Graphical VIX & VIXMO calculations

Wednesday, November 12th, 2014 | Vance Harwood
 

The chart below graphically represents the calculation for the VIX® and the legacy VIX (ticker VIXMO) which was used from September 22, 2003 through October 5th, 2014.  My apologies for the small size / non-expandable format, but this was the best near real time (20 minute delayed) solution I could figure out using Google Sheets. The actual VIX is located on the black dotted line in the left center of the graph. Click here for a larger snapshot for 12-Nov-2014. The VIX now uses an interpolation between two VIX style calculations (VIN and VIF) on SPX options series that are a week apart—bracketing the 30 day target horizon of the VIX.  The legacy calculation uses SPX monthly options (now published as VINMO and VIFMO) which requires significantly longer interpolation/extrapolation periods.

 

Since its inception on October 6th, 2014 the new VIX has often differed significantly from the older calculation, often running 5% or more lower than the legacy number.   This is disconcerting and I initially wondered if the reduced volume/open interest of the SPX weekly options used in the new calculation or some other factor was distorting things, but as I look at the data I’m becoming comfortable with the new calculation as a significant improvement in the accuracy of the index.

The dynamically updated chart above uses delayed quotes from Yahoo Finance.  For more information on these VIX calculations see Calculating the VIX and Calculating the VIXMO.

The VXST is the CBOE’s 9 day version of the VIX, and  VXV is the CBOE’s 93 day version.

There are two somewhat parallel markets associated with general USA market volatility: the S&P 500 (SPX) options market and the VIX Futures market.  SPX option prices are used to calculate the CBOE’s family of volatility indexes, with the VIX® being the flagship.  VIX futures are priced directly in expected volatility for contracts expiring up to 9 months out.  The nearest VIX Future synchronizes with the VIX once a month—on its expiration date.

Additional resources:



Calculating the New VIX—The Easy Part

Wednesday, October 22nd, 2014 | Vance Harwood
 

The movements of the CBOE’s VIX® are often confusing.  It usually moves the opposite direction of the S&P 500 but not always.  On Fridays the VIX tends to sag and on Mondays it often climbs because S&P 500 (SPX) option traders are adjusting prices to mitigate value distortions caused by the weekend.

In addition to these market driven eccentricities the actual calculation of the VIX has some quirks too.  The VIX is calculated using SPX options that have a “use by” date.   Every week a series of SPX options expire.  This schedule of expirations forces a weekly shift in the VIX calculation to longer dated options.  For many years the CBOE’s VIX calculations only used monthly SPX options, but starting October 6th, 2014 it switched to using SPX weekly options when appropriate.  See “Why the Switch” section towards the bottom of this post for more information.

The VIX provides a 30 day expectation of volatility, but the volatility estimate from SPX options changes in duration every day.  For example, on October 13, 2014 the SPX options expiring on the 7th of November provide a 25 day estimate of volatility, while the November 14th options provide a 32 day estimate.  In this case to get a 30 day expectation the VIX calculation uses a weighted average of the volatility estimates from these two sets of November options.

The newly updated S&P 500 VIX calculation is documented in this white paper.  It computes a composite volatility of each series of SPX options by combining the prices of a large number of puts and calls.  The CBOE updates these intermediate calculations using the ticker VIN for the nearer month of SPX options and VIF for the further away options.  The “N” in VIN stands for “Near” and the “F” in VIF stands for “Far”.  These indexes are available online under the following tickers:

  • Yahoo Finance as ^VIN, ^VIF
  • Schwab $VIN, $VIF; historical data available
  • Google Finance INDEXCBOE:VIN, INDEXCBOE:VIN; historical data available
  • Fidelity:  .VIN, .VIF;  limited historical data

The final VIX value is determined using the VIN and VIF values in a 30 day weighted average calculation.  Graphically this calculation looks like the chart below most of the time:

VIX-calc-typ

 

As shown above the VIX value for October 13th is determined by averaging between the November 7th SPX options (VIN) and the November 14th SPX options (VIF) to give the projected 30 day value.  If you look closely you can see that the interpolation algorithm used between VIN and VIF does not give a straight line result; I provide calculation details later in “The Weighted Average Calculation” section

The chart below shows the special case when the VIX is very close, or identical to the VIF value.

