Testing the CBOE Volatility Index (VIX)

Issue 15 January 11, 2011 Testing the CBOE Volatility Index (VIX) By Erik Skyba, CMT Senior Market Technician, TradeStation Labs TSLabs@TradeStation.com Summary The CBOE Volatility Index, also known to traders as implied volatility, or simply the VIX, represents future volatility expectations as expressed in the options markets. The index has become increasingly popular over the years, as it has been applied to the financial markets and active trading in a myriad of ways. This paper presents an overview and background of the VIX, while examining two of the more common rules applied when using the index as a trading signal. The question we ask is whether these rules can be used to produce successful trading results. Focus Technical Study Markets Equities Futures Time Perspective Short & Intermediate term Studies/files Included Workspace Introduction The CBOE Volatility Index, ticker symbol $VIX.X in the TradeStation platform, is an index that represents a consensus expectation for the market s annualized volatility (S&P 500 Stock Index) 30 calendar days into the future. As mentioned, it is also referred to as implied volatility as the expectation for future market volatility is implied by S&P 500 index option prices. The index is calculated as a weighted average of many near-term and next-term outof-the-money SPX option prices (Calls & Puts). Figure 1 below is a list of CBOE broad market and commodity volatility indexes in the TradeStation platform. We chose to conduct our analysis on the CBOE Volatility Index because it is the favorite of these indexes amongst equity and equity-index traders. 1 P a g e

Figure 1 Implied Volatility Index Symbols Background In 1993, the CBOE introduced the VIX index. It was originally conceived based on S&P 100 OEX at-the-money index options (ticker symbol $VXO.X in the TradeStation platform). These index options were the most liquid during that time period. The main reason the CBOE created the index was to satisfy an industry need for a benchmark that characterized expected future short-term volatility as implied by options prices. A secondary reason to build the index was to facilitate the creation of a volatility futures contract, which was introduced in 2004. In 2003, the CBOE recalculated the index to use S&P 500 SPX index options. This change came about as the SPX index options became more popular and much more liquid than the OEX index options. The VIX is often referred to as the Fear Index. This is because, in a sense, it represents the market sentiment of institutions. The index options that embody the VIX are utilized as portfolio insurance by institutional traders and institutional investors to protect long positions against market declines. Because the premiums on these options are expensively priced as the market decreases in value, institutions are the predominant participants, as few retail traders or investors can afford them and wind up buying much cheaper out-of-the-money options. Purchases of options will cause the VIX to increase with the price movement in the options. As Figure 2 exemplifies, levels over 30 on the index characterize market sentiment as fearful, while levels under 20 generally correspond to market environments that are complacent. 2 P a g e

Figure 2 VIX Index - 10 Years, 30 level (green), 20 level (red), Weekly Interval Practical Trading Application VIX Index There are many ways to apply the VIX Index as a trading signal. As you can see from Figure 3, the VIX has a mean reversion quality to it and it moves inversely to the S&P 500 Index. Over longer periods of time the VIX reverts back toward its longer-term average or mean. It exhibits this behavior not only on longer time frames but on shorter ones as well, as Figure 4 shows. Figure 3 Mean Reversion Behavior - Monthly interval, VIX Index (Blue), S&P500 Index (Red & Blue) 3 P a g e

Figure 4 Mean Reversion Behavior - Intraday 30 minute interval, VIX Index (Blue), S&P500 Index (Red & Blue) When we examined the possibilities of generating trading signals, we determined that, because of its nature, the bulk of the trading signals belonged to the category of mean reversion. As a result, our testing of the index focused on two mean-reversion rules that we felt best described how the index was being used to trade by discretionary and systematic traders. Testing Scenario Before we begin to examine our results, let us describe the testing conditions, shown in Figure 5 for this study. Figure 5 Testing Conditions Strategy/Study Style Short-term Asset Type Futures Symbol 1 (for backtest) @ES.D Symbol 2 (for backtest) $VIX.X Alternative Symbols to Trade SPY, QQQQ, IWM Rule 1 Data Interval 30 minutes Rule 2 Data Interval Daily Rule 1 Period Tested 12/28/04-12/28/10, (6 years) Rule 2 Period Tested 12/28/98-12/28/10, (12 years) Contracts Traded 1 Contract Commission/Contract $2.50 4 P a g e

When testing or trading other stock-index futures or ETFs such as those listed in Figure 5 as Alternative Symbols to Trade, please consider testing some of TradeStation s index-specific CBOE Volatility indexes as listed in Figure 1 above. Defining the Rules to Test In reviewing the Long and Short entry rules, remember the inverse tendency of the VIX and equity-index values. Long Entries (each long entry is tested separately): 1. Buy the S&P 500 E-mini contract if the percentage difference between the VIX and its 20-period moving average crosses above and then below 1, 2 or 3 positive standard deviations of the percentage difference between the VIX and its 20-period moving average. (We tested each standard deviation individually using a 30-minute interval.) 2. Buy the S&P 500 E-mini contract if the daily return of the VIX is greater than 2, 4, 6, 8, and 10 percent. (We tested each percentage level individually using a daily interval.) Exit Rules: 1. Exit the trade after a defined holding period, as measured in bars (1 30 bars for the 30-minute interval). 2. Exit the trade after a defined holding period, as measured in bars (1 15 bars for the daily interval). Short Entries (each short entry is tested separately): 1. Sell short the S&P 500 E-mini contract if the percentage difference between the VIX and its 20-period moving average crosses below and then above -1, -2 or -3 standard deviations of the percentage difference between the VIX and its 20-period moving average. (We tested each standard deviation individually using a 30-minute interval.) 2. Sell short the S&P 500 E-mini contract if the daily return of the VIX is less than -2, -4, -6, -8, and -10 percent. (We tested each percentage level individually using a daily interval.) Exit Rules: 1. Exit the trade after a defined holding period, as measured in bars (1 30 bars for the 30-minute interval). 2. Exit the trade after a defined holding period, as measured in bars (1 15 bars for the daily interval). As an example, Figure 6 demonstrates how a long trade from Rule 1 is initiated using a 30-minute data interval. First, the blue part of the histogram (greater than 0) is the difference in percentage terms between the VIX Index and its moving average. This histogram spread must become large enough to penetrate the upside standard deviation band (red). Our testing included 1, 2, and 3 standard deviation moves. A trade can then be entered when the histogram difference closes back below the same standard deviation band (red). In our tests, we chose to keep the look-back window for the average and standard deviation calculations the same, at 20 periods each which was an arbitrary value. Figure 6 also shows how Rule 1 relates to the trades on the chart, as the blue and red arrows indicate the long entries and subsequent exits, respectively. 5 P a g e

Figure 6 Rule 1 Long Entry Example Trading @ES.D Figure 7 shows a short entry setup for Rule 2 using a daily interval. We can see that a short trade is initiated when the daily return of the VIX exceeds the negative 10% level. For this rule we tested the VIX s daily returns, looking for returns to exceed values between -2% and -10%. When the daily return exceeded the specified percentage level a trade was entered. Figure 7 Rule 2 Short Entry Example Trading @ES.D 6 P a g e

Analysis of the Results When we analyzed the data there were a few pieces of information that stood out. First was how well long entries performed for Rule 1 after 3 positive standard deviations. As we can see from Figure 8, 3 standard deviation moves outperformed both 1 and 2 standard deviation moves, as average net profit and average max drawdown improved. The average MAR (Managed Account Reports ratio = Avg. Net Profit / Avg. Max Drawdown) for 3 standard deviation moves was greater than both. Figure 8 Results for Long Entry Rule 1 Average results for holding periods of 1 through 30 bars (Long Trades Only) 30 Min. Interval 1 SD 2 SD 3 SD Avg. Net Profit $-11,162 $5,138 $18,992 Avg. Max Drawdown $-35,679 $-15,595 $-5,379 Avg. MAR 0.32 3.53 Avg. Profit Factor.92 1.05 1.53 Avg. Trades 601 401 160 Note: 6 years of data tested Short entries for Rule 1 as shown in Figure 9 fared better than long entries for 1 and 2 standard deviations but underperformed the long entry for 3 standard deviations. When analyzing the equity curves for the long entry, 3 standard deviation moves performed much more consistently during both bull and bear markets. Short entries for Rule 1 tended to do better during bear markets and performance was slightly negative during bull markets. Figure 9 Results for Short Entry Rule 1 Average results for holding periods of 1 through 30 bars (Short Trades Only) 30 Min. Interval -1 SD -2 SD -3 SD Avg. Net Profit $5,350 $10,175 $-4,606 Avg. Max Drawdown $-17,287 $-11,599 $-8,655 Avg. MAR.30.88 0 Avg. Profit Factor 1.04 1.14.84 Avg. Trades 630 363 148 Note: 6 years of data tested Rule 2 was more impressive than Rule 1. Short entries outperformed long entries overall. But as you can clearly see from Figures 10 and 11, both long and short entries improved as the daily return of the VIX increased and decreased. For long entries, the 10% level provided the best risk/reward tradeoff with the MAR value being at.63. 7 P a g e

