The Archives

Browse the content below to find what you're looking for.

1.5X UVXY & -0.5X SVXY Open/High/Low/Close values: March 2004–March 2018

 
Tuesday, May 1st, 2018 | Vance Harwood
 

Some volatility trading systems use intra-day open, high, low (OHL) prices as part of their algorithms for determining when to trade. UVXY and SVXY didn’t start trading until late 2011—just after the 2011 correction and well past the 2008/2009 bear market so there’s no actual trade data from those important downturns.

To fill that deficiency I did some simulations a few years ago using the OHL values of  VIX futures to calculate OHL data for many of the volatility Exchange Traded Products (ETPs) including UVXY and SVXY.

The Freaky Fifth of February

The events of February 5th, 2018 caused a death and some changes. In addition to XIV’s termination by Credit Suisse due to its losses that day ProShares decided to reduce the leverage factors on UVXY and SVXY. Those leverage changes took effect the 28th of February, 2018.

UVXY and SVXY’s ticker symbols did not change so the publically available OHLC data is a mix of the old 2X and -1X and new 1.5X and -0.5X leverage factors—the data before February 28, 2018, only applies to the discontinued leverage factors.  For people wanting to do simulations on the new funds based on historical data, this is a problem. To address this need I did simulations for the 1.5X UVXY and -0.5X SVXY to generate the OHLC data from March 2004 through March 2018—these are available at the bottom of this post and here.

The New IV Close Values

Generating the simulated Indicative Value (IV), the ~4:15 PM ET close values for the new 1.5X UVXY and -0.5X SVXY was straightforward, I adjusted the appropriate multipliers in the algorithms and used the official VIX futures settlement values as inputs into the calculations. The resulting IV Close results match closely (within +-0.15%) to the values published by ProShares on the web pages for UVXY and SVXY.

Generating Open/High/Low data for the Reduced Leverage UVXY & SVXY ETPs

Using the combination of the OHL for the original funds and reduced leverage IV close values I generated simulated OHL data for the reduced leveraged funds.

The process I used was relatively straightforward. I assume that for the 1.5X leveraged UVXY the intraday percentage moves from the previous day’s IV close would be reduced by ratio of the leverage changes (1.5/2 or 0.75 for UVXY). For example, if the old UVXY open was 3% higher than the previous day’s IV close the simulated open for the new 1.5X fund would be 2.25% higher than the previous 1.5X UVXY IV close. See the end of the post for an example equation.

Using the same approach, the new SVXY open values would be 50% (0.5/1.0) of the old SVXY’s OHL opening percentage moves relative to the previous day’s closing IV value.  This same calculation was used for computing the intraday high and low values.

The source OHLC data that I use starts in March 2004 and has a major transition on 28-Oct-2013. On the October 2013 date, I switched from using VIX futures to simulate the OHL values to using the publically available trade dat.  O the October date the Cboe extended the trading hours of the VIX futures to the extent that they were no longer a good proxy for the normal NYSE trading hours. See this post for a detailed discussion on why I made the transition and the various uncertainties involved.

The 4 PM “Fake Close”

With historic trade data, there is also a “close” price in addition to the open/high low data. This close number is the last trade before or at the 4 PM market close of the equity markets—however, SVXY & UVXY official close isn’t until around 4:15 PM ET when their underlying securities, the two next to expire VIX futures settle.

Most brokers disseminate the 4 PM number as the “Close”. This causes no end of confusion—I’ll call this 4 PM close the “Fake Close” (FC). Often there are significant moves in the volatility markets in the remaining 15 minutes of trading—which can result in big differences between the Fake close and the IV close values. The leveraged ETPs rebalance is based on the IV close values so if you use the FC value for your calculations you will often conclude that the ETPs are not moving with the correct leverage the next day (see If you think your ETP is broken ).

While the Fake close generates confusion it does have one redeeming quality—it gives us one more piece of intraday data at an interesting time.

Action at the End

The Fake close allows us to better characterize the last 15 minutes of trading—on days with big volatility moves there is often a lot of action in this time window. The graph below shows the historical UVXY percentage moves in the 15 minutes from Fake close to the IV close.

 

The 102% move on 5-Feb-2108 was a 29 sigma move—a good indicator that assuming a normal distribution for $UXVY day end percentage moves is a really bad idea…  For more on outsize sigma moves see: Not All High Sigma Events are Black Swans.