VIX-calc-Wed

 

Wednesdays are important days for the VIX calculation:

  • The VIX calculation is dominated by the VIF values.
  • The SPX options used switch such that the old VIF becomes VIN and the options with 36 days to expiration become VIF.
  • Once a month on a Wednesday VIX futures and options expire (expiration calendar).  Soon after market open a special opening quotation of VIX called SOQ is generated.  Its ticker is VRO and it’s used as the settlement value for the futures and options.  Unlike the VIX’s normal calculation, the SOQ uses actual trade values of the underlying SPX options not the mid-price between the bid and ask.  Only one series of options, the ones with exactly 30 days to expiration are used.

Although SPX weekly options are available for 5 weeks in the future, the VIX calculation uses the SPX monthly options (expiring the 3rd Friday of the month) instead of the weeklies when they fit into the 24 to 36 day window used by the calculation.   The SPX weeklies expire at market close on Friday but the monthly options expire at market open on Friday.  By using these monthly options the CBOE keeps the VIX futures / options settlement process identical with the previous month based VIX calculation.

Why the Switch?

The chart below illustrates how the CBOE changed the VIX calculation methodology.

VIX-new-VS-old



This particular snapshot  shows the old VIX calculation (ticker: VIXMO) doing an extrapolation using SPX monthly options expiring November 22nd and December 20th (11 and 39 days away from the 30 day target)—a hefty distance.  If you would like more details about the old VIX calculation see “Computing the VIXMO—the easy part“.  The new VIX calculation on the other hand always does an interpolation over a much shorter period of timenever using options with expirations more than +-7 days from the 30 day target.  This CBOE article gives a good overview of the advantages of the new approach.

If you look closely at the chart, you can see that in this case the VIX calculation using the two methods arrives at slightly different answers (black line).  The new method gives a result of 21.16, 1.5% higher than the old method’s 20.85.  While I’m confident that the new calculation will be better in the long run because of the tighter VIN / VIF brackets I do have some concerns about the current volumes and low open interest in the SPX weekly options that are 4 to 5 weeks out.   I have seen the VIX / VIXMO differ by up to 5%—so for the time being I’m keeping both indexes on my watch lists. 

The Weighted Average Calculation

If you want to compute the VIX yourself using the VIN and VIF values you can’t just do a linear interpolation / extrapolation because volatility does not vary linearly with time.  Instead you have to convert the volatility into variance, which does scale linearly with time, do the averaging, and then convert back to volatility.  The equation below accomplishes this process.

VIX-VIN-VIF-eq



How Does the CBOE’s VIX® Index Work?

Saturday, November 1st, 2014 | Vance Harwood
 

The CBOE did not create the VIX as an academic exercise, or as a service to stock market prognosticators everywhere.  They created it because they wanted to make money on volatility.  It took them two tries, but the CBOE succeeded in developing a volatility index that forms the backbone of a host of volatility products.  The CBOE offers some of these products, but other companies have built on the success of VIX to offer their own volatility based products.

To have a good understanding of how the VIX works you need to know how its value is established, what it tracks, what it predicts, and how the CBOE makes money with it.

How is VIX’s value established?

  • The VIX is a computed index, but unlike indexes such as the Dow Jones Industrial Average or the S&P 500 it’s not computed based on stock prices.  Instead it’s based on option prices.  Specifically the prices of options on the S&P 500 index (ticker SPX).
  • One component in the price of SPX options is an estimate of how volatile the S&P 500 will be between now and the option’s expiration date.  This estimate is not directly stated, but is implied in how much buyers are willing to pay.  If the market has been gyrating like mad option premiums will be high whereas in a quiet market they will be much cheaper.
  • There are various ways of extracting the volatility information from option prices.  The standard way is via the Black & Scholes model, but those equations assume that volatility will be the same for all available options—something that is definitely not the case and they also underestimate the risk of a market crash.
  • The CBOE’s approach combines the prices of many different SPX options (hundreds) to come up with an aggregate value of volatility. Their approach has some particular advantages—more on this later.
  • There are many good posts here, here, and here on the details of the actual VIX calculation, so I won’t reinvent the wheel.
  • The VIX is an estimate of volatility for the next 30 days, but by convention volatility measures in the stock market are reported in terms of annualized volatility.  Volatility doesn’t increase linearly with time, so the annualized number is not 12 times the 30 day estimate but rather ~3.5 times the monthly number. For example if the intermediate VIX calculation computes the expected 30 day volatility to be +-4.3%, the reported VIX will be 15%.  For more on this see Volatility and the Square Root of Time
  • There’s nothing magical about the 30 day estimate.  The CBOE uses the same methodology to compute 9 day (VXST), 93 day (VXV), and 180 day (VXMT) volatility indexes.

 

What does VIX track?

  • The moves of the VIX track prices on the SPX options market, not the general stock market—this is a key point.  The SPX options market is big, with a notional value greater than $100 billion, and is dominated by institutional investors. A single SPX put or call option has the leverage of around $200K in stock value—too big for most retail investors.
  • Generally options premiums move inversely to the market.  In a rising market, stock prices tend to be less volatile and option premiums low—hence a lower VIX.  Declining markets are volatile (the old saying is that the market takes the stairs up and the elevator down) and option premiums increase.  Much of this increase occurs when worried investors pay a large premium on puts to protect their positions.
  • While S&P 500 option premiums generally move opposite to the S&P 500 itself they sometimes go their own way.  For example, if the market has been on a long bull run without a pullback institutional investors will become increasingly concerned that a correction is overdue and start biding up the price of puts—leading to a rising VIX in spite of a rising S&P.   Historically 20% of the time the VIX moves in the same direction as the S&P 500—so please don’t claim the VIX is “broken” when you see the two markets move in tandem.
  • The daily percentage moves of the VIX tend to be around 4 times the percentage moves of the S&P 500, but unlike the stock market the VIX stays within a fairly limited range.  The all-time intraday high is 89.53 (24-Oct-2008) and the all-time intraday low is 9.39 (15-Dec-2006) with the current methodology.  Within this 10 to 1 range option premiums run from incredibly expensive to dirt cheap.  It’s unlikely that the VIX will go much below 9 because option market makers won’t receive enough premium to make it worth their while.  At the high end things go could go higher (if the VIX had been available in the October 1987 crash it would have peaked around 120), but at some point investors refuse to pay the premium and switch to alternatives (e.g., just selling their positions if they can).  The chart below shows the historical distribution of VIX values since 2002.

    VIX-histo

    Data Source: CBOE

 

  • Another way to look at the moves of the VIX is to recognize that it’s almost always a few percentage points higher than the recent historical volatility of the S&P 500.  In general it’s a good assumption that the future volatility of the market will be the same as recent volatility—but obviously this relationship doesn’t always hold.   Option market makers demand a premium to justify the risk they assume in buying / selling options in the face of this uncertainty—and this premium shows up as a VIX value greater than historical volatility.

How does VIX trade?

  • So far, no one has figured out a way to directly buy or sell the VIX index.  The CBOE offers VIX options, but they are based on the CBOE’s VIX Futures not the VIX index itself.  VIX futures usually trade at a significant premium to the VIX.  The only time they reliably come close to the VIX is at expiration, but even then they can settle up to +-5% different from the VIX level at the time.
  • There are 22 volatility Exchange Traded Products (ETPs) that allow you to go long, short, or shades in-between on volatility (see here for the complete list), but none of them do a good job of matching the VIX over any span of time.   For more on ways to trade volatility see  How to Go Long on the VIX, and How to Go Short on the VIX.

What does the VIX predict?

  • In my opinion nothing.  I think it does a good job of reflecting the current emotional state of the overall market (e.g., fearful, optimistic), but I don’t think the SPX options market is any better at forecasting the future than any other market or index.  We don’t take the value of the Dow Jones Industrial Average as a predictor of the future, so why should the value of the VIX be any different?

How does the CBOE make money on the VIX?

  • The “O” in CBOE stands for options.  In the early 90’s the CBOE wanted to sell options on volatility, but there was a problem—options need to be based on an underlying tradable security to function, and there wasn’t one.   To address that gap the CBOE created an index that could form the basis of a volatility futures market.  Once that market was functioning then options could be introduced.
  • Version one  of the VIX index (now named VXO) was introduced in 1992, but futures based on it were never available.   For a futures market to function the market makers need to be able to cost effectively hedge their positions.  Hedging the 1992 version of the VIX required frequent rebalancing of SPX options that was too expensive to implement.
  • Undeterred the CBOE introduced version 2 in 2003.  The new methodology allowed market makers to hedge their positions with a static portfolio of SPX options that could be held until the VIX futures expired.  VIX Futures started trading in 2004 and in 2006 options on VIX futures were rolled out.
  • VIX futures and options have been very successful with recent daily volumes in the hundreds of thousands. The CBOE is generating hundreds of millions of dollars in annual revenues from these products—primarily from highly profitable transaction fees.

The VIX frustrates a lot of investors.  It’s complicated, you can’t directly trade it, and it’s not useful for predicting future moves of the market.  In spite of that, the investment community has adopted it, both as a useful second opinion on the markets, and as the backbone  for a growing suite of volatility based products.

But what impresses me is the vision and persistence of the people at the CBOE in advancing the highly theoretical concept of stock market volatility from an academic exercise to an effective commercial product.  It was a multi-decade  project and they were successful.


For more information:



Top 11 Questions About the CBOE’s VIX

Wednesday, July 16th, 2014 | Vance Harwood
 

Based on searches that lead people to Six Figure Investing, these are the top 10 questions people ask about volatility investing:

  1. How can I buy/trade/invest in the CBOE’s VIX® index?   The short answer is that you can’t.  No one has figured out how to do this economically.

    However, there are quite a few investment approaches that allow you to trade in volatility, including futures, options on futures, various Exchange Trade Products (ETPs), and options on ETPs.

    • VIX Futures.  The CBOE Futures Exchange offers VIX futures with expirations up to 9 months out.   Most of the time they trade at a significant premium to the current VIX value—the only firm exception is when a contract expires.   Even at expiration the VIX and the VIX futures can differ by a couple of percent.  For more on VIX futures see VIX Futures—Crystal Ball or Insurance Policy?
    • VIX options.  These are options on VIX Futures not the VIX index itself.  They are tied to specific futures months (e.g., November options are tied to November futures).  They are European exercise and expire on different days than regular stock/ETP options.  For more see Things You Should Know About VIX options.
    • VIX related ETPs (Exchange Traded Funds / Exchange Traded Notes).   All of these funds invest in VIX futures in some way or another in order to give the investor exposure to volatility.  They offer long funds, short funds, long/short, option hedged fund, and combinations with various equities.   For the complete list of USA volatility funds, associated websites, and volatility timeframes see Volatility Tickers.
    • VIX related options on ETPs.   Only 6 of the current 22 volatility funds have options available (VXX, VIXY, UVXY, SVXY, VXZ, VIXM).  For more on ETP volatility options see VXX Options.
  2. How can I go long on the VIX?  For going long on VIX using Exchange Traded Products see this post

  3. How can I go short on the VIX? For going short on VIX using Exchange Traded Products see How to Short The VIX,  for specific information on shorting VXX see How to Short VXX.  

  4. How does the VIX index work? For an equation free explaination of how the index works see How does the CBOE’s VIX index work 

  5. What is the best ETF / ETP for tracking the VIX?  All of them are pretty horrible at tracking the VIX index.  UVXY and CVOL are the least bad.  For more see Tracking the VIX Index.