Figure 10 Results for Long Entry Rule 2 for positive percentage movements in the VIX - Average results for holding periods of 1 through 15 bars (Long Trades Only) Daily Interval 2% 4% 6% 8% 10% Avg. Net Profit $-7,660-1,134 $10,941 $10,657 $13,498 Avg. Max Drawdown $-40,738 $-36,244 $-30,044 $-24,049 $-21,387 Avg. MAR 0 0.36.44.63 Avg. Profit Factor.96.99 1.08 1.12 1.23 Avg. Trades 307 256 207 145 106 Note: 12 years of data tested Short entries shown in Figure 11 for Rule 2 provided the most exciting results. Their equity curves on average seemed very similar to the equity curves for Rule 1 s short entries, although their trades did better in bullish markets. As the daily return penetration level increased, from 2% to 10%, average net profit and maximum drawdown both improved with the 10% level providing the best results, while the MAR was 2.94. Figure 11 Results for Short Entry Rule 2 for negative percentage movements in the VIX - Average results for holding periods of 1 through 15 bars (Short Trades Only) Daily Interval -2% -4% -6% -8% -10% Avg. Net Profit $10,379 $15,608 $23,900 $16,592 $32,280 Avg. Max Drawdown $-28,150 $-24,319 $-21,461 $-16,384 $-10,967 Avg. MAR.37.64 1.11 1.01 2.94 Avg. Profit Factor 1.05 1.11 1.22 1.22 1.85 Avg. Trades 322 270 191 110 65 Note: 12 years of data tested Note: All strategy performance data included in figures 8, 9, 10, and 11 was exported from TradeStation to Excel. Conclusion When we began our investigation on the VIX Index we chose two rules to evaluate. One focused on intraday, 30 minute bar intervals in Rule 1, while Rule 2 used daily bar intervals. The long entries were similar to many of the mean reversion strategies we ve tested in the past although Rule 1 s long entry for 3 standard deviation trades seemed to buck the trend in dealing with the issue of the ever increasing drawdown associated with bear markets. Three standard deviation moves for Rule 1 long entries apparently reflect enough of an oversold condition in the short term that the markets need to take a breather and rally. This rule tended to outperform in bear market cycles, as volatility is usually greater, which causes more 3 standard deviation moves. In bull market cycles there are a greater number of 1 and 2 standard deviation moves. These shallow pullbacks are momentary pauses that on average result in profitable moves as they eventually resume in the direction of the longer term bullish trend. However, in bear market cycles, 1 and 2 standard deviation moves for the long entry had negative 8 P a g e

performance, with 1 standard deviation moves fairing the worst. Rule 1 s short entry, for 1 standard deviation, showed mediocre performance in bull and bear market cycles, while 2 standard deviation moves had better overall performance but much of that return came from bear market cycles. The most encouraging results came from Rule 2, which provided impressive risk/reward returns. Both long and short entries from Rule 2 exhibited the same behavior. As the daily return of the VIX exceeded increasing levels of positive returns for long entries and negative returns for short entries, performance on both long and short entries improved. Short entries had the better overall performance, but this performance was largely attributed to bear market cycles. However, unlike short entry Rule 1, performance was not as adversely affected by bull market cycles. Rule 2 long entry returns improved as the VIX returns exceeded 6% but experienced occasions of underperformance in bear market cycles. In conclusion, the overall results were average, with the Rule 2 short entry providing the ultimate bull and bear market cycle performance, as well as the most tradable risk/reward preference. To use the files provided with this issue of Analysis Concepts: Files with extension.eld These contain EasyLanguage documents: analysis techniques and strategies. Double-clicking on this file will start the Easy Language Import Wizard. Follow the prompts to completion. The analysis techniques or strategies will automatically be placed in the correct locations for your use in TradeStation. This should be done before opening any workspaces provided. Files with extension.tsw These are TradeStation workspaces. These may be stored in any folder where you choose to save TradeStation workspaces. Files with extension.txt These are text versions of the EasyLanguage documents and are generally used only by advanced EasyLanguage users. Other supporting documents or files may also be attached to the report. All support, education and training services and materials on the TradeStation Securities website are for informational purposes and to help customers learn more about how to use the power of TradeStation software and services. No type of trading or investment advice is being made, given or in any manner provided by TradeStation Securities or its affiliates. This material may also discuss in detail how TradeStation is designed to help you develop, test and implement trading strategies. However, TradeStation Securities does not provide or suggest trading strategies. We offer you unique tools to help you design your own strategies and look at how they could have performed in the past. While we believe this is very valuable information, we caution you that simulated past performance of a trading strategy is no guarantee of its future performance or success. We also do not recommend or solicit the purchase or sale of any particular securities or derivative products. Any symbols referenced are used only for the purposes of the demonstration, as an example ---- not a recommendation. Finally, this material may discuss automated electronic order placement and execution. Please note that even though TradeStation has been designed to automate your trading strategies and deliver timely order placement, routing and execution, these things, as well as access to the system itself, may at times be delayed or even fail due to market volatility, quote delays, system and software errors, Internet traffic, outages and other factors. 9 P a g e