The Volatility Term Structure is Driven by OTM Puts

Saturday, December 6th, 2014 | Vance Harwood
 

The CBOE’s VIX® methodology calculates a single theoretically grounded number that quantifies virtually the entire volatility landscape for a specific point in time—pretty cool.  Prices for hundreds of different options with different expiration dates can be involved in the calculation.   This single number is very useful, but obviously lots of information is discarded in the distillation.  I’ve wondered if the VIX’s compression is hiding some information on the values of volatility over time—the term structure.  So I’ve done a little digging into the details of option pricing.

But first some background.   The CBOE provides an online chart  that shows the results of doing the VIX calculation on standard SPX options (S&P 500) listed out over the next two years.  Unlike the standard 30 day VIX these calculations are tied to specific option expiration dates.  So for example the chart below has options that expire anywhere from 15 to 834 days from the September 4th, 2013 snapshot date.   The CBOE interpolates/ extrapolates using the 1st two months listed to generate the 30 day VIX, and interpolates between the 3rd and 4th months to generate the 93 day VXV.  For more on this see Calculating VIX—The Easy Part.

VIX-term-4Sept



One of the striking things about this graph is the dramatic upward slope of VIX values over time—with the December 2015 value being 50% higher than September 2013’s.  The Nobel Prize winning Black and Scholes options pricing model asserts that this volatility curve should be a horizontal line—it’s fair to say that there’s a difference of option between theory and the market.

One interpretation is that the market is predicting increasing volatility in the future, but volatility is always spiking and declining over time—it never acts like a hot growth stock in its glory days…

Most theoreticians agree that the market is compensating for a weakness in the Black and Scholes model—which assumes that the market’s returns can be acurately modeled as a Gaussian or Normal distribution (actually lognormal if you’re being picky). The reality is that market panics create Fat Tails (Black Swans if you are a Taleb fan) that invalidate that assumption.

VIX Futures follow a similar curve, the graphic below is from VIX Central, but the futures only go out for 9 months.

4sept-VIXCentral

VIX Futures Term Structure 4-Sept-2013

 

Typically the VIX Futures volatility values carry a 3% to 9% premium  over the equivalent SPX options VIX values.  A premium I attribute to the costs of arbitrage.

Enough background already…

I was curious how much these widely disparate volatility values over time impacted the price of the options themselves.   On September 4, 2013 I took a snapshot of  two sets of SPX put options, those with a strike prices currently at-the-money (1650), and another set that was about 10% out-of-the-money (1475).  The graph below shows the actual prices for the ATM options, and the prices the Black & Scholes model predicts with an implied volatility (IV) of 16 over the next 15 months (dotted line). I chose 16 as the target volatility because that was the 30 day VIX value when I captured the data.

SPX ATM prices



In spite of a 21% ramp in volatility over the span of the VIX futures (from 16.87 to 20.4) the ATM options are priced nearly identical to the baseline during calendar 2013 and only diverge by 12 percent 9 months from now.  Clearly ATM options prices are not driving the term structure.  The next chart shows both the ATM and OTM option prices over the next 27 months.

SPX ATM+OTM prices

 

The OTM options have dramatically higher premiums in the short term over the baseline and premiums in the 70% range for a year or two out—these premiums boost the implied volatility of the term structure.  Some people wonder about the robustness of this price structure.  If lots of people try to go short on volatility will that change the status quo?   With options, the open interest is a good indication of the robustness of the market.   By that measure SPX options look good—for just the two strikes 1650 and 1475  the open interest for all expiration dates totalled over 300K contracts for 1650 and over 180K for 1475.   The notional value of the options is greater than $50B and $27B respectively.

The next chart switches back to a volatility based view of things.

SPX Vol Term Structure

 

The short term OTM put options show elevated IVs in the short term—prices presumably driven up by buyers of short term insurance.  The ATM put options, SPX VIX values and VIX Futures are layered on top of each other as expected, however I was surprised that the SPX VIX value climbed above OTM IVs in 2015.  A little investigation revealed a significant of activity and open interest in deep OTM Dec 2015 puts—with IVs as high as 65 driving the VIX calculation higher.

Some people think the existing volatility structures are ominous, others feel they are unrealistic and likely temporary, but the data suggests that the structure is driven by investors voting with their portfolios to assert that the world is riskier than Black and Scholes believed.



A 3D View of the S&P 500: Price, Time, and Markets

Tuesday, February 26th, 2013 | Vance Harwood
 

There are lots of valid ways to look at the market.  Obviously price is important, but a number alone (e.g., 1487.85—Feb 25th‘s S&P 500 close) doesn’t mean much.  Price related metrics like percentage changes and support/resistance levels add value, but adding time as a factor enables some really interesting measures like moving averages and momentum trackers.    My favorite time related metric is term structure—how the prices of various options and futures vary depending on their expiration dates.

February 25th‘s market action provided a very interesting set of views.

On the price dimension the percentage moves of the S&P 500 (SPX) and the CBOE’s VIX® index were unusual.  At 3:41 EST the SPX was at 1497.7 down 1.21% from the previous close.  The VIX on the other hand was up 26.7%, which was -22X the SPX move.  The average move is -4.77%, so this was a tad unusual.

On the time dimension the term structure of SPX options was moving rapidly into backwardation—the implied volatility of the near term options climbing dramatically compared to longer dated options.

At open:



At 3:26 EST:



Options in general and SPX options in particular are thought to be traded by more sophisticated investors and institutions.  This sort of term structure change indicates they were buying option based protection like mad—even though the market had only fallen 1.21% at the time.

The third dimension that I like to watch is how different markets react to the same set of circumstances.   At 2:44 EST the VIX futures market was still unimpressed with the SPX price action of the day—with the term structure looking almost ruler straight.



The March front month VIX future was only up 5.4% even though the VIX was up 16.7% at that point—and almost equal to the 3rd month future price.   The term structure looked a little different at market close.



It shows a dramatic shift into backwardation.

Although VIX futures are also linked to SPX options, the linkage is pretty weak.  The front month futures only reliably align with SPX options once a month—on the future’s expiration date.  Far fewer investors trade VIX futures and they are likely more sophisticated than SPX option traders.   Clearly the VIX futures market at 2:44 EST was much less impressed with the general market pullback than the SPX options market.

By market close the VIX futures market was serious about the market move, but judging by the position of the VIX close above the 6th (!) month VIX future value the VIX futures market is still not that worried.

The chart below shows the situation at close on February 26th:

VIXCentral.com

VIXCentral.com

 

The VIX dropped 11% and although lumpy the VIX Futures term structure straightened out.  For at least 26th the VIX Futures crowd called it right.



The Cost of Contango—It’s not the Daily Roll

Saturday, March 2nd, 2013 | Vance Harwood
 

A while back I developed a spreadsheet that consolidates the CBOE’s historic VIX futures data into a single spreadsheet.  Using this spreadsheet I calculate the short (SPVXSTR) and medium term (SPVXMTR) rolling indexes that underlie the various volatility Exchange Traded Products (ETP) like VXX, UVXY, XIV, and ZIV  The image below shows a small sample comparing my calculations (M1-M2 Short Term Rolling Index) with the official value of the short term index.

M1-M2-Sample



The  percentage differences between my index and the official index (e.g, -0.000256%) aren’t cumulative and are probably due to rounding.

Once I had verified my index calculations I wanted to look at the nemesis of the long volatility funds like VXX and UVXY—yield losses.  These losses, which can be 5% to 10% per month occur when the CBOE S&P 500 Volatility Index (VIX) Futures that underlie these ETPs are more expensive than the market, or “spot” price.  This situation is called contango, and is typical when the overall market is bullish or flat. The graph below from VIX Central shows VIX Futures in a contango configuration.

vixcentral.com

vixcentral.com



I wanted to quantify this loss with my spreadsheet without the noise of everyday volatility moves, so I left the term structure in contango, but held the futures prices constant in my spreadsheet from day to day as an experiment. The results were surprising.

M1-M2-OnlyC



My calculations showed no daily roll costs in the index. The 0.01 upticks in the index are due to treasury bill interest.

The usual explanation for roll costs, discredited in the sample above, asserts that losses are incurred when funds sell cheaper shorter term contracts and buy more expensive longer term contracts every day as specified by the indexes they follow—a sell low, buy high situation.   A closer look illustrates the flaw in this explanation.   A simple example of a $10 million position after market close on 19-Oct-12— after the contract rolls. Fractional contracts aren’t supported, so unused money goes in the cash bucket.

Nov Contracts Nov Value % Dec Contracts Dec Value % Cash Total Value
500 $8.8 Million 88% 65 $1.19925 Million 12% $750 $10 million



Now moving to the end of the next day, neglecting transaction costs and interest, and assuming no change in the futures values.

Nov Contracts Nov Value % Dec Contracts Dec Value % Cash Total Value
477 $8.3952 Million 84% 86 $1.5867 Million 16% $18100 $10 million



The number of contracts changes, but the total value doesn’t.

There’s no doubt that these indexes lose money when the VIX Futures term structure is in contango—so where do the losses come from?

The chart below shows the real root cause:

Nov / Dec VIX Futures vs VIX

Nov / Dec VIX Futures vs VIX



Plotting actual November and December VIX futures values during a period of contango vs the CBOE’s VIX®, we see that both contracts decline in value over time, eventually converging with the “spot” VIX price at their expiration. With both sets of contracts held by the long volatility funds generally declining it’s not surprising the overall value drops. Since we are typically looking at term structures over the span of multiple months, the small daily “slide” down the curve isn’t noticeable—especially when obscured by the up and down moves in volatility driven by daily stock market fluctuations.

This analysis also explains why the mid-term volatility index SPVXMTR which holds contracts that are 4 to 7 months out also declines rapidly in contango situations, even though 2/3rds of the contracts (M5 & M6) aren’t rolled on a day to day basis.

