How Does VXX’s Daily Roll Work?

Thursday, February 5th, 2015 | Vance Harwood
 

All volatility Exchange Traded Products (ETPs) use indexes that track a mix of two or more months of the CBOE’s VIX Futures.  Calculating this mix is not trivial and has resulted in a lot of bleary eyes—including my own.  My intent with this post is to help you understand, and if you desire accurately compute the key indexes used in VXX and other short term volatility funds using Excel or similar tools.

Why do we need a roll anyway?

If we could directly buy the CBOE’s VIX® index none of this would be necessary.  Unfortunately no one has figured out a cost effective approach so we are forced to use the next best thing—VIX Futures.  Like options, VIX futures have fixed expiration dates so volatility indexes need a process of rotating their inventory of futures in order to have consistent exposure to volatility.   This rotation process is evident in the open interest chart below—the next to expire futures being closed out and the next month of futures being opened.

OI-VIX-Futures



Indexes and Funds—are different things

Before we dive into the details of how this rotation is dealt with, I’d like to address one source of confusion.  ETP’s are not obligated to follow the approach detailed in the indexes.  They are allowed to use other approaches (e.g., over-the-counter swaps) in their efforts to track their indexes.  When ETPs are working properly, their prices closely track the index they specify in their prospectus minus their fees that are deducted on a daily basis.

Because indexes are theoretical constructs they can ignore some practical realities.  For example they implicitly assume fractional VIX futures contracts exist and that the next day’s position can be put in place at market close—even though calculating that position requires market close information.  I’m sure these issues cause headaches for the fund managers, but to their credit the funds usually closely track their index.

The Index Calculation

 The details for the index (ticker SPVXSTR) that VXX tracks are detailed in VXX’s prospectus, pages PS-21 through PS-22. The math is general enough that it covers both the short term index that VXX uses and the midterm index VXZ uses—which adds to its complexity.  The equations use Sigma notation, which probably makes it challenging for people that haven’t studied college level mathematics.   I will present the math below using high school level algebra.

Except for interest calculations all references to days are trading days, excluding market holidays and weekends.

The volatility indexes used by short term volatility ETPs (list of all USA volatility ETPs) utilize the same roll algorithm—at the end of each trading day they systematically reduce the portion of the overall portfolio allocated to the nearest to expiration contracts (which I call M1) and increase the number of the next month’s contracts (M2).

The mix percentages are set by the number of trading days remaining on the M1 contract and the total number of days it’s the next to expire contract (varies between 16 and 25 days).  So if there are 10 days before expiration of the M1 contract out of a total of 21 the mix ratio for M1 will be 10/21 and 11/21 for M2.  At close on the Tuesday before the Wednesday morning M1 expiration there’s no mix because 100% of the portfolio is invested in M2 contracts.

It’s important to understand that the mix is managed as a portfolio dollar value, not by the number of futures contracts.   For example, assume the value at market close of a VIX futures portfolio was $2,020,000, and it was composed of 75 M1 contracts valued at 12 and 80 M2 contracts at 14 (VIX futures contracts have a notional value of $1K times the trading value).   To shift that portfolio to a 9/21 mix for M1 and 12/21 for M2 you should take the entire value of the portfolio and multiply it by 9/21 to get the new dollar allocation for M1, $865,714  (72.14 contracts) and 12/21 times the entire portfolio value to get the dollar allocation for M2,  $1,154,286 (82.45 contracts).

Value weighting gives the index a consistent volatility horizon (e.g., 30 calendar days)—otherwise higher valued futures would be disproportionately weighted.

The next section is for people that want to compute the index themselves.  Yes, there are people that do that.   If you are interested in the supposed “buy high, sell low” theory of roll loss you should check out the “Contango Losses” topic at the bottom of this post.

 

The Variables

 Lower case “t” stands for the current trading day, “t-1” stands for the previous trading day.

The index level for today ( IndexTRt ) is equal to yesterday’s index (IndexTRt-1) multiplied by a one plus a complex ratio plus the Treasury Bill Return TBRt.  The index creators arbitrarily set the starting value of the index to be 100,000 on December 20th, 2005.

 The number of trading days remaining on the M1 contract is designated by “dr” and the total number of trading days on the M1 contract is “dt.”

M1 and M2 are the daily mark-to market settlement values, not the close values of the VIX futures.  The CBOE provides historical data on VIX futures back to 2004 here.

 

The Equations

When dr is not equal to dt: 

Index-normal

 

 

 

When dr = dt (the day the previous M1 expires):

Index-exp

 

 

 

Yes, this equation could be simplified, but then it wouldn’t fit as nicely into the equation below which uses a little logic to combine both cases:

Index-combined

 

 

The equation assumes that the entire index value is invested in treasury bills.

 

Contango Losses

  • An interesting special case occurs when you assume that the M1 and M2 prices are completely stable and in a contango term structure for multiple days—for example, M1 at 17 and M2 at 18. In that situation the equation simplifies to:

Index-contango

 

 

  • This special case illustrates that there is no erosion of the index value just because it’s selling lower price futures and buying higher priced futures—in fact it goes up because of T-bill interest. It’s the equivalent of exchanging two nickels for a dime—no money is lost.  For more on this see: The Cost of Contango—It’s Not the Daily Roll.

 For more information:



Hedging the Market with Volatility

Monday, August 18th, 2014 | Vance Harwood
 

It’s expensive to buy securities that track volatility.  Their holding costs are so high that your timing has to be exquisite in order to end up with a profit.  However, if you’re hedging a short volatility position, or poised to jump into the general market at a possible transition point a long volatility position might make sense.

Consider this chart:

SPYtrend

 

Will the market bounce off this trend line for the fifth time, or will it go into a correction?

If the market breaks through the trendline it’s likely volatility will really spike.   Alternately if  the market rallies then volatility will quickly fade, so an asymmetric bet (e.g., call options) is attractive.   If volatility spikes you benefit from the rapid run-up, but if it’s a false alarm your losses are limited.

The next question is to determine what underlying volatility product is best for this hedge and how large a position is needed to balance the risk in your general market position.  Investing in the CBOE’s VIX® would be ideal, but unfortunately there’s no way to directly invest in the VIX, so we’re left with a set of compromised choices—volatility Exchange Traded Products (ETPs) like TVIX, VXX, or VIXM  (see volatility tickers for the complete list), or VIX futures.  Later in this post I’ll analyze how three specific investments would have performed during an actual correction, but first I’ll examine a key issue—how much will the volatility products move up if the market drops.

 

The Choices

The chart below shows how the volatility ETPs have historically reacted during negative S&P 500 (e.g., SPY) market moves.  The data uses simulations of ETP prices from 2004 until their inceptions and actual data after that.

 

The median value of these ratios stays fairly stable over a wide range of percentage moves.  For example the median percentage moves of 1X short term ETPs like VXX will consistently cluster around negative 2.25 times the percentage moves in the S&P.  A daily -1% move in SPY typically results in a VXX positive move of around 2.25%.

These ratios aren’t guaranteed—they’re statistics.  In fact 20% of the time the volatility products move in the same direction as the S&P 500.  Fortunately, when the market is dropping the distribution of ratios tightens up

The chart below shows the historical distribution of VXX percentage moves compared to SPY moves of  > -0.1% and  > -1%.  SPY moves of less than +-0.1% are excluded because they can generate high ratios that aren’t meaningful.

 

When the S&P makes a 1% or larger negative move the median doesn’t shift much, but the number of results on the positive side drops from 21% of the total down to under 5%.

Since these ratios are relatively stable regardless of the size of the market moves we can view these ratios vs. the various ETPs / indexes.

 

Remember these are one day relative % ratio numbers.  While TVIX & UVXY ratios are close to the VIX’s on this metric, the contango losses in holding these ETPs other than during a market downswing are ruinous.   The 1X short term ETPs (e.g., VXX) aren’t much better.

So far I’ve only discussed the CBOE’s indexes and some of the volatility ETPs.  There are also VIX futures that have various sensitivities to the moves of the S&P 500.  These products differ from the indexes and ETPs in that they have expiration dates like options.



As these futures get closer to expiration their sensitivity increases.  Interestingly, a simple natural log relationship (shown on the chart)  gives a good match to the data.

There are also VIX weekly futures based on the CBOE’s 9 day VXST index, but I’ll discuss those in a different post.

 

The Hedge

Circling back to the trend chart at the beginning of this post—what would be a volatility hedge that would protect you if you bet on a 5th upward bounce?

