Volatility White Papers and Presentations

Updated: Sep 16th, 2018 | Vance Harwood | @6_Figure_Invest

Below I’ve collected links to some of my favorite white papers and presentations on volatility. I’ve organized them in the following categories:

  • Volatility Concepts & Volatility Trading
  • Probability Distributions—Normal and Otherwise
  • The VIX and VIX Futures
  • Volatility Contagion—Will Short Volatility Destroy the World?
  • Variance Swaps—the Technology That Underlies VIX & VIX Futures

For an index of my 60+ posts on volatility see here.


Volatility Concepts & Volatility Trading

  • Volatility: A New Return Driver?” by Greggory Flinn & Roger Schreiner
    • A good non-mathematical overview of volatility, volatility products including futures and a couple example trading strategies using volatility Exchange Traded Products
  • Easy Volatility Investing by Tony Cooper
    • Available via free download on the SSRN repository, this paper provides a good non-mathematical overview of volatility investing. It includes a good discussion on the Volatility Risk Premium (VRP) which is an important concept.  It also provides detailed analysis of several volatility based trading schemes
  • Volatility Trading: Trading Volatility, Correlation, Term Structure and Skew” Bennett & Gil
    •  Over 200 pages of wide-ranging information—from covered calls to exotic options, to links between CDS spreads and implied volatility.  Something for everyone.

Probability Distributions—Normal and Otherwise 

  • Tales of the Unexpected by Andrew Haldane
    • This accessible paper (only one equation) is the best that I’ve ever read on the differences between processes accurately modeled by Gaussian/normal distributions and those better matched by power law distributions. I have seen this distinction made many times, but this paper provided examples and reasoning that really helped me internalize the differences.   Most of our stock market computations (including Black & Scholes for option pricing) and risk management formulas assume normal (or log-normal) distributions but this paper lays out a compelling case for why power law distributions are often a better match.
  • The normal distribution is the log-normal distribution by Werner Stahel & Eckhard Limpert
    • This presentation does a very nice job of distinguishing between the normal and log-normal distribution and providing guidelines for when they should be used. Bottom line, for stock price distributions we should use the log-normal distribution.

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Using the VIX Futures Term Structure to Predict Volatility ETP Prices

Updated: Oct 4th, 2018 | Vance Harwood | @6_Figure_Invest

Status quo forecasting is sometimes very easy to do.  For example, if you predict that tomorrow’s high temperature will be the same as today’s high, your estimate will be close to the actual high much of the time.  Predicting volatility Exchange Traded Products (ETP) prices is not so straightforward.

The VIX futures that volatility ETPs like VXX, SVXY, UVXY, and TVIX track are similar to stock options in that they have a time value that usually decaying.  Generally the longer the VIX future has until expiration the higher its price.  If you plot VIX futures prices versus time until expiration the chart often looks like the one below from VIX Central.  This curve is called the VIX Futures Term Structure.

The term structure curve can be relatively stable for significant periods of time—which raises the question of whether we can use the term structure to predict volatility ETP prices.

Even if the price vs time curve of the VIX Futures stays exactly the same, several underlying factors that impact the prices of the volatility ETPs are in a state of change.  For example:

  • The individual VIX future’s prices change as they approach expiration
  • The mix of VIX futures that determines the ETP values changes based on their time to expiration and their prices
  • The position size of VIX Futures held by the leveraged ETPs (e.g., TVIX, UVXY, SVXY, VMIN, ZIV) changes on a daily basis based on the previous day’s percentage moves

Assuming the VIX futures term structure is stable (including the Cboe’s VIX spot price) allows us to project how much decay/gain is “built-in” to the prices of the long/inverse volatility ETPs. This information can help us set strike prices for option strategies, set limit prices, and determine risk/reward parameters.  More than 80% of the time, the VIX Future Term Structure is in a configuration called contango, where futures with more time until expiration are priced higher than the “spot” VIX price.  While in contango, decay factors on long volatility funds like VXX, UVXY, and TVIX can be considerable as can the boost factors on inverse funds like SVXY, VMIN, and ZIV.