  6. Why is the VIX moving with the S&P 500, instead of against it today?  Normally the moves of the VIX are negatively correlated to the general market, but around 20% of the time it moves in the same direction.

    The VIX index is based on the prices of options on the S&P 500 index (SPX), and sometimes the actions of those SPX option buyers/sellers are contrary to the general market mood.  For example if a big event (e.g., Fed announcement) occurred that reassured the investment community then option premiums might drop dramatically— even if the market was somewhat down for the day.  For more see How Much Should We Expect VIX to Move?

  7. Why are VIX Futures not tracking the VIX today? The VIX futures market is independent from the S&P 500 options market.   Sometimes these two markets have different opinions about what is going to happen.  Generally the prices of the VIX futures tend to trade at a 3% to 9% premium over the equivalent VIX value computed from SPX option prices.   For more see VIX Futures—Crystal Ball or Insurance Policy?

  8. Why are VXX, TVIX, and UVXY not tracking the VIX today?  VXX invests in the two nearest months of VIX futures, so it tracks the movements of the VIX futures not the VIX itself.  The same goes for TVIX and UVXY except they are 2x leveraged versions using  the same VIX futures.

    For other, more nuanced reasons why there are apparent discrepancies in the volatility ETPs see If you think your ETF is broken.  

  9. Why do VXX, TVIX, always go down?  They don’t go down all of the time— just 70% to 80% of the time.   Their appalling erosion is due to the typical price structure of the VIX futures, where  the prices you pay for the further out contracts are significantly higher than the short term futures.   Because of this the value of the futures that these funds hold  typically decline over time, much like option premiums decline.   Of course, if  volatility really spikes these funds will respond, but their moves will be muted compared to the VIX itself.  For more see The Cost of Contango—It’s Not the Daily Roll. 

  10. When do VIX options and Futures expire?    VIX options and VIX futures expire on the same day, the Wednesday immediately before or after the Friday expiration of regular options.   See here for a yearly calendar of VIX expirations.

    The CBOE selected this unusual date because it wanted the expiration for VIX futures to be exactly 30 days before the expiration of the next month’s SPX options.   Since SPX options expire on the 3rd Friday of the month—which can be as early as the 15th or as late as the 21st, the VIX future’s date has to jump around to satisfy the 30 day requirement.   For more see Calculating the VIX  and VIX Timescape

  11. How low can the VIX go?    The record low close for the index was 9.31 on December 22nd, 1993.   It rarely drops below 10.   The most recent close below 10 was 9.89 on January 24th, 2007.

     

VIX-histo-a More questions?  Checkout the 40 volatility related posts I’ve indexed on the right side of  this page.


Graphical Representation of CBOE’s VIXMO Calculation

Wednesday, November 12th, 2014 | Vance Harwood
 


 

The dynamically updated chart above uses delayed quotes from Yahoo Finance.  It details the interpolation / extrapolation process that computes the 30 day VIXMO from two close-in months of SPX options (VINMO and VIFMO).  This calculation is the legacy version of the VIX that was used from 23-Sept-2003 through 5-Oct-2014.  On October 6th, 2014 the CBOE modified the calculation to start using SPX weekly options when appropriate—reducing the amount of interpolation / extrapolation required. For more information on that process see Calculating the VIXMO—the Easy Part.  VXST is the CBOE’s 9 day version of the VIX, and  VXV is the CBOE’s 93 day version.

On 1-Oct-2013 the CBOE started providing the VXST index, which gives a 9 day estimate of volatility.  It uses the standard VIX methodology, but uses soon-to-expire SPX options (SPXPM, and SPX).   In the chart / data above I show the 20 minute delayed VXST.

There are two somewhat parallel markets associated with general USA market volatility: the S&P 500 (SPX) options market and the VIX Futures market.  SPX option prices are used to calculate the CBOE’s family of volatility indexes, with the VIX® being the flagship.  VIX futures are priced directly in expected volatility for contracts expiring up to 9 months out.  The nearest VIX Future synchronizes with the VIX once a month—on its expiration date.

Additional resources: