VXST Futures—Not a Bad Proxy for the VIX index

Wednesday, September 17th, 2014 | Vance Harwood

The CBOE”s VXST futures have been trading for over six months now—enough time get a feel for how they behave. The CBOE provides historical data —on a per future basis (VSW), which requires some work to get it into a consolidated format.   I organized the data by weeks, with the next to expire future prices labeled week 1, the next to expire week 2, and so on.  Typically there are four sets of VXST futures active at any point in time, with a set expiring every week on Wednesday morning.

VXST-data

The “#NA”s occur on week 4 futures because the CBOE currently waits a day after expiration day before initiating trading on futures that are 4 weeks out.

The expiration value of a VXST future is tied to a special quote of the VXSTsm index (SVRO), which is linked to actual bid/ask values of SPX options near the market opening on Wednesday mornings.  This process is important because among other things it enables VXST futures market makers to hedge their positions with SPX options

I charted how the futures were tracking the underlying VXST index:

VXSTvsVXST-futures

 

Visually the two look like they’re tracking reasonably well, but from a percentage basis it’s not all that great.

VXST-VXSTfutures-percent

 

There are frequent differences greater than +-10%, and the 20 day moving average error is around 5%.

I also looked at the VXST futures values compared to the VIX® index.

VIXvsVXST-futures

 

These traces are considerably closer to each other, with only 3 occasions having  greater than +-10% error and a 20 day average error of around -1%.    This relationship isn’t too surprising because volatility futures tend to trade at a premium to their indexes, and the longer the time horizon (e.g., 9 days vs 30 days) the higher the futures tend to be priced.

Bottom line, the next to expire VXST futures look like a decent proxy to the non-tradable VIX index.  Unfortunately this is only useful if your timeframe is pretty short (e.g., a week) — otherwise the carry costs of the futures are probably prohibitive.

 

VXST Exchange Traded Products

Currently there are no Exchange Traded Funds (ETF) or Exchanged Traded Notes (ETN) using VXST futures, but that situation could change quickly.   The chart below shows the simulated performance of a very short term volatility fund that uses the same rolling futures strategy that VXX uses—except it uses VXST futures instead of VIX futures.

VSXXvsVXX

 

The simulated very short term fund behaves as you would expect—more volatile than VXX and larger contango losses during the quiet periods.

I then compared the very short term fund to UVXY, a 2X leveraged short term volatility fund.

VSXXvsUVXY

 

Surprisingly similar.   If this behavior continues (likely) there won’t be an advantage for an Exchange Traded Product based on VXST futures versus the existing 2X leveraged UVXY and TVIX funds.  Bummer.

Of course, there is nothing set in concrete that the exact same futures rolling strategy that the existing short term funds use must be used in a very short term fund.  For example, mixes of the first four weeks’ futures could be used, but I suspect that would just end up with performance in-between VXX and UVXY—not something particularly useful.

VXST futures have not been a great success so far, with volumes for the nearest two week contracts combined averaging around 50 contracts per day, and open interest of twice that, but if they continue to show a good short term correspondence to the VIX then I can imagine their popularity will grow.

 



Simulating Volatility ETP Open and Intraday High / Low Values

Tuesday, September 2nd, 2014 | Vance Harwood

Previously I’ve done simulations, based on VIX futures, of volatility Exchange Traded Products (ETPs) back to 2004.  In these simulations I only generated the closing values, but I’ve had requests for open / high / low (O/H/L) values.   Now I’ve extended my backtests to generate ETP opening and intraday highs and lows for many of the short term volatility funds—specifically VXX, VIXY, TVIX, UVXY, XIV, and SVXY.

The volatility ETPs (complete list of USA funds) are all based on two or more sets of VIX futures.  The CBOE provides historical open/high/low/close/settlement values for these futures starting in March 2004.  Since the indicative values (IV) of the volatility ETPs are directly tied to these futures, the futures’ opening values can be used to accurately compute the ETP’s opening values—as long as the VIX futures and ETPs start trading at the same time of day.   This was the case until December 10th, 2010 when the CBOE starting shifting the opening times of VIX futures—more on this later.

The ETP intraday high / low values can also be calculated using the appropriate VIX futures intraday values but one additional assumption must be made—that the futures hit their intraday highs and lows at the same time.   I didn’t expect that assumption to introduce a huge amount of error with the simulated values, but I wanted to verify that by comparing my simulation results to actual data.

To evaluate the magnitude of these errors I used O/H/L indicative value data from Barclays’ VXX short term volatility fund from June 1st, 2012 through July 16th, 2012.   I would have preferred pre-December 2010 data, but I don’t have access to intraday IV data that goes that far back.   A chart showing the relative percentage error is shown below.

VXX-OHL-errors

 

Considering the uncertainties, worst cases errors in the +-3% range seem reasonable.  Sixty five percent of the data points had errors less than 1%.   Six values had errors less than 0.01%, which suggests to me that my methodology is correct.

The next chart shows the differences between the actual trades (not the IV values) and simulated O/H/L values for VXX, starting January 30, 2009.

IVvsOHLactual

 

This chart illustrates a couple of additional difference terms that emerge when comparing the IV values to real trade data.  First of all, there’s no guarantee that a trade will occur coincident with the open or the intraday high / low of the ETP’s IV.   For example, the big -25% dip for the highs occurred on 6-May-2010—the Flash Crash.  It’s not surprising that no one traded at the indicative intraday high of 42.13 (open was at 23.34!).

Other differences come from bid/ask spreads and tracking errors.  The indicative value is computed from real time VIX futures values and updated every 15 seconds, but volatility fund market makers are not obliged to trade at that value.  Unless the fund is heavily traded the spread between the bid and ask price will be at least several cents and if demand is unbalanced on the buy or sell side the offered spread values may be significantly different from the IV value.

This next chart zooms into the +-5% portion of the chart.

5perZoomOHL



The 22 trading day moving averages show the impact of the CBOE’s shift in the open time starting in December 2010—the average difference between the simulated IV values and trade data moves from close to zero to somewhere between +-0.5% and +-1.0%.

I cut off the O/H/L simulation on the 25th of October, 2013 because on the 28th the CBOE changed the Tuesday through Friday opening times to 4:30PM the previous day.  This change was in preparation for the eventual move to nearly 24 hour VIX future trading which began June 2014.   This change meant that the VIX futures were trading many hours before the volatility ETPs began trading—making VIX futures an unreliable proxy for ETP open/high/low levels.   The close time, 4:15PM ET, has remained consistent, so VIX futures can still be used to compute ETP closing values.

I verified with the CBOE that the historic VIX futures data published on its website tracks the shifted opening times and is no longer synchronized with the ETP trading times.    In the case of my simulations, there’s really no harm, because their primary value lies in predicting what the ETP’s O/H/L values would have been from March 29th 2004 until the various volatility funds started trading.    Actual trade O/H/L values exist for short term volatility ETP types (1X, 2X, -1X) prior to the 10-Dec-2010 shift in VIX trading hours.

 

The Spreadsheet

For more information on my ETP O/H/L simulation spreadsheet see this readme.  The spreadsheet includes the formulas that convert from various indexes (e.g., similar to SPVXSTR, etc.) to the IV values, but it does not include the VIX futures values or the index calculation formulas.

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 you can download the spreadsheet.  Please email me at vh2solutions@gmail.com if you have problems, questions, or requests.

 



Hedging the Market with Volatility

Sunday, August 17th, 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

 

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How Does the CBOE’s VIX® Index Work?

Thursday, July 10th, 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.  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 decided to create 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:

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Volatility and the Square Root of Time

Thursday, June 12th, 2014 | Vance Harwood

It’s not obvious (at least to me) that volatility theoretically scales with the square root of time (sqrt[t]).  For example if the market’s daily volatility is 0.5%, then the volatility for two days should be the square root of 2 times the daily volatility (0.5% * 1.414 = 0.707%), or for a 5 day stretch 0.5% * sqrt(5) = 1.118%.

This relationship holds for option prices too.  With the Black and Scholes model if an option due to expire in 30 days has a price of $1, then the 60 day option with the same strike price and implied volatility should be priced at sqrt (60/30) = $1 * 1.4142 = $1.4142  (assuming zero interest rates and no dividends).

Underlying the sqrt[t] relationship of time and volatility is the assumption that stock market returns follow a Gaussian distribution (lognormal to be precise).  This assumption is flawed (Taleb, Derman, and Mandelbrot lecture us on this), but general practice is to assume that the sqrt[t] relationship is close enough.

I decided to test this relationship using actual S&P 500 data.  Using an Excel based Monte-Carlo simulation1 I modeled 700 independent stock markets, each starting with their index at 100 and trading continuously for 252 days (the typical number of USA trading days in a year).  For each day and for each market I randomly picked an S&P 500 return for a day somewhere between Jan 2, 1950 and May 30, 2014 and multiplied that return plus one times the previous day’s market result.  I then made a small correction by subtracting the average daily return for the entire 1950 to 2014 period (0.0286%) to compensate for the upward climb of the market over that time span.  Plotting 100 of those markets on a chart looks like this:

100Mrkt



Notice the outliers above 160 and below 60.

Volatility is usually defined as being one standard deviation of the data set, which translates into a plus/minus percentage range that includes 68% of the cases.  I used two handy Excel functions: large(array,count) and small(array,count) to return the boundary result between the upper 16% and the rest of the results and the lowest 16% for the full 700 markets being simulated. The 16% comes from splitting the remaining 32% outside the boundaries into a symmetrical upper and lower half. Those results are plotted as the black lines below.

100Mrkt+1sig



The next chart compares those two lines to the theoretical result which takes the annualized standard deviation of the S&P 500 daily returns from 1950 to 2014 and divides it by the square root of time.

Standard Deviation (N) = Annualized Standard Deviation/ sqrt (252/N)

Where N is the Nth day of the simulation.

100Mrkt-vstheory-labels



Impressively close.

Since the simulated boundaries vary some from run to run I collected 32 runs and determined the mean

100Mrkt-vstheory-mean



Very, very close.

So, in spite of the S&P 500’s distribution of results not being particularly normally distributed (see chart below), the general assumption that volatility scales with the square root of time is very appropriate.

SP-Dist



Notes:

  1. Returns are expressed as the natural log of the current day’s close divided by the previous day’s close.  The specific daily return used is selected by randomly choosing a number between 0 and 16204 (Trunc(Rand()*16205)) and then using that number to index into the table of SPX returns.  The 16205 constant is the number of trading days from 3-Jan-1950 to 30-May-2014.  As mentioned in the post, the overall daily mean for that period (0.0286%) is subtracted from the result to compensate for the general upward bias of the market over that period.

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