There’re a lot of moving parts here (e.g., security, strike price, expiration date) and a lot of different strategies.  I’ll pick one general approach, and work through the details if the hedge had been applied during the 30-July-2014 through 8-Aug-2014 period.

My assumptions:

  • $100K invested in the SPY (betting that the market will start climbing again)
  • One percent of the market investment ($1K) invested in a volatility hedge—call options expiring around 16-Aug-2014.  It’s very likely the market will have gone one way or the other by then.
  • Goal of breaking even (losses in SPY & cost of the options offset by profits) if the market drops 3% or more.

I’ll review the results from three different trades—buying calls on UVXY (2x Short term), August VIX calls (based on next to expire VIX futures or M1 futures), and VXX (1X Short term).

The Setup  (30-July-2014) UVXY M1 VIX Futures VXX SPX
The median expected multiplier vs downward SPX % moves 5X (Stdev 10.8) 3X (Stdev 10.5) 2.55X (Stdev 5.4) -1X
For a -3% move in the SPX, the expect move from the earlier analysis 15X 9X 7.65 -3%
Closing value of underlying securities on 30-July-2014 27.16 13.55 29.08 197
Target value of underlying with -3% SPX move 31.23 14.75 31.30 191
Selected option strike prices 31 15 31
Expiration dates for selected options 16-Aug 20-Aug 16-Aug
Closing value of options on 30-July-2014 1.43 0.75 0.83
Number of option purchased for $1K 7 13 16
Approximate value of positions $1000 $1000 $1000 $100K

 

The Results  (8-Aug-2014) UVXY M1 VIX Futures VXX SPX
Actual value of underlying with -3% SPX move 34.74 16 33.21 191
Actual percentage move 28% 18% 14.2% -3%
Actual percentage multiplier 9.33X 6X 4.73X 1X
Difference from predicted multiplier 1.86X 2X 1.85X
Closing value of options on 8-Aug-2014 5.05 1.4 2.57
Intraday highs of options on 8-Aug-2014 7.6 (+50%) 2.4 (+71%) 4.15 (+61%)
Value of positions at close $3535 $1820 $3084 $97K
Initial investment required for break even at close 8-Aug-2014 $1144 $2175 $1328

 

So, in spite of the underlying volatility instruments moving around 2X more than expected, the $1K spent on hedges did not achieve the goal of break even with a 3% decline in the S&P 500—although UVXY was pretty close.  During this period the VIX ramped from 13.33 to 15.77—an increase of 18.3% (the expected move was 15%).  If the correction had continued volatility would have probably increased rapidly (the intraday option prices spiked > 50% on the 8th –when the VIX climbed to 17.09), so the hedges probably would have worked well protecting the S&P 500 position against further declines.

 

One of the challenges of trading is wrestling with strategies that work until they don’t.  With short term volatility hedges you can bet on the market going up—without paying too much for insurance in case you’re wrong.

SPY-trend-break

 



Backtest of VXX Volatility ETN From 2004 Including Yearly Fees

Tuesday, December 30th, 2014 | Vance Harwood
 

Volatility based Exchange Traded Funds and Notes (ETF / ETN) have only been on the market for a few years (see volatility tickers for the full list of USA based funds).  The oldest one, Barclays’ VXX only started trading in late January 2009.   Because of their relative youth we don’t have actual trade data on how they would have performed through critical periods—for example the 2008/2009 crash.  Fortunately the CBOE provides historical data starting in March 2004 for the VIX futures that underlie the VXX, so it’s possible to objectively simulate how it would have performed from that point forward.

Some aspects of the VXX simulation are tricky.  For example some VIX future expiration months did not trade in the 2004 to 2008 time frame so those values need to be interpolated / extrapolated.  The prospectus does not spell out whether closing or settlement values of the futures are used for the index calculations (they use settlement values), and the calculation using the daily rolled and rebalanced futures is not straightforward.  Even the final step, figuring out the daily fees is not a trivial exercise.

The chart below shows the reverse split adjusted results (as of Dec 2013).

VXX-sim



Clearly VXX would have performed horribly over the 2004 to 2013 time frame with a brief respite in 2008/2009.  If you had invested $1000 in VXX in March 2004 you would now have $1.80 left of your initial investment—a 99.8% decline.   The long volatility funds have a structural tendency to decline because they hold VIX futures that are historically in contango 70% to 80% of the time, for more on this process see How Does VXX Work? and The Cost of Contango.

