How Does VXX’s Daily Roll Work?

Monday, January 19th, 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:

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Near Real Time Graphical VIX Term Structure

Friday, January 16th, 2015 | Vance Harwood

Anyone that follows volatility closely knows that short term views on volatility are much more dynamic than longer term. For example, if the market is moving from a dip into a “V” style recovery the CBOE’s 9 day expectation of volatility VXST, will drop much more than the 30 day VIX.

A chart showing volatility expectations vs time is called a volatility term structure.  The updating chart below uses indexes published by the CBOE to provide up to 6 different points on the current VIX term structure.  The green dots show the numbers published by the CBOE.

 

The black vertical bar shows the level of the older style VIX calculation (VIXMO) and the top of the purple outline around it shows the VIX value.

All VIX style volatility calculations are annualized—they indicate how much the market would be expected to vary in a year if the volatility stayed at that level.  So for example if the volatility number is 15 then the model predicts that the market will stay between +-15% of the current value in the next year with a 68% probability.

The annualization process assumes that volatility drops off with the square root of time. This is a good assumption, however there is a question of what sort of time should you use.  For example the CBOE uses calendar time but I think there is a good case for using the actual amount that the market will be open instead—not counting evenings, weekends and holidays.  The triangles shown on the graph show the CBOE index values annualized with market time instead of calendar time.   Although the two calculations often agree sometimes there are significant deviations.

 

Additional Resources:

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One Reason Why the New VIX Calculation is Better

Monday, January 12th, 2015 | Vance Harwood

The CBOE changed the way the VIX® was calculated on October 6th, 2014—asserting the change would provide a more accurate assessment of expected volatility.  The new process does look better to me, but I’ve been surprised that the new VIX and the old VIX (listed as VIXMO) sometimes differ by as much as plus/minus 10 percent.

Disagreements between the two indexes are not due to only one factor, but clearly one improvement was to eliminate the week of the month where the VIX was calculated using extrapolation.

The VIX provides a 30 day estimate of volatility, but the S&P 500 options (SPX) used in the VIX calculation have fixed expiration dates.  The CBOE transforms the options’ data into the VIX by using volatility specific interpolation / extrapolation.  For example, if you have a volatility number for options that expire in 10 days and another for options that expire in 38 days you can reasonably assume that the VIX level should be between those two numbers.

One requirement with the old VIX calculation was that it couldn’t use options with less than 7 days to expire.  When the 7 day restriction was reached the calculation switched to using options that had more than 30 and 58 days until expiration.  The chart below shows the calculation right after that switch on January 12th, 2015.

VIX-Calc-12Jan15-extrapolation



The blue and red bars are the volatility numbers (VINMO & VIFMO) from the S&P options and the green bar is the VIX calculation extrapolated from those two numbers.  For details on that process see: Calculating the VIX Index—the Easy part

Normally this extrapolation was reasonable, but if the market is nervous the shorter term volatility values climb.  January 12th, 2015 was a case in point—notice how the light blue VXST bar (9 day volatility) is higher than the VIX estimate.

The next chart shows the new and old VIX calculations together.  The black dotted line shows the interpolation used for the new VIX calculation; the blue dotted line shows the old VIX extrapolation. The black vertical bar shows the VIX estimate.

VIX cacl-graph



Clearly the two calculations have a major difference of opinion —the new calculation’s result is 7.5% higher (19.60 vs. 18.15).

The CBOE’s new calculation always uses options that expire within a week of the VIX’s 30 days.  The red and orange triangles show their values on January 12th.

The old VIX calculation misses the fact that the shorter term volatility has ramped up.

The CBOE provides VIX style calculations on six different sets of options used in their VIX, VIXMO, and VXST calculations.  These calculations don’t need time extrapolations / interpolations so that source of potential errors is eliminated.   The chart below shows how they mapped out on January 12th, 2015 (click image to enlarge).

vix term c+m



The green dots on the top line represent the CBOE VIX style volatilities over time.  The vertical black bar shows the old VIX calculation and the purple outline above it shows the new VIX calculation.

In this case the new VIX calculation is more accurate, cleanly mapping into the overall volatility term structure.

