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-the- money. 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 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 2005. 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 2007. 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 19.46 while the average realized volatility for the S&P 500 was 14.64 or a difference of 4.72. 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 22.46 and average realized volatility was 18.39 resulting in an average difference of 4.07. The average closing price for VIX was higher over the 2008 – 2016 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 2008. Chart 1 shows the average monthly VIX close versus the following realized market volatility from 2008 to 2014. The Journal of Global Business Management Volume 14* Number 2 * October 2018 issue 21 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 2008. 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 3.9280. The standard deviation is higher for the 21-Day Realized Volatility by 2.1233. 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 (10.3200). The maximum for the VIX and the 21-Day Realized Volatility are similar of 80.8600 and 83.2986 respectively. Table 1: VIX & 21-Day Realized Volatility Descriptive Statistics VIX 21-Day Realized Volatility Mean 21.0783 17.1503 Standard Deviation 10.0166 12.1399 Skew 2.2945 2.7524 Kurtosis 6.6362 9.3863 Minimum 10.3200 4.6298 Maximum 80.8600 83.2986 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 11.0028 which is much higher than the 3.8876 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 -8.1772 6.1756 Standard Deviation 11.0028 3.8876 Skew -1.8147 1.3339 Kurtosis 2.5877 4.3827 Minimum -47.7627 0.0150 Maximum -0.0357 31.5545 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 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.