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Volatility ETP Price Projection Service

Updated: Oct 4th, 2018 | Vance Harwood | @6_Figure_Invest

I am offering a Volatility ETP Projection Service that calculates future volatility Exchange Traded Product (ETP) prices assuming the current VIX futures term structure is stable.
In my post Using the VIX Futures Term Structure to Predict Volatility ETP Prices, I show how this approach can be used to produce statistically valid ETP price projections and ranges.

This forecast does not attempt to predict upcoming volatility spikes or slumps—it’s totally focused on the price trends that would occur with a static VIX futures term structure.

With a stable term structure (and a stable spot VIX), the VIX futures prices that underlie the volatility ETPs like VXX, VXXB, UVXY, and SVXY do change but they precisely follow the price/days-til-expiration curve.  The VIX Central chart below shows the closing VIX futures prices for August 23, 2018.  If the term structure is stable then the curve at the end of the 24th would have the identical price vs time shape but the blue data points, representing futures values, would all be shifted slightly down and to the left.

The VIX futures that underlie the volatility ETP are volatile creatures—tomorrow’s values can be dramatically different than today.  I’m not trying to predict those sorts of changes.  What I am computing is the decay or boost that the volatility ETPs experience if the term structure stays in a stable contango or backwardation configuration.  This calculation is not an easy problem—there are a lot of moving parts even when the market is stable.

Historically the VIX futures term structure has been in a contango configuration 80%+ of the time.  Contango fuels a situation where the long volatility ETPs like VXX, UVXY, or TVIX suffer from high decay factors.  Anyone that’s looked at their long-term charts will see the massive impact of those decays over the long run.

Because of the typical decay in long volatility products, short volatility trades are popular but the possibility of volatility spikes makes risk management an important concern.  By estimating median prices and +-1 sigma ranges traders have some analytical results that can help quantify payoffs and establish appropriate risk management thresholds.

The chart below shows a typical SVXY projection when the term structure has been in contango for a while.

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How Does VelocityShares’ ZIV Work?

Updated: Jul 29th, 2018 | Vance Harwood | @6_Figure_Invest

Just about anyone who’s looked at a multi-year chart for a long volatility fund like Barclays’ VXX has thought about taking the short side side of that trade. VelocityShares’ ZIV is an Exchange Traded Product (ETP) that allows you to hold a short volatility position while avoiding some of the issues associated with a direct short position in VXX.  Because ZIV is tied to VIX futures with at least 4 months until expiration its daily percentage moves are considerably smaller than the moves of funds (e.g., VXX, UVXY, TVIX) that are tied to shorter term, more volatile VIX futures.

To have a good understanding of how ZIV works (full name: VelocityShares Daily Inverse VIX Medium-Term ETN) you need to know how it trades, how its value is established, its characteristics, its risks, and how VelocityShares (and the issuer— Credit Suisse) make money running it.

How does ZIV trade?

  • ZIV trades like a stock.  It can be bought, sold, or sold short anytime the market is open, including pre-market and after-market time periods.  With an average daily volume of 120 thousand shares, ZIV’s liquidity is good.  Its bid/ask spread tends to run around 10 cents, which is on the high side, but as a percentage of its trading value that’s ~0.15% so it’s not a big economic penalty.
  • Unfortunately, ZIV does not have options available for it.  However, both of its closest Exchange Traded Fund (ETF) equivalents, REX ETF’s VMIN and ProShares’ SVXY -0.5X short term ETF do have options available.
  • Like a stock, ZIV’s shares can be split or reverse split—but unlike VXX (with 5 reverse splits since inception) ZIV has only split once, a 1:8 split in June 2011 that took its price from  $129 down to $16. Unlike Barclays VXX, ZIV is not on a hell-ride to zero.
  • ZIV 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.

How is ZIV’s value established?