If you are interested in purchasing the results of the VXX  simulation back to March 2004  I have made a spreadsheet available for purchase (see bottom of post) that includes the simulated close values with the annual fee (0.89%).  The maximum deviation in my results from the Barclays’ published closing indicative values since the product started trading is less than +-0.04%.

Seperately I have done a simulation of VXX open / high / low values over that same period.   Those results are inherently less accurate, but still should be useful for testing strategies that are sensitive to intraday values.  For more information see this post.  That spreadsheet is also available for purchase at the bottom of this post.

The chart below shows VXX’s performance (in black) relative to a few other volatility based Exchange Traded Products.

VXX-log-bt



Among the long funds, the 2X leveraged short term TVIX from VelocityShares fares even worse than VXX, declining 99.99999%.  Barclays’ medium term VXZ only declines 78%.  The daily inverse funds do better with VelocityShares’ medium term ZIV going up 43% and its short term XIV going up 13 fold—however not without some serious dips along the way.

Earlier in this post I mentioned that computing VXX’s fee was surprisingly difficult.   The appropriate equation is not present in any ETP prospectus I have seen—instead you are treated to prose that would make an IRS agent proud.

Exchange Traded Products typically state their fees on an annual basis (e.g., 0.89%), but in practice they deduct a fee each day from the assets under management.   In computing the fees it’s tempting to start with the daily value of the underlying index (SPVXSTR in the case of VXX) but the actual calculation starts with the final indicative value of the ETP from the previous trading day.  It multiplies the previous value by the index gain at close for the current day (one if it is a non-trading day) and then applies the fee.  The applicable formula is:

AnnualFeeCalc



While it’s interesting to simulate how a security would have behaved in the past it’s only one of many possible outcomes.  If VXX had existed in 2004, it’s likely the VIX futures that underlie it would have been affected—at least in small ways.   Looking forward the uncertainties multiply—there’s no guarantee that VIX futures will behave the same way through upcoming corrections and market crashes and with the open interest on VIX futures growing 40% a year we can anticipate that someday they, and indirectly VXX will be influencing the behavior of the S&P 500 itself.

 

For more information on the VXX simulation spreadsheet see this readme.

If you purchase the spreadsheet  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 this link to reach the page where can download the spreadsheet.  Please email me at vh2solutions@gmail.com if you have problems, questions, or requests.



Backtests for Popular Long & Short Volatility Exchange Traded Products

Tuesday, January 20th, 2015 | Vance Harwood
 

I have generated the end of day trading day values for the most  popular long and short volatility Exchange Traded Products (ETPs) for March 26th, 2004 through December 12th, 2014

  • TVIX    VelocityShares Daily 2x VIX Short-Term ETN
  • UVXY  ProShares Ultra VIX Short-Term Futures ETF
  • VXX     Barclays S&P 500 VIX Short-Term Futures ETN
  • VXZ     Barclays S&P 500 VIX Mid-Term Futures ETN
  • XIV     VelocityShares Daily Inverse VIX Short-Term ETN
  • ZIV     VelocityShares Daily Inverse VIX Medium-Term ETN
  • SVXY  ProShares VIX Short-Term Futures ETF
  • VIXY  ProShares  Short VIX Short-Term Futures ETF

These ETP histories are required if you want to backtest various volatility strategies through the quiet times from 2004 to 2007, or the 2008/2009 crash.  The chart below shows the simulated values with a logarithmic vertical axis so that you can see a reasonable amount of information for each fund.

Pop-Vol-ETPs

 

The table below shows how much $1000 invested in each of these funds on March 26th, 2004 would have been worth on October 15th, 2013:
 
Symbol $ Value
TVIX $0.00012
UVXY $0.00014
VXX $2.10
VXZ $217
ZIV $1565
XIV $17865

 

The algorithms for generating these ETPs values are documented in the prospectuses for the various volatility ETNs and ETFs.    Barclays’ VXX/VXZ fund prospectus is a good example.   See Volatility tickers for the current universe of  USA based volatility ETPs and their associated reference indexes.    The futures settlement data required for these calculations is available on this CBOE website—in the form of 100+ separate spreadsheets.  To make the calculation of the indexes underlying the ETPs tractable  I created a master spreadsheet  that integrates the futures settlement data into a single sheet.  See this post for more information about that spreadsheet.

