The Volatility Landscape—October 2014

Friday, October 10th, 2014 | Vance Harwood

VIX + VIX Future Term Structure May 2011- March 2012

News

  • CBOE
    • On October 6th, the CBOE introduced an updated methodology for computing the VIX index.  Previously the index was computed using SPX options with 3rd Friday of the month expirations, but now SPX weekly options are used when they bracket the 30 day expectation maturity of the VIX.  For example the VIX for 9-October-2014 computes an implied volatility value for 8-November—since options don’t exist that expire on that date an interpolation is used between the 7-Nov-2014 and the 14-Nov-2014 SPX weekly options.  Calculations via the old methodology are reported under the VIXMO ticker.    While technically I think this is a sound move, the currently much lower volumes on SPX weekly options that far out may cause the new VIX to significantly diverge from the old VIX  (so far I’ve seen variations as high as +5%).   The CBOE’s new methodology does not impact the expiration process for VIX futures and options; they will continue to use the 3rd Friday options for that calculation.
    • The CBOE’s expansion to near 24 hour trading for VIX futures has gone well and they are planning to expand the trading hours of VIX and SPX options starting October 21st to the same Sunday Afternoon 6pm ET to Friday Afternoon at 4:15 ET span.  For more information see this note from the CBOE.
    • VXST futures have been trading since February 13th, 2014.  So far their reception has been lukewarm with volumes running around 50 per day, but their prices do seem to track the VIX index pretty well, significantly better than VIX futures.   For more see VXST FuturesNot a Bad Proxy for the VIX.
  • PHDG gains momentum
    • This PowerShares fund uses the same VEQTOR methodology as VQT, but it’s an ETF rather than an ETN.  Its assets under management have climbed to $431 million, gaining momentum in its quest to top Barclay’s $640 million VQT (source ETFdb.com).
    • PHDG distributes a dividend (currently around 1.6% per year).  Of the 22 USA volatility based funds only PHDG and VelocityShares’ SPXH and TRSK distribute dividends.
    • Recently options became available (30-July-2014) on PHDG.  I’ve wanted options on the VEQTOR based funds (VQT and PHDG) for a long time because they raise the possibility of a Covered Call Strategy That’s Long Volatility.   Unfortunately the market maker isn’t showing much enthusiasm, with huge spreads and no bid prices on ATM options.

 

Predictions 

 

White Papers

  • Volatility: A New Return Driver?
    • A good non-mathematical overview of volatility, volatility products including futures and a couple example trading strategies using volatility Exchange Traded Products
  • The VIX-VIX Futures Puzzle?”
    • A technical paper testing the forecast accuracy of VIX futures that includes a comprehensive technical overview of the VIX, VIX Futures, and volatility term structures.  It skips the calculus but provides a clear description and comprehensive formulas.
  • Variance and Convexity: A Practitioner’s Approach
    •  My favorite paper from the CBOE’s 2013 Risk Management Conference.  Sparse and very technical it addresses some of the differences between variance and volatility with regards to VIX futures.  Most of the other papers from the conference are posted here with links associated to the agenda items.
  • VIX White Paper
    • Complete details on the VIX calculation, recently updated (8-Oct-2014) to reflect the new methodology that utilizes SPX weekly options

 

Tools

Wish List



The Myth of Option Weekend Decay

Sunday, October 5th, 2014 | Vance Harwood

While doing simulations on volatility and the square root of time I started thinking about how options experience time—is it calendar time, market time, or something in-between?  The CBOE’s VIX® calculations use calendar time, a 365 day year, but most option gurus recommend using a 252 day year for volatility calculations—the typical number of trading days per year in the USA markets.

When it comes to option decay most people, including the gurus, believe that option values decay when the markets are closed—a position I believe conflicts with the 252 day approach to annualizing volatility.

The experimental discovery that led to the current theory of option decay occurred in 1825 when the botanist Robert Brown looked through his microscope at pollen grains suspended in water and noticed they were moving in an irregular pattern.  He couldn’t explain the motion but later physicists including Albert Einstein showed it was the result of water molecules randomly colliding with the pollen. This effect was named “Brownian Motion” in honor of Mr. Brown.

If you effectively stop time in Mr. Brown’s experiment (e.g., freeze the sample), the pollen will stop moving.  Or if you close a casino for a day (probably a better model for the market) the net worth of the associated gamblers stops dropping.

Defenders of the calendar time approach point out there are many activities / events with broadband impact that can move the value of the underliers while the market is closed.  Things like extended trading hours, activity in foreign markets, corporate announcements, geopolitical events, and natural disasters.