  • Unlike stocks, owning ZIV 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 ZIV.  While you’re at it forget about technical style analysis too, the major price moves of ZIV are not driven by supply and demand for ZIV itself but rather by the moves of the large, liquid VIX futures market.
  • Ultimately ZIV value is tied to the daily resetting inverse of an index (S&P VIX Medium-Term Futurestm) that specifies a hypothetical portfolio of VIX futures with 4 through 7 months until expiration.  Every day the index specifies a new mix of VIX futures in that portfolio. On any given day one-third of ZIV’s assets are allocated to VIX futures with 5 months till expiration, another third is allocated to 6th-month futures, and the final third is split between 4th and 7th-month futures. This mix of VIX futures gives ZIV the approximate performance of a VIX future with 153 days until expiration.
  • The index ZIV tracks, SPVXMP, is maintained by the S&P Dow Jones Indices.  The theoretical value of ZIV, if it were perfectly tracking the inverse of the index, is published every 15 seconds during market hours as the “intraday indicative” (IV) value.  Yahoo Finance publishes this quote using the ^ZIV-IV ticker. Because ZIV’s day end value is set by the settlement prices of VIX futures the closing IV value of ZIV is established around 4:15 PM ET not at the 4 PM NYSE close.
  • Wholesalers called “Authorized Participants” (APs) will at times intervene in the market if the trading value of ZIV diverges too much from its IV value.  If ZIV is trading sufficiently below the index they start buying large blocks of ZIV—which tends to drive the price up, and if it’s trading above they will short ZIV.  The APs have an agreement with Credit Suisse that allows them to do these restorative maneuvers at a profit, so they are highly motivated to keep ZIV’s tracking in good shape.  According to ETF.com ZIV’s median tracking error relative to its index is -0.04%.

How Does ZIV Behave?

  • Almost all the time the medium-term VIX futures that underlie ZIV are in a configuration called contango where the longer dated futures are more expensive than the ones closer to expiration.  Persistent contango sets up an attractive short trade because as long as contango persists the VIX futures shorted by ZIV will tend to go down in value over time.  Contango does not guarantee profits for the short seller because if volatility spikes the medium-term futures tend to go up in unison but historically around 75% of the time ZIV is increasing in value.
  • This situation sounds like a short sellers dream, but VIX futures occasionally go on a tear, turning the short volatility trader’s profits into losses very quickly. While not as volatile as the short-term volatility funds ZIV can drop dramatically.  Its record one day drop so far was -26% on February 5th, 2018 and one day drawdowns of over 10% are fairly common.
  • The chart below shows ZIV from 2004 using simulated values.

  • ZIV does not implement a true short of its tracking index.  Instead, it tracks the -1X inverse of the index on a daily basis and then rebalances investments at the end of each day.  For a detailed example of what this rebalancing looks like see “How do Leveraged and Inverse ETFs Work?
  • There are some very good reasons for this rebalancing, for example, a true short can only produce 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”.  ZIV, on the other hand, is up almost 500% since its inception on November 29th, 2010, and it faithfully delivers a daily percentage move very close to -1X of its index.
  • Detractors of the daily reset approach correctly note that ZIV and funds like it can suffer from volatility drag.  If the index moves around a lot and then ends up in the same place ZIV will lose value, whereas a true short would not, but as I mentioned earlier, true shorts have other problems.  Surprisingly, if the underlying index is trending down, daily resetting ETPs can deliver better than their stated leverage performance.  For more see “A Hat Trick for Inverse / Leveraged Volatility Funds
  • Historically ZIV has median moves of -0.21X compared to the CBOE’s VIX index.  If the VIX moves up 10% you can expect ZIV on average to move down 2.1%.  However, this relationship is not cast in stone.  At times ZIV and VIX will even move in the same direction.
  • Another important statistical ZIV relationship is its typical moves relative to the short-term volatility index which big volatility funds like VXX, UVXY, and TVIX are tied to.  Its median beta, the ratio of ZIV percentage moves to VXX moves, is around -0.44.  This ratio varies but as the chart below shows the variation since VXX started trading in January 2009 has remained between -0.2X and -0.72X.


What are the Risks?