Revised Daily High & Low Numbers

The publicly available trade data assumes that trading stops at 4 PM, so the stated high and low data may be inaccurate—because new lows and highs can be reached in the last 15 minutes of trading (and often are). In my simulation, if the IV close is lower than the trading low or higher than the trading high I set the intraday lows and highs to the IV close value as appropriate. Of course, the prices may have moved to higher highs or lower lows than the IV close during those 15 minutes but that trade data is not freely available.

Adjusting the February 5, 2018 data

Using old UVXY & SVXY OHLC data to generate simulated values for the new 1.5X and 0.5X funds is defendable for every day from March 26th, 2004 through February 27th, 2018– except for February 5th, 2018.

On that day the VIX set a new one day close-to-close record with a +116% jump (the previous highest was +62%) and the mix of VIX futures that UVXY and SVXY track (index SPVXSP) jumped +96% (the previous highest jump was +33%).  I won’t go into the details, I’ll defer that to another post but the bottom line is that the managers of UVXY and SVXY correctly predicted that the end of day settlement for VIX Futures would be the apex of a liquidity crisis and chose to buy VIX futures to do their required rebalancing before the VIX Futures closed. This meant that the funds ‘performance likely would not track their target index but in the end, counterintuitively, saved both the 2X long and -1X inverse shareholders money.

In an alternative universe, had the reduced leverage 1.5X UVXY and -0.5X SVXY been trading on February 5th the fund managers would probably not have started early with their rebalancing so my simulation used actual VIX futures settlement values to simulate the end of day values on February 5th, 2018 for the lower leverage funds.

Conclusion

 An important lesson, illustrated by the February 2018 travails of XIV and SVXY, is that when you’re testing trading strategies, you shouldn’t assume that past relationships (e.g., VIX percentage moves relative to VIX Futures percentage moves). will hold in the future. It’s critical to ask what can happen, especially when systems are highly stressed. It’s not enough to just look at the past.

 

 

Example Conversion Equation

New_Openday  = New_IV_Closeday-1* (1+1.5/2.0*(Old_Openday / Old_Closeday-1   -1))

Where:  New = 1.5X UVXY
Old = 2X UVXY

Purchase Information

If you purchase one of the spreadsheets below you will be eventually be directed to PayPal where you can pay via your PayPal account or a credit card. When you successfully complete the PayPal portion you will be shown a “Return to Six Figure Investing“ link.    Click on that link to reach the page where you can download the spreadsheet.  Please email me at [email protected] if you have problems, questions, or requests.

A Better Way to Model the VIX

 
Tuesday, November 28th, 2017 | Vance Harwood
 

Models are useful. They help us understand the world around us and aid us in predicting what will happen next. But it’s important to remember that models don’t necessarily reflect the underlying reality of the thing we’re modeling. The Ptolemaic model of the solar system assumed the Earth was the center of everything but in spite of that spectacular error, it did a good job of predicting the motions of the stars, planets, moon, and sun. It was the best model available for over a thousand years. But new data (e.g., phases of Venus as revealed by Galileo’s telescope) and errors in predicting the motions of the planets demonstrated that the sun-centric Copernican/Kepler models were superior.

There are a lot of models for the Cboe’s VIX. None of them are particularly good at predicting what the VIX will do tomorrow but they can be useful in predicting general behaviors of the VIX. The most popular model for the VIX (although people might not recognize it as a model) is simple mean reversion.

 Simple Mean Reversion

Car gas mileage is a good example of a simple mean reverting process.

Over time your car’s gas mileage will exhibit an average value, e.g., 28 miles per gallon. You don’t expect to get the same mileage with every tank because you know that there are factors that make a difference with your mileage (e.g., city vs highway driving, tire air pressure, and wind direction) but over time you expect your mileage to cluster around that average value. If you get 32 miles per gallon on one tank of gas you reasonably expect that next time you check it will likely be closer to 28. If the values start varying significantly from the average you start wondering if something has changed with the car itself (e.g., needs a tune-up)

A mean-reverting random walk is a relatively simple model and fits some of the basic behaviors of the VIX. Specifically, over time the mean value of the VIX has stayed stable at around 20 and the VIX exhibits range bound behavior—with all-time lows around 9 and all-time highs around 80.

However, there are many aspects of the VIX that aren’t well explained by a simple mean-reverting model. For example, a simple mean reverting process will have its mode value (the most frequently occurring values) close to its mean. This is not the case of the VIX; its mode is around 12.4—a long way away from its mean. The histograms below show that difference visually.

 

Another VIX behavior that departs from a simple mean-reverting process is the abrupt cessation of values below 9—almost a wall. For a normal mean reverting process you would not expect such a sharp cut off at the low end.

The Acid Test:  How good is the model for predicting the future?

Having a good model for a process is useful because it can help us predict at least some aspects of the future. For example, we can use our average gas mileage to decide whether we need to gas up before entering a long stretch of highway without gas stations.

A simple mean-reverting model is not particularly good at predicting the future moves of the VIX. If the VIX is low (e.g., 12 or below) a simple mean-reverting model predicts that since the VIX is far from its mean that will likely increase soon. But history shows this is usually not the case. Often the VIX can be quite content to hang around 12. This leads to news stories quoting various pundits stating “The VIX is broken” –when in reality they are just using an inferior model.

 As I said earlier there are VIX models out there that address some of these deficiencies. Unfortunately, the ones I know of are complex and not very intuitive. I believe the model that I describe below can improve our intuition considerably without adding too much complexity.

A Better VIX Model

A better way to view the VIX is that it behaves like the combination of two interacting processes: a specialized mean reverting process and a “jump” process. The jump process captures the behavior that all VIX watchers know—its propensity to occasionally have large percentage moves up and down. Since 1990 there’ve been over 86 times where the VIX has increased 30% or more in a 10 day period. The occurrence of these spikes is effectively random with a probability of happening on any given day of around 1.28%. It’s like a roulette table with 78 slots, 77 of them black and one red. If the ball lands on a black the normal reigns—if red then things get crazy. The graph below shows a histogram of the number of days between these 30% spikes in the VIX since 1990.

There’s nothing that prevents reds on consecutive spins nor is there some rule that reds become really likely if you haven’t had a red in a while. The roulette ball has no memory of where it landed on previous spins.

VIX jumps are generally not just one-day events; subjectively it looks like it takes around two weeks before the market reverts to more typical behavior. The model assumes that when a jump occurs it essentially drives the behavior of the VIX for 10 trading days.

The other process, the specialized mean reverting process, addresses the non-jump mode of the VIX—which is historically around 85% of the time. One of the key behaviors it needs to address is the slow relaxation in the mean value of the VIX after a big volatility spike rekindles a generally fearful attitude in the market. This decay process continues (unless interrupted by another VIX jump) until the average monthly VIX values drop into the 11-12 range.

The chart below illustrates this relaxation process.

 

This characteristic can be modeled by expecting the short term mean of the VIX (when it’s not jumping) to decay exponentially until it reaches its “quiet” mean of around 11.75. It works well to quantify this decay as having a time constant of 150 days.

With this approach, sans jumps, the difference between the current VIX value and its long-term quiet value will decay by 50% in 104 days. So if the VIX is at 30 the model predicts the mean will decline to 20.75 in 104 days [30- (30-11.5)*0.5=20.75].  If there are no jumps for the next 104 days the VIX’s mean would decline to 16.13. If a jump occurs in the interim the short term mean is reset to the VIX’s value at the end of the jump.

The other part of the specialized mean reverting process mimics the day-to-day volatility of the VIX. I used a formal mean reverting diffusion process (Ornstein-Uhlenbeck) to accomplish this. Despite its scary name, you can think of it as a random walk with the thing “walking” being attached to the mean with a spring—similar to walking a dog with a springy leash. The further the dog gets from you the larger the force pulling the dog back to you.

Unlike the simple mean-reverting model often used for the VIX, this process has a much tighter distribution, with the extreme values effectively limited to around +-20% from the mean. When the VIX is quiet this process replicates the firm lower limit on the VIX, a VIX of 9 is -21.74% lower than a quiet mean of 11.75.

Simulating the Model

 To implement/validate this model I estimated the key input variables and then used Excel to simulate 20-year volatility sequences. I then compared these time series to the actual VIX history and tuned the model’s parameters such that the key characteristics (e.g., volatility, mean, mode, decay rates) were similar to the VIX’s historic values.

Resulting histogram of historic VIX values vs the simulated combined process

 

The next chart shows an example 20 year time series of the simulated VIX combined process compared to the historic VIX. The two series aren’t time synchronized; my intent is to show how the simulated VIX time series has the same visual feel as the real VIX.

 

Conclusion

This improved model is not a path to riches. It isn’t any better than other models at predicting when VIX jumps will occur. However, this model does help us understand how the VIX behaves over longer time spans. In particular, during times of sustained low volatility, it predicts that the VIX will tend to stay low until the next significant VIX spike and not trend up like the simple mean-reverting model demands.

 

 

 

Quant Corner

  • The mean-reverting diffusion process used is an Ornstein-Uhlenbeck mean reverting diffusion process using a log-normal distribution. The volatility was set at an annualized 112% and the return to mean strength parameter ETA set to 0.3. The mean of the process is determined by the previous day’s VIX value minus the exponential decay factor that will decay the mean down to 11.75 over time if there are no additional jumps (Tau of 150 days). If the mean has decayed down to 11.75 the process acts very similarly to the VIX’s low volatility regimes (e.g., 2004-2006, 2016-2017) with the “return to mean” factor effectively acting to keep the VIX  higher than 9.0
  • The Jump process used (with a few small tweaks) is a compound Poisson process where the probability of a jump sequence is random with a probability of a jump being 1.28% per day. The jump sequence and its daily amplitudes are determined using a technique borrowed from rappers called sampling. Instead of trying to recreate the decidedly non-Gaussian distribution of VIX jumps I reused historic VIX jumps by randomly selecting, and replaying one of the more than 85 jump sequences since 1990 where the VIX jumped more than 30% in 10 days. Each jump sequence is 10 days long, with the first 2 days being the behavior before the jump.

How Much Should We Expect the VIX to Move?

 
Friday, March 10th, 2017 | Vance Harwood
 

Every couple of months it seems like there’s an uptick in articles about the CBOE’s VIX Index being broken or manipulated.   Generally I expect the percentage moves in the VIX to be around a factor of 4 in the opposite direction of SPX (S&P 500).  But there are significant eccentricities in the VIX that I factor in, for example Fridays tend to be down days, Mondays tend to be up.

The chart below shows the percentage moves at close for VIX (blue bars) and SPX (red line) for the first 12 trading days of November 2012, along with my -4X rule of thumb (green bars).  The black ovals show 5 days where the VIX went opposite the expected direction. In addition, on two days, the 1st and the 16th the VIX moved far more than a -4X factor.


One of these days, the 12th, has at least a partial explanation.  That was the day that the VIX calculation shifted from using November / December SPX options to December / January options.   If you’re interested see Bill Luby’s post for more information on this phenomenon.

I did an analysis of SPX and VIX since 1990 to see the actual historical ratios between their percentage moves.   I excluded daily SPX percentage moves of less than +-0.1% because they often give very high, nonsensical ratio values.


The average ratio value was -4.77, but as you can see there is a wide spread.   About 20% of the time the ratio is positive (data to the right of the red line).

Each of the blue bars in the histogram shows how many days had a VIX% / SPX% ratio in each 0.25 wide bin.  For example, there were 120 days where the ratio was between -3.25 and -3.5.   I also plotted a normal distribution—which shows this distribution is more concentrated and has wider tails than a Gaussian distribution.

While not broken, and probably not manipulated, the VIX as a fear gauge leaves a lot to be desired.   Given its past performance it’s not reasonable to expect it to negatively correlate with the S&P 500 every day.  However, I think it does give us a very good feel for the mood of the SPX options market.  A single SPX option has the leverage of a $200K+ investment in the S&P 500, so it tends to be the domain of professional / institutional investors.  They aren’t always right, but they aren’t dummies, and they’re voting with their wallets.   Last week they were trading as if they thought the market decline was over, and at least for today, it looks like they were right.

How to Vaporize $277 Million in Market Capitalization

 
Monday, March 12th, 2018 | Vance Harwood
 

Wednesday night, March 23, 2012, I was wondering if there was a graceful way for Credit Suisse to restore TVIX to working order and get its share creation process working again.   The Wednesday close was $14.43, roughly 2X the $7.62 indicative value (IV) giving a market capitalization of $587 Million.   The correct market cap, based on the indicative value was $310 Million.  Somehow $277 million needed to go away.

Thursday that problem departed—in a very ungraceful fashion.  Apparently, the word got out early, because by Thursday evening when Credit Suisse announced reopening of share creation on a limited basis, TVIX had plunged 29% to $10.2

It’s tough to keep a quarter billion dollar secret.

TVIX was trading at $9.00 in the Thursday after-market—still 15% away from its closing indicative value of $7.83.  Most if not all of that difference will go away Friday.

There was a lot of finger-pointing going on Thursday, but what surprised me the most was the level of ignorance displayed by some of the general media (e.g., CNBC, Forbes).  I don’t expect them to be experts on this corner of esoterica, but I do expect them to know that they didn’t understand this field and take the time to consult an expert.   It’s not like Bill Luby is an unknown person in the volatility arena.

Regarding Credit Suisse’s reopening, the first step, starting as soon as Friday, March 23rd will be to make TVIX shares available for lending—this will enable short sellers to drive down any remaining premium of  TVIX over its IV.

As early as the 28th, share creation may resume, but Credit Suisse can require market makers to sell them specified hedging instruments as part of the transaction.    This takes them close to the Exchange Traded Fund (ETF) model, where this is the standard process (e.g., UVXY).    TVIX is an Exchange Traded Note (ETN), which normally does share creation on a cash basis, but adding this requirement allows Credit Suisse to at least partially protect themselves if the underlying hedges (e.g.. VIX futures, variance swaps) get pricey.

To exactly hedge these VIX future based volatility funds all ETN and ETF providers (complete list) would need to roll their mix of futures on a daily basis.    In addition, most leveraged and inverse funds, with the exception of Barclays‘ products,  may need to rebalance their hedges as often as daily to setup for their daily percentage performance goal.   In volatile times, for a ETN of TVIX’s size,  this rebalancing can involve buying or selling hundreds of millions dollars worth of hedging instruments (example).   They can’t put the market makers on the hook for that, but if the market makers can get the hedging instruments at reasonable prices, Credit Suisse should be able to also.

In the interests of accuracy, I should point out that neither the volatility ETNs or ETFs are obligated to do their daily rolls or rebalancing in a certain way, or at all, based on what they say in their SEC documents.  It is up to them how they manage this, and they aren’t obligated to reveal their hedging or risk management processes.

The Credit Suisse press release is silent regarding the “internal limits” that caused this mess in the first place.  I’m assuming they won’t pull the plug again just based on fund size.  Their additional restrictions give them an objective way to halt share creations if hedging costs go out of line, and an ever-present possibility of creation resuming should help keep the share price close to the indicative value.

Volatility as an asset class is showing some growing pains.   People have flipped out because the futures rolling/hedging needs of the volatility ETN / ETFs now dominate the VIX futures market, and a lot of people have learned the hard way that a gap between the market value of an ETF / ETN and the indicative value can vaporize in an instant.  But it doesn’t look like growth has changed the underlying structure of the market—the volatility marketplace does not show any objective signs of distortion.  Sure the VIX futures term structure is in major contango, but most people feel the market is overdue for a correction, so that is not surprising.

Feel free to place your bets if you think those are distorted prices.

 

 

The VIXs of Christmas Past

 
Monday, July 24th, 2017 | Vance Harwood
 

One of the persistent characteristics of the CBOE‘s VIX® index is the Christmas Effect—the tendency for VIX to drop down to relatively low levels during the Christmas holidays.  The CBOE’s VIX volatility December futures predict this drop for months in advance, and it has come to pass again this year.   I am aware of at least three possible explanations for this:

  1. Option market makers and others short options reduce their prices before the holidays so that they don’t get stuck with time decay (theta) during the multiple days off
  2. Traders in general go on vacation the end of December, volume drops, and the market becomes lethargic, reducing volatility
  3. People expect volatility to decrease, trade accordingly, and it becomes a self-fulfilling prophecy

I am skeptical about calendar based trading strategies (e.g., “crash prone” October was +8.5%, -1.8%, +4%  2011 through 2013) but the Christmas effect has been persistent— perhaps because it’s not easy to profit from it.   The VIX index itself is not investable, and the December VIX futures already discount the effect.

I was curious  how the VIX behaved over the last few years in December and January, so I generated the chart below using VIX historical data from the CBOE.

Xmas-VIX


To make the chart more readable I carried over closing values over weekends/holidays and used a 3-day moving average.  I excluded 2008, even though it shows the Christmas effect because the market that year was clearly in an unusual state.

There does seem to be a fairly consistent low around the 23rd of December and the VIX has consistently increased right after that—at least for a few days.   By mid-January things seem to have settled back into their random ways.

I also wondered how VIX futures behaved around the holidays.     I used my VIX futures master spreadsheet  to generate the chart below showing the behavior of the front month VIX futures, the next ones to expire.
Xmas-VIX-Futures

With the VIX futures the December dip comes a few days earlier.

In my experience, the future is often uncooperative in repeating the past, but this VIX Yet to Come, looks like a reasonable bet for a post-Christmas boost.