 

Additional Resources:



Prediction: Dec 31, 2015 S&P 500 close at 2346 up 13.9%

Thursday, January 1st, 2015 | Vance Harwood

My 2015 year end prediction is based on the trend channel shown below, which has been in place since around May 2012.

SPX-trading-channel



There’s nothing magical about this channel. The market will transition from it at some point, and I think it’s important to plan for that, but for the moment the channel is the trend.

This sort of trend channel has characterized the last three bull markets.

SPX channels 1995



The blue line in the chart is the 250 day simple moving average.

I suspect these patterns originate from random market moves—which often look like trend channels— interacting with human / computerized pattern matchers that transform random patterns into a self-fulfilling prophecies.  When the market starts approaching the top of the channel followers start selling, and they buy when the low channel is breached—reinforcing the pattern.

Anyone using that approach would have done very well the last two years.

As bull markets move into the territory of bubbles and nose-bleed valuations the risk of the trend ending increases, but predicting the end is notoriously difficult.  You can be years early in calling the top.  In Jack Schwinger’s excellent book “Hedge Fund Market Wizards”, he comments, “Predicting the top of a bubble is like trying to predict the weather a year out.”  In the book hedge fund manager Colm O’Shea agrees, but adds, “But you can notice when things have changed.”

Colm relates how in 2006 and 2007, “I was thinking the markets were in a completely unsustainable bubble.”, but rather than try to pick the top his firm stayed long.  “We were quite happy to be part of the bubble.”  However they did limit their risk by doing trades with limited downside (e.g., buying options rather than the securities themselves), and they waited for things to change.  When they did notice a big change (LIBOR rates spiking in August 2007) they moved to bearish positions.

In the chart above, the last two bull markets signaled they were really over when the index was below the channel and below the 250 day moving average for more than a couple days.  I will certainly be watching those metrics during 2015.

I will also be matching the health of the overall US economy, because fundamentally the market relates to the economy.  The next recession and the next bear market will be linked together.  Some of the factors I will be watching:

Interest rates

  • The Fed has signaled that it may start raising interest rates in 2015. While the market might falter when this happens, I think the biggest issue will be the inflation rate behavior compared to the Fed’s 2% target.  Some feel that the Fed’s actions in expanding the money supply created a powder keg that will explode once inflation starts rising.   Others worry that increasing rates will undermine the recovery, risking sliding back into deflation and recession.   I favor the latter because the Monetarists who think only the money supply matters regarding inflation have been completely wrong the last 5 years.

Oil prices

  • The dramatic drop in oil prices has something for everyone. Commuters and airlines loving it, drilling equipment manufacturers hating it, oil tanker business loving it, holders of junk grade debt from energy companies hating it, and so on.   Overall I think these impacts will mostly cancel out and since the energy segment of the economy was overheated I think some scaling back will be healthy.

Wage Growth

  • The majority of USA workers have seen their wages barely increase over the last decade while corporate profits have increased dramatically. Unless power shifts back to labor, unlikely I think, we won’t see general wages increases much over the rate of inflation.

Stock Buybacks

  • In the last four quarters S&P 500 companies spent $567 billion buying back their own shares—a year to year increase of 27%. While it pains me that companies apparently don’t think that they can find a better place to invest this money, I understand that preventing share dilution from stock options / restricted stock issuance makes sense (although most of these shares go to already highly compensated employees).  What I abhor is companies (like IBM) going into debt to finance stock buybacks in an attempt to hide a deteriorating business.  This behavior has bubble possibilities because the next recession will knock out these companies and those that hold this toxic debt.

Geopolitical

  • The European austerity policies, rather than solving problems have extended its recession and exacerbated unemployment. The Eurozone poses no danger of overheating the global economy.   As the US economy grows the dollar will continue to climb—providing a natural braking mechanism as imports get cheaper and exports relatively more expensive to trading partners.

In the year or two before the tech crash of 2000 and the financial crisis of 2008 the market felt overheated to me.  Before those crashes there was an outrageously overvalued tech sector, and a vastly overheated home building / mortgage industry respectively.  So far I don’t see the next bubble forming.   Yes, trillion dollar student loan debt is worrisome, but I don’t see it crashing the economy.  Yes, oil prices dropping 50%+ will put the pinch on oil business, but again I don’t see the domino effect that goes with the collapse of a bubble.  To destroy the momentum of a growing economy requires a collapse on multiple fronts—no single facet has enough impact.