However it occurs to me that most noteworthy events that happen outside of market hours tend to be bad news.  For example, I’m not expecting to see headlines any time soon stating, “ISIS disbands, ‘We realized it was all a terrible misunderstanding’”, or “Harmless landslide reveals huge cache of gold”.  This tendency towards negative moves is reflected in the average annual growth rate of off market hours for the last 20 years, -0.37% vs +9.59% for market hours.   And bad news tends to make option prices go up…

If option time is still running when the markets are closed I would expect the market’s opening value to be different from the closing value.  Below is a quick look at the last 20 years of data:

S&P 500 Returns 1-Jan-1994 through 22-Aug-2014 (5197 market days)

Market Time: Open to Close (occurrences) Market Time: Close to Open (occurrences)
No change 0.1%  (5) 58% (3046)
Change less than 0.05% 5.2%  (270) 81% (4249)
Changes >= 1% 27% (1396) 0.04%  (3)



I was surprised how often the market opened at no-change from the previous close (3046 times) and how seldom it has gapped overnight more than +-1% (3 times).

So what?

So far my arm-waving arguments give the edge to market time over calendar time, but really, so what?

Practically there are two things where this makes a difference: the dynamics of option decay and the accuracy of implied volatility calculations on soon to expire options.

Option Decay

Novice options traders are usually disappointed if they try to profit from Theta decay over the weekend.  If the underlying doesn’t move, options prices typically open on Monday unchanged from the Friday close.  Commentators explain this phenomena noting that market makers, not wanting to be stuck with Theta losses over the weekend, discount prices, overriding their models before the weekend to move their inventory—just like a fruit vendor would.

I think the market makers are right for the wrong reason.  Their computer models are (or at least were) based on calendar day assumptions—which assume option decay during the weekend.   By overriding their models they are pricing according to what really happens—no decay when the market is closed.

Annualizing factors  

For longer term expectations of volatility it doesn’t matter much which approach you use.  For options expiring a month from now the differences in implied volatility are only a few percent between the 365 vs 252 day models.  However for shorter expirations the differences can be dramatic.

The chart below compares per minute values between the two annualizing approaches and shows the percentage difference.  The calendar based approach is the black line and the green line is the market time.  Notice how the difference peaks at Monday open and drops to near agreement at Friday close.

CalvsMrkt-ann



This “weekend” effect is sometimes visible in the CBOE’s VIX index, and is pretty dramatic with their new shorter term VXSTSM index—not surprising since this new index is based on S&P 500 (SPX) option prices with at most 9 days until expiration.

There are good reasons to use a calendar day approach to annualization.  It isn’t sensitive to holidays, unexpected market stoppages, or differences in trading calendars between countries.  I expect that’s why it became a de facto standard in the volatility world.  But the rise of shorter term volatility products like weekly options has shifted the volatility landscape enough that I think we need to at least know what is technically correct.

 An analytic approach to a solution

Normally we take a shorter term (e.g., daily) volatility and multiply it by the appropriate annualizing factor to get the annualized volatility.  Since the annualizing factor is the thing in question I decided to take the historical annual volatility for the last 64 years of the S&P 500 and divide it by the daily volatility to solve for the actual historical annualizing factor.

First I validated this approach with a Monte Carlo simulation1 that computed the theoretical annualizing factor for a simulated 64 year market period—and then repeated that exercise 10000 times to get the statistics of the calculation.  I then applied the same calculation to the S&P 500’s returns2 over the last 64 years. The result:

Sim-Ann-Factors



The square of the annualizing factor comes is only 0.87% from the theoretical median value3 of 252 and the actual S&P 500 result of 243.5 is only 2.5% from the median value.  The S&P result of 243.5  is almost 3 sigma away from the competing answer of 365.

The S&P 500 data is consistent with a 252 day based annualizing model—which doesn’t support option decay while the market is closed.  The data also indicates that when you see suspiciously high short term volatility numbers at the beginning of the week you should chalk it up to flawed algorithms, not anything real in the market.

 

Notes:

  1. For each day of the simulation I used the standard deviation of the previous 252 days natural log of daily returns for the short term volatility number.  For the yearly return I used the simulated market value one year hence divided by the current day’s market value.  Volatility drag is an important second order effect that needs to be included in the calculations.
  2. I offset the actual results by the average annualized growth rate to compensate for the non-zero mean of actual returns over the last 64 years
  3. My simulation results have a median value of 252.2 (0.08% error) if I use a volatility drag coefficient of 0.6 instead of the standard 0.5.  I believe my model slightly under corrects for volatility drag.



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.

 

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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 and medium term volatility funds—specifically VXX, VIXY, TVIX, UVXY, XIV, SVXY, VXZ, and ZIV,  in addition to the closing values.

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/C 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.

 

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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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