  • Along with their impressive upsides, inverse volatility funds like ZIV carry considerable risks. The risks include the inevitability of volatility spiking up during market scares, corrections, or bear markets. Since its inception in 2010, ZIV has experienced 30 single day drawdowns of -5% or more, including the previously mentioned -24% crash. As scary as this is the other inverse volatility funds -0.5X SVXY and VMIN carry even more drawdown risk with worse case one-day drawdowns of -48% and -38% respectively. Buying and holding these securities is not for the faint of heart.
  • Another risk is termination. ZIV’s prospectus states that if ZIV drops 80% or more in a single day it will likely terminate. Before February 2018 there was a lively debate on whether this was a credible risk even for the higher leveraged former -1X short term inverse funds XIV and SVXY—which were much more likely to terminate than ZIV.
  •  On February 5th, 2018 both XIV and SVXY dropped more than 90%.  XIV was subsequently terminated by Credit Suisse and SVXY was deleveraged by ProShares down to -0.5X.  Based on that day’s behavior it would take a one-day VIX spike of over 300% to put ZIV in risk of termination (the 5-Feb-2018 VIX spike was 115%).  If VIX futures became even more reactive than they were on the 5th it might require a lower VIX jump than that but the bottom line is that it would likely take an event equivalent or bigger than the October 1987 crash to terminate ZIV.


How do VelocityShares and Credit Suisse make money on ZIV?

  • Credit Suisse collects a daily investor fee on ZIV’s assets—on an annualized basis it’s 1.35%.  With current assets at $120 million, this fee brings in around $1.6 million per year.  That should be enough to cover Credit Suisse’ ZIV costs and be profitable.  My understanding is that a portion of this fee is passed onto to VelocityShares for their technical and marketing activities.
  • Unlike an Exchange Traded Fund (ETF), ZIV’s Exchange Traded Note structure does not require Credit Suisse to report what they are doing with the cash it receives for creating shares.  The note is carried as senior debt on Credit Suisse’s balance sheet but they don’t pay interest on this debt.  Instead, they promise to redeem shares that the APs return to them based on ZIV’s daily closing indicative value.
  • Credit Suisse could hedge their liabilities by shorting VIX futures in the appropriate amounts, but they almost certainly don’t because there are cheaper ways (e.g., over-the-counter swaps) to accomplish that hedge.

With XIV delisted and SVXY deleveraged ZIV has a comparable leverage factor with the remaining inverse volatility funds (VMIN, and -0.5X SVXY).  Historically it has declined less than its competitors on the really high volatility days (5-Feb-2018 and Brexit shocks).  ZIV can’t guarantee that advantage in the future but it is comforting to see a track record of smaller drawdowns during historic VIX spikes.  In the post-February 2018 volatility landscape, ZIV is an attractive choice for shorting volatility.

 For more information 

Simulation of the Longer Duration VMIN & VMAX

Updated: Jun 29th, 2018 | Vance Harwood | @6_Figure_Invest

When they were introduced by REX ETF in May 2016 VMIN and VMAX were the first actively managed volatility Exchange Traded Funds (ETFs).  REX’s strategy was to offer higher effective leverage than the popular unleveraged long VXX and the daily resetting inverse volatility funds (XIV & SVXY).  In 2017 REX ETF’s strategy paid off with VMIN delivering an eye-popping 190.6 percentage gain, bettering XIV & SVXY returns by 4.7%. For more on how VMIN and VMAX worked during that timeframe see this post.

Then Came February 5th, 2018…

XIV plunged 96%  on February 5th, 2018.  Since VMIN’s expressed strategy was to offer higher leverage than XIV you’d reasonably have expected VMIN on that date to drop below zero and be terminated—but it didn’t die.  It “only” dropped 87%.

How is that possible?

Most likely the managers of VMIN recognized that the end of day VIX futures settlement on the 5th was likely going to be disastrous, and covered at least some of their VIX future short positions before the typical rolling/ rebalancing trade time of ~4:15 PM ET.  By acting preemptively they avoided the worst of the VIX Future’s end-of-day spike—and dodged what would have been a likely death blow to VMIN.