So, for the short term—at least for a week or two—the trend channel is safe.

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Volatility Related Indexes and Tickers

Sunday, December 7th, 2014 | Vance Harwood

Unless you have access to a Bloomberg terminal or something similar finding quotes and historical data for volatility indexes can be an adventure.  Below I’ve assembled links to the online resources that I’ve been able to find.  Links marked with a “$SFI” are historical data sets that I offer for sale—they don’t match the official indexes exactly, but they are very close.

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

If you are looking for symbols/tickers for volatility exchange traded products then you should go to this post where I list information on all 23 USA traded volatility style funds.  Simulated histories for some of these funds back to 2004 are available here.

Historical data from different sources can differ—often because they use different closing times.  Sites like Yahoo and Google Finance use standard NYSE hours, but the CBOE’s hours are different (close is 4:15 ET) and open times vary.  For example with the advent of near 24 hour trading on VIX futures the open time for VIX futures for Tuesday through Friday is 4:30PM the previous day and Sunday at 5PM is the opening time for Monday.  When used for computing other indexes (e.g., when VIX is used in computing the index used by VQT), the CBOE data should be used.

If you have an account with Fidelity’s Active Trader Pro  you can get historical intra-day data for many volatility tickers by exporting data from their charts.  Schwab’s StreetSmart Edge allows export of watch list information, including option Greeks.

 

Standard long volatility indexes

Index Quotes/Charts Used by:(not exhaustive) Historical Data Resources Description
SPVXSTR ?? VXX Barcays3 (since Jan 09)
$SFI (Mar 04-Feb12)
Methodology Short Term Volatility Total Returns1
SPVXSP /SPVXSPID MarketWatch
FT.com
(includes OHLC)
Yahoo
Quicken
XIV
TVIX
VIXY
SVYX
UVYX
FT.com
Market Watch
$SFI (Mar 04-Feb12)
Methodology Short Term Volatility Excess Returns2
SPVXMTR ?? VXZ Barclays3 (since Jan 09)
$SFI (since Mar 04)
Methodology Mid Term Volatility Total Returns1
SPVXMP MarketWatch
FT.com
Yahoo
ZIV
VIXM
FT.com
MarketWatch
(single dates)
$SFI (since Mar 04)
Methodology Mid Term Volatility Excess Returns2

Notes

  1. The term “Total Returns” (TR) denotes that dividends/interest is included in the index. For example for SPTR it would be the dividends from the underlying 500 stocks in the S&P 500. In the case of SPVXSTR it would be interest from 13 week treasury bills.
  2. “Excess Returns” (ER) in this context indicates that the calculation does not include dividends or interest.
  3. Barclays data includes some non-USA trading days, the values are carried over from the previous trading day

Related Posts

 

Hedged style volatility fund indexes 

Index Quotes/Charts Used by Historical Data Resources Description
SPVQDTR/ SPVQDTID BigCharts
FT.com
VQT
PHDG
FT.com
$SFI (since Mar 04)
Barclays (VQT IV only)
Methodology S&P 500® Dynamic VEQTOR Index TR
SPVQDER BigCharts
FT.com
Used within VQT/PHDG calculations FT.com Methodology S&P 500® Dynamic VEQTOR Index ER
SPVQSER Yahoo Finance
FT.com
VQTS FT.com Methodology S&P 500® VEQTOR Switch Index ER
SPVXVSP Google Finance
FT.com
SPXH FT.com Methodology
33% 2X ST
66% -1X ST
White Paper
VelocityShares
Prospectus
Volatility Hedged Large Cap Index
SPVXTRSP Google Finance
FT.com
TRSK FT.com Methodology
45% 2X ST
55% -1X ST
White Paper
VelocityShares
Prospectus
Tail Risk Hedged Large Cap Index
SPDVIXTR ?? XVZ Barclays3
$SFI (since Mar 04)
Methodology S&P 500 Dynamic VIXFutures Index
VXTH CBOE VIXH Methodology
White Paper
CBOE VIX Tail Hedge Index

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VIX style Indexes and Settlement quotes 

Index Quotes/Charts Used by Historical Data Resources Description
VXSTSM Yahoo ^VXST
Google Finance
INDEXCBOE:VXST
VXST options & futures CBOE (since Jan-2011)
Ft.com
White Paper Measure of 9 day IV of (SPX) Index options.
VIX® Yahoo ^VIX
Google INDEXCBOE:VIX
VIX options & futures VQT
PHDG
XVZ
CBOE (since Jan1990) White Paper
Near real time calc graph
Measure of 30 day IV of (SPX) Index options
VIXMO Google Finance
indexcboe: VIXMO
FT.com
Google
Calc the VIXMO—the easy Part VIX index previous to Oct 6, 2014
Measure of 30 day IV of (SPX) Index options using SPX monthly options
VXV Yahoo ^VXV XVZ CBOE (since Dec 2007)
Yahoo
Measure of 3-month IV of (SPX) Index options.
VXMTSM Google Finance
indexcboe:VXMT
CBOE (since Jan 2008)
Google
FT.com
Measure of 6-month IV of (SPX) Index options.
SVRO Yahoo ^SVRO VXST options & futures CBOE Settlement process Exercise-settlement value for VXST options & futures
VRO Yahoo ^VRO VIX options /&futures CBOE Settlement process Exercise-settlement value for VIX options  & futures
VVIXSM Yahoo ^VVIX CBOE (since March 06)
FT.com
White Paper VIX methodology applied to VIX options (VIX of VIX)

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VIX Style Calculation Indexes  (used by CBOE to compute VXST, VIX, VIXMO, VXV, VXMT)

Index Quotes/Charts Used by Historical Data Resources Description
VSTN Google VXST Google White Paper CBOE Near-term VXST Index
VSTF Google VXST Google White Paper CBOE Far-term VXST Index
VIN Google4 VIX Google4 White Paper CBOE Near-term VIX Index
VIF Google4 VIX Google4 White Paper CBOE Far-term VIX Index
VINMO Google VIXMO Google CBOE Near-term VIX monthly only
VIFMO Google VIXMO Google CBOE Far-term VIX monthly only
VIX(#)  CBOE VIX CBOE (since 2010) CBOE per month VIX calculations

Notes

  1. The CBOE changed its VIX calculation on 21-Oct-14 to use weekly options bracketing the 30 day VIX target expectation. Before that the VIN/VIF values reflect the old calculation that only used monthly SPX option series.

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Support Indexes

Index Quotes/Charts Used by Historical Data Resources Description
13Wk T Bills ?? VXXVXZ US Treas
SFI
Conversion 13wk US Treasury bills
Libor FRED VQTPHDG FRED
SPX  Yahoo (^GSPC) Yahoo SPX total returns (dividends applied but not re-invested)
SPTR ?? VQTPHDG CBOE(since 1988)
Eoddate (reg required)
SPX total returns with dividends reinvested

 

 

VIX Futures

Ticker Quotes/Charts Used by Historical Data Resources Description
VXST CBOE (e.g, 2VSW/Z4)  select VSW on Futures VXST options CBOE VSW VXST Futures, Options, Index Futures on VXST index
VIX CBOE (e.g. vix/z4, VX series)
Google (e.g.  indexcboe:VIXJan)
BarChart.com
VIX optionsVolatility Funds CBOE
Google
Month Codes
Expiration Calendars
Futures on VIX index

Related posts

 

 

Some other interesting indexes currently not used by volatility funds

Index Quotes/Charts Ratio Historical Data Resources Description
SPVXTRMP / SPVXTRMT Google Finance 60% 2X MT long, 40% -1X ST short FT.com Methodology
ETF.com article
S&P 500  VIX futures Tail Risk ER Mid-Term
SPVXVMP/ SPVXVMT Google Finance 45% 2X MT long, 55% -1X ST short FT.com Methodology
ETF.com article
S&P 500  VIX futures variable long / short mid-term
SPVXVHSP / SPVXVHST Google Finance 10% 2X ST long, 90% -1X ST short FT.com Methodology
ETF.com article
S&P 500  VIX futures volatility hedged Short term
SPVXVHMP / SPVXVHMT Google Finance 30% 2X MT long, 70% -1X ST short FT.com Methodology
ETF.com article
S&P 500  VIX futures Tail Risk Midterm