Day Realized Volatility VIX 21-Day Realized Mean Standard Deviation Skew Kurtosis Minimum Maximum Hypothesis 2: The VXV is a way to estimate the 64-Day Realized Volatility. The VXV was used to estimate today s 64-Day Realized Volatility. This was done using a regression with the VXV as the independent variable and the 64-Day Realized Volatility as the dependent variable. The R-squared value for the time frame is The F score is and the p-value is 0. Table 7 has the statistical output. Table 7: Hypothesis 2 Regression Output SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 2267 ANOVA df SS MS F Significance F Regression E-218 Residual Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 64 Day Realized VXV E The statistical output demonstrates the daily VXV does a poor job predicting the daily 64-Day Realized Volatility. The VXV does not perfectly generate the day s volatility but gives the market an estimate roughly 35% of the time. This result is consistent with the VXV s tendency to over-state volatility or over-react to volatility in the upcoming three-months. Table 8 demonstrates the descriptive statistics of both the VXV and the 64-Day Realized Volatility. The average VXV ( ) is higher than the average 64-Day Realized Volatility ( ). The standard deviation for both the VXV (8.5586) and 64-Day Realized Volatility ( ) are similar as are the skew of (VXV) and (64-Day Realized Volatility). Similarly, the kurtosis of the VXV The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue 27

9 (4.5402) and 64-Day Realized Volatility (7.1046) are similar. The maximum values are also similar VXV ( ) and 64-Day Realized Volatility ( ). The minimum values are different with the VXV ( ) being higher than the 64-Day Realized Volatility (6.2837). Table 8: VIX and 21-Day Realized Volatility VXV 64-Day Realized Mean Standard Deviation Skew Kurtosis Minimum Maximum Hypothesis 3: The VIX is a better estimator of the 21-Day Historical Volatility than estimating the 21-Day Realized Volatility. The R-square value for the estimation of the 21-Day Historical Volatility is The R-square value for the estimation of the 21-Day Realized Volatility is (see Hypothesis 1 for data output of estimation of 21-Day Realized Volatility. Table 9 demonstrates the regression output for the VIX estimating the 21-Day Historical Volatility. Table 9: Hypothesis 3 Regression Output SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 2267 ANOVA df SS MS F Significance F Regression Residual Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% VIX E Day Realized Table 10 demonstrates the descriptive statistics of the VIX, 21-Day Historic Volatility and the 21- Day Realized Volatility. The VIX has the highest average ( ) whereas the 21-Day Historic Volatility average ( ) is very similar to the 21-Day Realized Volatility average ( ). The standard deviation for the VIX ( ) is lower than both the 21-Day Historic Volatility ( ) and the 21-Day Realized Volatility ( ). The skew for all three VIX (2.2945), 21-Day Historic Volatility (2.7535) and 21-Day Realized Volatility (2.7524) are all similar. The kurtosis for the VIX (6.6362) is much lower than the 21-Day Historic Volatility (9.4214) and the 21-Day Realized Volatility (9.3863). The minimum value for the VIX ( ) is much higher than the 21-Day Historic Volatility (4.6298) 28 The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue

10 and the 21-Day Realized Volatility (4.6298). The maximum for the VIX ( ) is similar to the 21- Day Historic Volatility ( ) and the 21-Day Realized Volatility ( ). Table 10: VIX, 21-Day Historic, 21-Day Realized Volatility VXV 21-Day Historic 21-Day Realized Mean Standard Deviation Skew Kurtosis Minimum Maximum Hypothesis 4: The VXV is a better estimator of the 64-Day Historical Volatility than estimating the 64-Day Realized Volatility. The R-square value for the estimation of the 64-Day Historical Volatility is The R-square value for the estimation of the 64-Day Realized Volatility is (see Hypothesis 2 for data output of estimation of 64-Day Realized Volatility. Table 11 demonstrates the regression output for the VXV estimating the 64-Day Historical Volatility. Table 11: Hypothesis 4 Regression Output SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 2267 ANOVA df SS MS F Significance F Regression Residual Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% VXV E Day Historic Table 12 demonstrates the descriptive statistics of the VXV, 64-Day Historic Volatility and the 64- Day Realized Volatility. The VXV has the highest average (22.580) whereas the 64-Day Historic Volatility average ( ) is very similar to the 64-Day Realized Volatility average ( ). The standard deviation for the VXV (8.5586) is lower than both the 64-Day Historic Volatility ( ) and the 64-Day Realized Volatility ( ). The skew for all three VXV (1.9507), 64-Day Historic Volatility (2.5299) and 64-Day Realized Volatility (2.5316) are all similar. The kurtosis for the VXV (4.5402) is much lower than the 64-Day Historic Volatility (7.1499) and the 64-Day Realized Volatility (7.1046). The minimum value for the VXV ( ) is much higher than the 64-Day Historic Volatility (7.0627) and the 64-Day Realized Volatility (6.2837). The maximum for the VXV ( ) is similar to the 64-Day Historic Volatility ( ) and the 64-Day Realized Volatility ( ). The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue 29

11 Table 12: VXV, 64-Day Historic, 64-Day Realized Volatility VXV 64-Day Historic 64-Day Realized Mean Standard Deviation Skew Kurtosis Minimum Maximum Hypothesis 5: The new model combing VIX and VXV proves to be a better estimator of the 3-month or 64-Day Realized Volatility. The new model combines VIX and VXV, thus creating a new indicator. The model is formed using two different techniques equally weighted VIX and VXV as well as multiple regression. The combination of the two indexes combines the market sentiment of both the short-term and long-term, providing more information than either index individually. The combination of the two generates better accuracy for the 64-day realized volatility. Table 13 demonstrates the linear regression output of the 50/50 model. 50% of the model is the VIX and 50% of the model is the VXV. The model generates an R-square value of to estimate the 64- Day Realized Volatility. Table 13: Hypothesis 3 50/50 Regression Output 50/50 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 2267 ANOVA df SS MS F Significance F Regression E-263 Residual Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 64-Day Realized / Table 14 demonstrates the descriptive statistics of both the 50/50 Model and the 64-Day Realized Volatility. The average 50/50 model ( ) is higher than the average 64-Day Realized Volatility ( ). The standard deviation for both the 50/50 model (9.9355) and 64-Day Realized Volatility ( ) are similar as are the skew of (50/50 model) and (64-Day Realized Volatility). Similarly, the kurtosis of the 50/50 model (6.5040) and 64-Day Realized Volatility (7.1046) are similar. The maximum values are also similar 50/50 model ( ) and 64-Day Realized Volatility ( ). 30 The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue

12 The minimum values are different with the 50/50 model ( ) being higher than the 64-Day Realized Volatility (6.2837). Table 14: 50/50 Model and 64-Day Realized Volatility 50/50 64-Day Realized Mean Standard Deviation Skew Kurtosis Minimum Maximum Table 15 demonstrates the linear regression output of the multiple regression model. The two inputs into the model are the VIX and the VXV. The model generates an R-square value of to estimate the 64-Day Realized Volatility. Table 15: Hypothesis 3 Multiple Regression Output Multiple Regression SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 2267 ANOVA df SS MS F Significance F Regression E-288 Residual Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 64 Day Realized VIX VXV Table 16 demonstrates the descriptive statistics of the VXV, VIX and the 64-Day Realized Volatility. The VXV has the highest average (22.580) whereas the VIX average ( ) is very similar to the 64-Day Realized Volatility average ( ). The standard deviation for the VXV (8.5586) is lower than both the VIX ( ) and the 64-Day Realized Volatility ( ). The skew for all three VXV (1.9507), VIX (2.2945) and 64-Day Realized Volatility (2.5316) are all similar. The kurtosis for the VXV (4.5402) is much lower than the VIX (6.6362) and the 64-Day Realized Volatility (7.1046). The minimum value for the VXV ( ) is much higher than the VIX ( ) and the 64-Day Realized Volatility (6.2837). The maximum for the VXV ( ) is similar to the VIX ( ) and the 64-Day Realized Volatility ( ). The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue 31

13 Table 16: VXV, VIX and 64-Day Realized Volatility VXV VIX 64-Day Realized Mean Standard Deviation Skew Kurtosis Minimum Maximum CONCLUSIONS This study demonstrates VIX and VXV being good estimate indicators for both the 21-day and 64- day realized volatility, respectively. However, the accuracy of the VXV is roughly 35% as compared with the accuracy of the VIX at 60.1%. Furthermore, both of the indexes prove to be better indicators of historical volatility than realized volatility. Using the same time period from January 2, 2008 through December 31, 2016 we find the VIX estimates the 21-Day Historical Volatility with 83.70% accuracy. Similarly, we find the VXV estimates the 64-Day Historical Volatility with 84.52% accuracy. This model developed by this study utilizes seven years of market data. This time period was chosen due to the amount of data available. The Chicago Board Options Exchange has calculated VIX data going back as far as 1986, but only has data for VXV beginning in late The limited amount of data used in this study may have an impact on the use of the model as a predictor of future realized volatility. A proposed model of combining the VIX and VXV to better estimate the 64-Day Realized Volatility was proposed using two techniques a weighted average and a multiple regression. The combination of the two indexes combines the market sentiment of both the short-term and long-term, providing more information than either index individually. The combination of the two generates better accuracy for the 64-day realized volatility. In the weighted average model, 50% of the model is the VIX and 50% of the model is the VXV. The model generates an R-square value of to estimate the 64-Day Realized Volatility. The multiple regression uses both the VIX and VXV as two independent variables. The two inputs into the model are the VIX and the VXV. The model generates an R-square value of to estimate the 64- Day Realized Volatility. REFERENCES Arak, M. & Mijid, N. (2005). The VIX and VXN volatility measures: Fear gauges or forecasts? Derivative Use, Trading, & Regulation Volume Twelve Numbers One/Two: Arnold, T. & Earl, J (2007). Calculating the VIX in Excel. Bekaert, G. & Hoerova, M. (2014). The VIX, the variance premium and stock market volatility. European Central Bank Eurosystem Working Paper Series Number Carr, P. & Wu L. (2006). A Tale of Two Indices. The Journal of Derivatives Spring, 2006: Chow, K., Jiang, W. & Li J. (2014). Does VIX Truly Measure Return Volatility? Working Paper. Degiannakis, S. (2008). Forecasting VIX. Journal of Money, Investment, and Banking, 4: Ding, L., Huang, Y. & Pu X. (2014). Volatility linkage across global equity markets. Global Finance Journal, 25: The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue

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