Reflection often follows a near-death experience and that was the case with REX ETF also.  Given the record VIX percentage move and unprecedented level of correlation of the VIX futures with the VIX during the spike, they reasonably concluded that they should reduce the leverage of their funds.  Starting March 7th REX ETF started shifting allocations and reached their target leverage on March 23rd, 2018.


More Time until Expiration

In order to reduce their effective leverage, REX ETF changed VMIN & VMAX’s holdings to a rolling mix of 3rd, 4th, and 5th-month VIX futures.  The funds always hold 50% of their assets in the 4th-month futures and allocate the remaining 50% between the 3rd and 5th-months.  The 3rd vs 5thmonth holdings shift in proportion to the time remaining until the 3rd month becomes the 2nd-month future.  The last contracts in the 3rd-month futures are closed out the night before they become the 2nd-month futures. This algorithm results in a mix of VIX futures that have an effective duration of around 110 days.


The New Leverage Factors

Based on historical patterns this mix of futures should produce VMIN/VMAX percentage moves that are ~0.26 of the CBOE’s VIX’s percentage moves  (compared to 0.51 previously).  The comparable metric for Barclays’ VXX is 0.45.

VIX futures and the VIX index don’t always track well (sometimes they even go in opposite directions!) so another useful metric is how closely the new VMIN/VMAX will track VXX.  I simulated VMIN/VMAX performance, using its new allocation strategy, from 2004 on using the Cboe’s futures historical data.  Based on that simulation I’m estimating that the new VMIN/VMIN percentage moves (leverage) will typically be around 0.53X of VXX’s percentage moves.  While more consistent than the VIX percentage tracking, this leverage also varies somewhat because the VIX futures term structure between the 1st and 2nd months sometimes shifts relative to the 3rd through 5th months.  The chart below shows how that leverage has shifted historically when averaged over a calendar month period.


Drawdown / Termination Risk

My backtest also allows us to answer questions like how much the new VMIN would have dropped on 5-Feb-2018 (a -38% drop), how it would have fared through the 2008/2009 bear markets (drawdown of 85%), and 2011 correction (drawdown of 51%).  A chart of the simulation is shown below.

With this new allocation strategy, VMIN has a much lower risk of termination and reduced drawdowns during volatility spikes—at the cost of not harvesting contango as effectively as the funds with higher leverage.


Fees and Dividends

I have included REX ETF’s annual fees of 2.85% for VMAX and 3.46% for VMIN in the simulation.  I could not find any mention of Treasury bill interest in the prospectus so that is not included.

To comply with the securities act of 1940 VMIN and VMAX  must distribute any capital gains as dividends at least yearly.  I did not attempt to simulate this process, instead, the values shown are effectively adjusted for any splits and dividends assuming that any dividends distributed were immediately reinvested in the funds.



Time will tell whether 2018’s February 5th event was an aberration or foreshadowing of future volatility spikes.  The changes to VMIN/VMAX greatly increase their chances of complying with the number one rule of investing—no matter what; make sure you preserve capital to trade another day.


Simulation Spreadsheet

I am making my VMIN/VMIX simulation spreadsheet available for purchase.  The spreadsheet uses an index derived from the 3rd through 5th-month VIX futures and includes the formulas for computing annual fees and calculating the inverse daily resetting function of VMIN from that index.  The spreadsheet does not include the VIX Futures values or formulas for converting from the VIX futures values to the index.  If you cannot see purchase information below please click this link and look at the bottom of the page.

If you purchase the spreadsheet you will be directed to PayPal within a few minutes where you can pay via your PayPal account. When you successfully complete the PayPal portion you will be shown a “Return to Six Figure Investing” link. Click on this link to reach the page where you can download the spreadsheet.  Please email me at [email protected] if you have problems, questions, or requests.  It’s easy to miss the “Return to Six Figure Investing” link.  If you don’t get it / can’t find it please email me.