My simulated values very closely track the published indicative values (IV) of the funds except for VelocityShares’ TVIX—which has had severe tracking problems since early 2012.  Barclays provides a full set of IV values for VXX and VXZ—my simulation tracks them within +-0.04% and +-0.025% respectively.   Sampled IV values for the other funds give error terms of  +-0.2% for Proshares UVXY,  and for VelocityShares XIV and ZIV +-0.2% and +- 0.01% respectively.   My TVIX simulation tracks sampled IV values within +2%/-4%.

If you need simulated intraday open, high, low values also checkout this post.

These ETP prices reflect the contribution of 91 day treasury bills on their overall performance.   Thirteen week Treasuries yields averaged 0.05% in 2013,  but in February 2007 they yielded over 5%— things have changed a bit…   The simulated ETP values do  include applicable fees which vary from fund to fund.   The fee calculation is surprisingly difficult.  For more on that see Backtest on VXX Including Annual Fees

I am making these 6 simulation spreadsheets (values only, no formulas)  available for purchase, individually, or as a complete package. The VXX package is also available here.   If you cannot see purchase information immediately below then please click this href=”http://sixfigureinvesting.com/2011/12/historical-volatility-rolling-indexes-2004-2011/”>link to the stand-alone post and look at the bottom of the page.

For more information on the spreadsheets see readme.

If you purchase the spreadsheet  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 this link to reach the page where can download the spreadsheet.  Please email me at vh2solutions@gmail.com if you have problems, questions, or requests.



Next VXX Reverse Split—April 2015?

Wednesday, February 12th, 2014 | Vance Harwood
 

For a security doomed to decrease in value over time Barclays’ VXX does amazingly well.  Its volume averages over 29 million shares per day and its assets under management have stayed above $1.0 billion for the last couple of years.  Not bad for a product that has averaged a 64% annual loss since its inception in January 2009.

It was only 13 months between the last two reverse splits, but that was a strong bull market phase with very little volatility—which is especially bad for volatility products like VXX.  I’m expecting volatility to kick up some in the next year, so I’m estimating it will take 18 months this time around before Barclays’ needs to reverse split this product again.

According to its prospectus Barclays can reverse split VXX any time after it closes below $25 and that reverse splits will always be at a four to one ratio.

Event Dates Reverse Split Ratio Inception / close price right before reverse split (split adjusted)  Months since inception /last split
Inception 30-Jan-2009 100 (6,400)
1st Reverse Split 8-Nov-2010 4:1 13.11 21
2nd Reverse Split 4-Oct-2012 4:1 8.77 23
3rd Reverse Split 8-Nov-2013 4:1 12.84 13
4th Reverse Split April 2015 (est) 4:1 13.00 (estimated) 18 (estimated)



The first and second splits of VXX occurred after about 22 months, but 2012 did not provide a volatility bump like 2010 and 2011, so the 3rd reverse split was only 13 months after the 2nd one.   The chart below, both log and linear scaled, shows VXX’s sordid split adjusted price history.

VXX split adjusted



Given its horrid track record, it’s fair to ask why people keep investing in VXX.  I had assumed it was mostly retail investors, but a recent quarterly Nasdaq report indicates otherwise:

VXX-holdings

 

Over fifty percent of VXX’s ownership (as of 30-Sept-13) was institutional.   Barclays is number one on the list, with  5 million shares outstanding.  They of all people should know this ETN is a dog.

A closer look at the institutions and activity on this list (e.g., Goldman Sachs, Susquehanna, UBS, Deutsche Bank), suggests that most of these holdings are transient, related to the activities of Exchange Traded Product (ETP) issuers, market makers, and Authorized Participants (AP).  These are the people that facilitate / use arbitrage to keep ETP prices close to their index values—and make money in the process.  For more on this see this very good IndexUniverse article.

I suspect retail investors on the other hand are trying to hedge their equity holdings with VXX because it is one of the few securities that reliably goes up when the market is panicking.  Unfortunately this strategy rarely works well.  Unless your timing is very good  owning enough VXX to effectively hedge your portfolio is prohibitively expensive.

For more see: