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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.


 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.

How Did the Old -1X SVXY Work

Saturday, April 21st, 2018 | Vance Harwood


As of February 28th, 2018 SVXY will target -0.5 leverage instead of -1X.  This change was in response to the events of February 5th, 2018 when a massive VIX futures spike occurred in the last 30 minutes of trading, probably in part due to the rebalancing required by the 2X UVXY and -1X SVXY funds.  This change to SVXY will reduce its rebalancing requirements and make it less susceptible to a termination event if VIX futures were to increase 100% or more from the previous day’s close.  This leverage change will reduce SVXY’s performance when VIX futures are dropping in value.  Proshares Press Release


Just about anyone who’s looked at a multi-year chart for a long volatility fund like Barclays’ VXX has thought about taking the other side of the trade. ProShares’ SVXY is an Exchange Traded Fund (ETF) that allows you bet against funds like VXX while avoiding some of the issues associated with a direct short.

To have a good understanding of how SVXY works (full name: ProShares Short VIX Short-Term Futures ETF) you need to know how it trades, how its value is established, what it tracks, and how ProShares makes money with it.

How did -1X SVXY trade?

  • SVXY trades like a stock. It can be bought, sold, or sold short anytime the market is open, including premarket and after-market time periods.  With an average daily volume of 8 million shares, its liquidity is excellent and the bid/ask spreads are a few cents.
  • SVXY has options available on it, with five weeks’ worth of Weeklys and strikes in 50 cent increments.
  • Like a stock, SVXY’s shares can be split or reverse split—but unlike VXX (with 4 reverse splits since inception) SVXY has done three 1:2 splits to bring its price down into optimum trading levels. Unlike Barclays VXX, SVXY is not on a hell-ride to zero.
  • SVXY can be traded in most IRAs / Roth IRAs, although your broker will likely require you to electronically sign a waiver that documents the various risks with this security.  Shorting of any security is not allowed in an IRA.
  • SVXY is subject to termination risk.  Termination can occur (and did with XIV, a very similar fund on February 5th, 2018) if the daily positive move in the VIX futures market approaches or exceeds a 100%.  ProShares guarantees that SVXY will not go negative so to protect themselves they will cover their short positions and terminate the fund if things get bad enough.  For more on this see XIV Termination.

How was  -1X SVXY’s value established?

  • Unlike stocks, owning SVXY does not give you a share of a corporation. There are no sales, no quarterly reports, no profit/loss, no PE ratio, and no prospect of ever getting dividends.  Forget about doing fundamental style analysis on SVXY. While you’re at it forget about technical style analysis too, the price of SVXY is not driven by its supply and demand—it is a small tail on the medium-sized VIX futures dog, which itself is dominated by SPX options (notional value > $100 billion).
  • The value of SVXY is set by the market, but it’s closely tied to the daily percentage moves of the inverse of an index (S&P VIX Short-Term Futurestm) that manages a hypothetical portfolio containing VIX futures contracts with two different expirations. Every day the index methodology specifies a new mix of VIX futures in the portfolio. On a daily basis SVXY moves in the opposite direction of the index with a leverage factor of -0.5X, so for example, if the index (ticker SPVXSPID) moves up 0.3%, then SVXY will move down precisely 0.15%. This post has more information on how the index itself works. The index is maintained by S&P Dow Jones Indices.
  • As is the case with all Exchange Traded Funds, SVXY’s theoretical share value is just the dollar value of the securities and cash that it currently holds divided by the number of shares outstanding. This theoretical value is published every 15 seconds as the “intraday indicative” (IV) value. Yahoo Finance publishes this quote using the ^SVXY-IV ticker. The end of day value is published as the Net Asset Value (NAV).  The NAV is computed at 4:15 ET, not the usual market close time of 4:00 ET, because VIX Futures don’t settle until 4:15.
  • If the trading value of SVXY diverges too much from its IV value wholesalers called Authorized Participants (APs) will normally intervene to reduce that difference. If SVXY is trading enough below the index they start buying large blocks of SVXY—which tends to drive the price up, and if it’s trading above they will short SVXY.  The APs have an agreement with ProShares that allows them to do these restorative maneuvers at a profit, so they are highly motivated to keep SVXY’s tracking in good shape.

What did -1X SVXY track?

  • SVXY makes lemonade out of lemons.  The lemon, in this case, is the index S&P VIX Short-Term Futurestm that attempts to track the CBOE’s VIX® index—the market’s de facto volatility indicator. Unfortunately, it’s not possible to directly invest in the VIX, so the next best solution is to invest in VIX futures. This “next best” solution turns out to be truly horrible—with average losses of 5% per month. See this post for charts on how this decay factor has varied over time. For more on the cause of these losses see “The Cost of Contango”.
  • This situation sounds like a short sellers dream, but VIX futures occasionally go on a tear, turning the short sellers’ world into something Dante would appreciate.
  • Most of the time (75% to 80%) SVXY is a real moneymaker and the rest of the time it is giving up much of its value in a few weeks—drawdowns of +90% are not unheard of. The chart below shows SVXY from 2004 using actual values from October 2011 forward and simulated values before that.


  • Understand that SVXY did not implement a true short of its tracking index. Instead, it attempted to track the -1X percentage inverse of the index on a daily basis.  To maintain this -0.5X behavior the fund must rebalance/reset its investments at the end of each day.  For a detailed example of how this rebalancing works see “How do Leveraged and Inverse ETFs Work?
  • There are some very good reasons for this rebalancing, for example, a true short can only deliver at most a 100% gain and the leverage of a true short is rarely -1X (for more on this see “Ten Questions About Short Selling”.  -0.5X SVXY, on the other hand, would be up over 200% if it had been trading since the original -1X SXVY started trading 3-Oct-2011.  It faithfully delivers a daily percentage move very close to -0.5X of its index.
  • Detractors of the daily reset approach correctly note that SVXY and funds like it can suffer from volatility drag. If the index moves around a lot and then ends up in the same place SVXY will lose value, whereas a true short would not, but as I mentioned earlier, true shorts have other problems.  Even with volatility drag daily reset funds don’t always underperform. If the underlying index is trending down, they can deliver better than -1X cumulative performance. The chart below shows the relative one-year performance of SVXY and a true short starting with $1K invested in January for 2011 through 2016.


How did ProShares make money on -1X SVXY?

  • An Exchange Trade Fund like SVXY must explicitly hold the appropriate securities or equivalent swaps matching the index it tracks. ProShares does a very nice job of providing visibility into those positions. The “Daily Holdings” tab of their website shows how many VIX futures contracts are being held. Because of the -1X nature of the fund, the face value of the VIX futures contracts will be very close to the negative of the net “Other asset/cash” value of the fund.
  • ProShares collects a daily investor fee on SVXY’s assets. The fee is stated as a 0.95% annual fee, but it’s implemented by subtracting 0.95/365 of a percent from each share’s value every calendar day. With current assets at $1 billion, this fee brings in around $9.5 million per year. That should be enough to be profitable, however, I suspect the ProShares’ business model includes revenue from more than just the investor fee.
  • Exchange Traded Funds like SVXY recoup transaction costs in a non-transparent way. Transaction costs are deducted from the fund’s cash balance—resulting in a slow divergence of the fund’s IV value from the theoretical value of the index that it’s tied to. This differs from the approach that Exchange Traded Notes (ETN) use, their theoretical value is directly tied to the moves of the index itself, so the ETN issuers must pay for transaction costs other ways (e.g., out of the annual investor fee, or other explicit fees). In the case of SVXY, this hidden transaction fee has averaged around 0.28% per year.
  • One clue on ProShares’ business model might be contained in this sentence from SVXY’s prospectus:
    “A portion of each VIX Fund’s assets may be held in cash and/or U.S. Treasury securities, agency securities, or other high credit quality short-term fixed-income or similar securities (such as shares of money market funds and collateralized repurchase agreements).”  Agency securities are things like Fannie Mae bonds. The collateralized repurchase agreements category strikes me as a place where ProShares might be getting significantly better than money market rates. With SVXY currently able to invest around $250 million this could be a significant income stream.
  • I’m sure one aspect of SVXY is a headache for ProShares. Its daily reset construction requires its investments to be rebalanced at the end of each day, and the required investments are proportional to the percentage move of the day and the amount of assets held in the fund. SVXY currently holds $400 million in assets, and if SVXY moves down 10% in a day (the record negative daily move is -24%, positive move +18 %) then ProShares must commit an additional $20 million (5% of $400 million) of capital that evening. If SVXY goes down 10% the next day, then another $18 million capital infusion is required.

SVXY won’t be on any worst ETF lists like Barclays’ VXX, but its propensity for dramatic drawdowns (e.g. -91%! in the Jan/Feb 2018  timeframe) will keep it out of most people’s portfolios. Not many of us can handle the emotional stress of holding on to a position with huge losses—even though the odds support an eventual rebound.

The eye-popping inverse volatility gains in 2016 and 2017 pushed SVXY’s assets beyond VXX’s but with its February 5, 2018 reset it dropped well below that level. It will be interesting to see how the next few years go.  I suspect we’ll see additional bloodletting as people rediscover short volatility can be very volatile in its own right.

Free Bitcoin/Bitcoin Futures/GBTC Quotes, Charts, & Historical Data

Wednesday, December 27th, 2017 | Vance Harwood

Finding quotes and historical data for Bitcoin, Bitcoin futures, Bitcoin options can be an adventure.  Below I’ve assembled links to the online resources that I’ve been able to find.

In many cases, data is available from multiple sources.  I did not attempt to list all of them.

BTC Quotes

BTC Charts

 BTC Historical Prices

BTC Futures

  • CBOE/CFE  Symbol: XTB
    • Quotes
      • Spot: Gemini exchange
      • Cboe (including bid/ask)
        • Use “Enter Symbol” Field
        • Ticker construction:  XBT/ followed by month-year code (e.g, XBT/F8 = January 2018 expiration)
          • F=Jan, G=Feb, H=Mar, J=April, K=May, M=June, N=July, Q=Aug, U=Sept, V=Oct, X=Nov, Z=Dec
      • Cboe/CFE  (all months)
    • Historical Data  CBOE
    • Term Structure  Chart:  VIX Central/bitcoin
    • Reference exchange:  Gemini
    • Contract Size:  1 Bitcoin, cash settled  (Contract Specifications)
    • Initial customer margin 44%
      • Brokers may require much more margin ( e.g., Interactive Brokers is requiring $40K per contract–around 130%–on short contracts)
    • Trading Hours (USA Central Time)
      Type of Trading Hours Monday Tuesday – Friday
      Extended 5:00 p.m. (Sunday) to 8:30 a.m. 3:30 p.m. (previous day) to 8:30 a.m.
      Regular 8:30 a.m. to 3:15 p.m. 8:30 a.m. to 3:15 p.m.
    • Future settlement quote (once per day)
    • Option availability:  Earliest probably around March 2018


  • CME  Symbol: BTC
    • Quotes
    • Reference exchanges:  Bitstamp, GDAX, itBit, Kraken (combined into a composite quote via BRTI & BRR)
    • Contract Size:  5 Bitcoins, cash settled  (Contract Specifications)
    • Initial customer margin 35%
      • Brokers may ask for much more than this, especial for short contracts
    • Trading Hours:  Scheduled to start trading 18-Dec-2017
      CME Globex: Sunday – Friday 6:00 p.m. – 5:00 p.m. (5:00 p.m. – 4:00 p.m. CT) with a 60-minute break each day beginning at 5:00 p.m. (4:00 p.m. CT)
      CME ClearPort: Sunday – Friday 6:00 p.m. – 5:00 p.m. (5:00 p.m. – 4:00 p.m. CT) with a 60-minute break each day beginning at 5:00 p.m. (4:00 p.m. CT
    • Future settlement quote: BRR (once per day)  methodology) )   Historical Data 

BTC Mutual Funds

  • GBTC  Bitcoin Investment Trust  (A closed-end mutual fund)  Available for trading in regular brokerage accounts and IRAs
    • Shares outstanding & Bitcoin holdings GBTC  (as of 27-Dec-2017  1868700 shares,  171,796 Bitcoins)
    • Quotes Bloomberg  Yahoo 
    • Historical Data  Yahoo
    • Tracking Error with BTC
      • As of 27-Dec-2017  GBTC had premium over BTC of +57%   (GBTC price / NAV as reported by Bloomberg)

BTC Options & Swaps

  • LedgerX offers Bitcoin settled options
    • Their options are “physically” settled with Bitcoin
    •  To participate if appears you must be an institution or a high net worth ($10 million+) individual
    • See this page for a currently listed options and swaps


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.



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 do VelocityShares’ EVIX and EXIV Work?

Monday, May 21st, 2018 | Vance Harwood

In May 2017 VelocityShares introduced two volatility funds, EXIV and EVIX, which track European volatility futures.  In digging into these funds I’ve encountered a dense mashup of the familiar and the foreign.  The differences between European Volatility futures and VIX futures are relatively small so it’s reasonable to view EXIV and EVIX as close cousins of ProShares SVXY and Barclays’ VXX, however, these funds depend on a set of securities and processes with subtle and not so subtle differences with the mainstay USA volatility funds.

If you are not familiar with VIX futures based volatility Exchange Traded Products (ETPs) then I recommend you first take the time to read these posts on ProShares’ SVXY and Barclays’ VXX before you tackle these new arrivals.  One thing to remember is that after the February 5, 2018 “Vol Tsunami” SVXY’s leverage factor was lowered by Proshares from -1.0X to -0.5X of its reference index.  EXIV’s leverage factor remains at -1.0X.

Some Basics

  • EVIX is a short-term long volatility fund that will tend to go up if European stocks go down significantly.
  • EXIV is a short-term inverse volatility fund that tracks the opposite of EVIX’s percentage moves on a day only basis. Because EXIV adjusts its assets at market close to achieve its daily tracking goal it does not behave like a true short of EVIX—which can be a good thing or a bad thing depending on the market moves.
  • The Swiss bank, UBS AG, is the issuer of both of these Exchange Traded Notes (ETNs). They are structured as unsecured long-term debt securities.  As of May 2018, Moody’s rating of UBS’ long-term debt was: “A1 Possible Upgrade”  The investor fee charged by UBS AG is 1.35% annualized for EVIX and EXIV, this compares to 0.95% for SVXY and 0.89% for VXX.
  • The European Volatility futures that these funds track settle at expiration to the European volatility index VSTOXX. VSTOXX uses a methodology very similar to the CBOE’s VIX but instead of being based on the prices of S&P 500 (SPX) options the VSTOXX is based on STOXX option prices.
  • The STOXX index is comprised of 50 of the largest companies in the Eurozone and is capitalization-weighted like the S&P 500. It does not include companies from the UK. These 50 stocks represent around 60% of the Eurozone stock market value. In comparison, S&P 500 represents around 80% of the total USA stock market capitalization. Similar to the S&P 500 index, the STOXX index does not include dividends, so the returns of actually holding the constituent stocks would be higher than the index indicates.  For the last 5 years, the STOXX dividends have averaged 2.5% vs 1.9% for the S&P 500.
  • EVIX and EXIV track indexes (VST1MSL & VST1MISL respectively) that theoretically hold a mixture of the two VSTOXX futures nearest to expiration. The mixture gives an expiration horizon of 30 days, similar to the VIX future based short term volatility funds like VXX and SVXY.  These funds are fully divested out of expiring futures the day before their expiration/final settlement.
  • Both funds effectively do a daily end-of-day rebalance that adjusts the number of volatility contracts that they hold in order to maintain a 30-day average horizon. At the same time EXIV also does an asset rebalance such that its daily percentage move will closely match the opposite of EVIX’s next day daily percentage move (see How Does SVXY Work? for more on this).


  • Standard processes and rough equivalences in key securities


Generic Securities


European Version USA Version Standard Processes
Volatility Futures VSTOXX futures VIX futures Settlement
30-day Volatility Index VSTOXX VIX Index calculation
Large Cap Stock Index STOXX 50 S&P 500 Stock index selection
Large Cap Stock Options OESX SPX Settlement, Cash Settled, European exercise


    • The key European securities and processes are similar to the USA markets but in no case have I found a pair of processes that are identical. For example, VIX futures settle to a special opening quotation of the CBOE’s VIX® soon after market open on expiration days whereas VSTOXX futures final settlement price is determined by the average VSTOXX index level between 11:30 and 12:00 CET on the day of expiration.
    • A significant difference between the VIX and the VSTOXX index is that the VSTOXX calculation does not incorporate options with bid prices below 50 Euro. This contrasts with the VIX’s calculation which uses options with bids as low as $5—which increases the chances that an institutional player might attempt to influence the VIX’s settlement value in their favor by buying or selling cheap out-of-the-money puts.
  • Quotes / Historical Data
    • While free quotes for EXIV and EVIX are easy to get with the usual sources (Online brokers, Yahoo, Google), obtaining quotes for the underlying securities/indexes is tougher. The ones I’ve found so far are:
    • STOXX
    • VSTOXX (ticker V2TX or DVY00)
    • VSTOXX Futures
    • VST1MSL (EVIX’s dollar denominated index)
    • VST1MISL (EXIV’s dollar denominated index)
    • Intraday Indicative value (IV) quotes for EXIV and EVIX are available from some brokers and Yahoo Finance. The symbols within Yahoo are ^EXIV-IV and ^EVIX-IV


  • Hours
    • Typically the European continent is 6 hours ahead of USA Eastern time. Standard closing time on the European continent exchanges is 5:30 PM, so they are closing at 11:30 Eastern time. The IV values for EXIV and EVIX don’t update after 11:30 ET because the OESX options used to compute VSTOXX are not trading past then. The Yahoo finance chart below illustrates EXIV’s IV value flat-lining during the afternoon.
    • The VSTOXX futures referenced by these funds trade from 7:30 to 22:30 CET.


  • Termination risk
    • EXIV will terminate if there is a large enough volatility spike.  Once thought by some to be unlikely the termination of XIV in February 2018 demonstrated that this can happen. The funds are guaranteed to not go below zero and the issuers will not commit extra capital to meet margin calls in that sort of extreme situation.  In EXIV’s case, the fund will be automatically terminated if the drop in the intraday IV value is 75% or more from the previous day’s close.  For the USA markets, historical data suggests it would take a VIX intraday spike of at least 80% to result in a 75% drawdown in the inverse volatility funds and I suspect that the VSTOXX/ VSTOXX futures sensitivities are similar. In the case of termination, shareholders would receive a final share value reflecting the net value of the fund a few days after the triggering event.  The value is not guaranteed to be 25% of the previous day’s value, it is only guaranteed to be zero or higher.

Comparing Markets—and Indexes

The chart below compares the historical values of the S&P 500 and the STOXX as well as the VIX and VSTOXX since January 1998.

  • A few things stand out when looking at the STOXX (red line)
    • The STOXX fully participated in the 2000 dot-com crash and the 2008/2009 bear markets
    • The STOXX is still well below its 2000 highs—the lack of recovery in the STOXX after the 2008/2009 financial crash is striking
  • Looking at VSTOXX (purple) vs the VIX (black) above:
    • The VSTOXX shows mean-reverting behavior similar to the VIX. Sharp spikes up are followed by fairly rapid decays towards the mean values.
    • Periods of low volatility can persist for a long time but eventually, the VSTOXX reverts back to values closer to the mean
    • Generally, the VIX and the VSTOXX are closely correlated
    • The VSTOXX value is almost always higher than the VIX’s value
  • Some statistics for the S&P 500 and the STOXX, January 1999 through July 2017:
Compound Annual Growth (dividends not included) 3.75% -0.25%
Annualized Volatility (365 day year) 23.4% 28.1% (20% higher than S&P 500)
Worst Case Drawdown -56% (2009)


-65% (2003)
Correlation of % moves 0.54 (moderately high) between S&P 500 and STOXX


  • Statistics for the VIX and the VSTOXX, January 1999 through May 2018
Average 20.05 24.40 22% higher
Median 18.2 22.54 23% higher
Low 9.14 10.68 14.5% higher
High 80.86 87.51 8% higher
Annualized Volatility

(365 Day Year)

129.3 114.42   13% lower
Value Correlation .905 (high) between VIX and VSTOXX values
Correlation of % moves 0.544 (moderately high) between VIX and VSTOXX % moves
Biggest one day drop -29.5%  (10-May-10) Flash Crash aftermath -35.2%  (24-Apr-17) Le Pen defeat
Biggest one day spike +115.5% (5-Feb-18) “Vol Tsunami” +38.8% (24-Aug-15)  China scare II
Mode (most common value)  [0.1 pt bins] 13.3 23.1


The chart below shows a histogram of values for the VSTOXX and the VIX

  • A few observations:
    • The VSTOX distribution is shifted notably higher in value than the VIX
    • While the two index distributions have truncated left “shoulders” and big fat tails on the right the VSTOXX has a significantly more balanced distribution around its mean compared to the bottom-heavy VIX.
    • The difference between the mode (the most common value rounded to 0.1 pts) and the record low is only 45% with the VIX compared to 116% for the VSTOXX


Historic Performance

  • By using a simulation starting in June 2009 of EXIV and EVIX  we can get a feel for their performance relative to SVXY and VXX.  The chart below shows relative performance when starting with portfolios of $10K fully invested in each of the funds.


  • The two lines starting high on the left (red and blue lines) are long volatility funds that reference the left axis scale. The long volatility funds exhibit the typical long volatility fund race to zero, with VXX slightly better at losing value.
  • The two inverse volatility funds (green and purple lines) referencing the right scale perform much better than the long funds. Overall the -0.5X SVXY’s performance is better with an approximate 12X growth since 2009.  Both funds lost approximately 50% of their value in the February 5th, 2018 volatility spike.

Using a log scale on the vertical axis provides a more accurate visual way to judge relative performance. The first chart shows VXX index vs the EVIX index


  • The two portfolios begin diverging in early 2010 and don’t return to a similar loss rate until 2016.
  • Over the 2010 to 2015 period EVIX’s decay rate was significantly lower than VXX’s. It’s likely that the VSTOXX futures had considerably lower contango levels during that period compared to the VIX’s futures
  • Looking at the inverse volatility side of things EXIV lagged SVXY until around 2015.  At that point, the improvements in the European markets fueled a strong period of contango driven growth in EXIV.

The chart below, starting in January 2016 more clearly shows how EXIV has outperformed the  -0.5X SVXY in the last couple of years. The non-leveraged long USA and European based funds have tracked each other relatively closely over that same period.  The chart below shows the result of the simulation.

When to Use These New Funds

  • An obvious application for these new funds is placing a bet on an upcoming European event with potentially major impact (e.g., a Brexit vote, or the Le Pen / Macron election). In “known/unknown” cases like this the date of the event is well-known, but the result is uncertain and potentially economically impactful.  It’s certain that the VSTOXX will go up before an event like this, the interesting, and potentially lucrative question is what will happen to volatility after the event—panic/distress or a collapse back to the status quo.
  • Diversification is another application. Obviously, the European markets are not in lockstep with the USA markets and this distance will tend to smooth out some of the volatility shocks.
  • Having EVIX and EXIV gives traders a way to profit if they see an upcoming convergence or divergence between the volatility indexes in the two markets. For example, if you believe a recent volatility jump in USA markets will propagate to Europe you could do a straight EVIX purchase or a pairs trade between EVIX and a long volatility fund like VXX.
  • It might be possible to do some form of contango arbitrage with these funds. It’s certain that the contango losses/gain won’t be identical between the two sets of futures markets, a pairs trade might allow a trader to profit from the difference in contango rates with an overall reduced risk exposure.


  • There are differences in the trading hours of these two markets. On the USA side of things, the Intraday Indicative (IV) quotes will be frozen on EVIX and EXIV past the normal close of the European markets, depriving us of an important piece of trading information that’s useful for trading low volume ETPs like these. On the European side, we have times when the volatility securities are trading while the USA markets are closed. For example, you might want to close out EXIV positions if the STOXX was crashing, but if the USA markets are closed there would be no direct way to do that.
  • Since VSTOXX futures are denominated in Euros and EVIX/EXIV are dollar-denominated, exchange rate changes will have effects, although compared to the normal hysteria of volatility markets I doubt it will be significant. Since EXIV is effectively short VSTOXX futures the impact of currency rate changes will be in the opposite direction of EVIX which holds long positions.
  • The EVIX/EXIV calculations assume that cash not needed for margin on the futures will be “invested” in short term German treasury bills—which have been running at negative interest rates (May 2018 -0.33%). Negative rates will result in a minor drag on these fund’s values.
  • Options are available on EVIX, but not on EXIV. You might guess that the CBOE shies away from options on inverse volatility funds because of their termination risk, but options are offered on ProShares’ SVXY so this argument doesn’t hold up.  My understanding is that the SEC has a blanket prohibition on options for leveraged (-1X or 2X on up) Exchange Traded Notes (ETNs).  This seems a bit arbitrary, the big banks that issue the ETNs typically have investment grade credit ratings, but ETFs do have the advantage of transparency into what assets the issuer is actually holding.


It’s head spinning to introduce a whole new set of securities and indexes into the already confusing area of volatility investing but as I reviewed the different ways to use EVIX and EXIV it appears well worth the trouble to learn a few new things. These funds open up new volatility based opportunities in geographic-based investing, diversification, and arbitrage style trades.