Volatility Futures aren’t always in contango.  If the markets are panicky enough the futures contracts get less expense than the VIX index.   The chart below from VIX Central shows the June 10, 2010 situation when the VIX index closed at 36.57.

TS-7Jun10



In this configuration, called backwardation, the long volatility funds have the wind at their backs, every day the futures they hold are sliding up the curve, getting closer to the spot price.

Knowing the real reason for term structure based losses / gains hasn’t changed my volatility investment strategy, but it has removed one source of confusion in understanding the daily moves.



10 Questions about Mid-Term Volatility

Saturday, February 23rd, 2013 | Vance Harwood
 

Why is mid or medium term volatility defined as being 4 to 7 months out?

  • In January 2009 Barclays introduced VXZ, the first medium term volatility Exchange Traded Product (ETP).  Its tracking index (SPVXMP) relies on 4 to 7 month VIX futures.  I suspect that range was selected because historically (2004 through 2008) the term structure on the 4th through 7th month VIX futures was relatively flat but still tracked general volatility trends.
  • By using the 4 to 7 month range Barclays could minimize transactions costs by holding futures for a full 3 months when it came to implementing VXZ’s hedging strategies.
  • The chart below from VIX central shows the VIX futures term structure on 3 different dates:

vixcentral.com

vixcentral.com with annotations for 4 to 7 month futures



How does the mid-term rolling volatility index(SPVXMP) work?

  • At the end of every trading day the index models the selling of a portion of the 4 month futures that it holds and uses the proceeds to buy an equivalent dollar amount of 7 month futures.  The process sells the last of the 4 month futures the evening before the nearest (1 month) futures expire.

Can I invest in mid-term volatility?

  • There are 7 ETPs that hold at least some of their assets in mid-term VIX Futures.  Specifically:
    • 1X long:   VXZ, VIIZ, VIXM (ETF)
    • 2X long, daily reset:  TVIZ
    • -1X inverse, daily reset:  ZIV
    • Hybrids that hold a portion of their assets in mid-term futures: XVIX, XVZ
  • See Volatility Tickers for the full list of USA volatility related ETPs, their websites, prospectus, etc.
  • For a mid term volatility investment strategy that utilizes the VIX for timing see Taming Inverse Volatility with a Simple Ratio.

What does it mean when mid-term volatility futures are in contango?

  • Contango is a futures market term signifying that contracts with more time until expiration are more expensive than shorter term contracts.  In commodities markets (e.g., natural gas) this is the typical state if supply and demand are in balance and the product has carrying costs (e.g., storage).
  • When futures markets are in contango it’s expensive to hold (be long) futures because the contracts are decreasing in value over time.  Of course if the underlying commodity/index that the future is based on increases enough it will compensate for those losses.

How often are mid-term VIX Futures in contango?

  • Historically around 75% of the time—typically when the equities markets are bullish or trading within a range

How do you compute contango on mid-term volatility?

  • The total amount of contango is just the percentage difference between the 7 month and 4th month futures’ price  (e.g,  (M7-M4)/M4).  Divide this result by 3 to get an estimate of how much the value of a medium term position in volatility will decrease in a month due to contango.

What happens if medium term VIX futures have a negative slope (longer term contracts cheaper then shorter term)?

  • This situation is called backwardation.   It happens when the markets are very fearful.  In this case the rolling index will tend to increase in value because the contracts get more valuable as they get closer to expiration.
  • A contango calculation in this case will yield a negative number

How volatile is medium term volatility compared to short term (1 to 2 months)?

  • Medium term volatility tends to experience about half the volatility of short term.   In 2012 the annualized volatility was around 35%, compared to 70% for the short term rolling indexes.

Has the general behavior of mid-term VIX futures been stable?

  • For the first 6 years of VIX futures trading (starting in 2004) the mid term futures term structure tended to be quite flat during quiet times.  However, starting in late 2009 the typical structure has shifted to a fairly steep structure, with the 4th month futures trading for significantly less than the longer dated futures.   Recently the slope has been hitting historic highs.
  • The reasons for this shift are not clear, but during that period the VIX Futures market has increased dramatically in open interest and volume.   I suspect the current shape better reflects the true costs of that the futures market makers have in hedging these contracts.

What are the advantages / disadvantages of investing in mid-term volatility?

  • Disadvantages
    • Mid term volatility moves much slower than the 1 to 2 month short term volatility measures.  If you are trying to catch the full impact of a volatility spike mid term is not for you
  • Advantages
    • If you want to be short volatility, the medium term investments are not as scary.  An overnight volatility event (e.g., earthquake, terrorist event) will not move the mid term indexes near as much as the short term.
    • The contango losses in the rolling indexes are lower than the short term indexes, lowering the costs of holding a long volatility position.  However the contango losses in medium term volatility have increased to painful levels—often running in the 3 to 5% per month level.


The Volatility Watcher’s Toolkit

Monday, December 8th, 2014 | Vance Harwood
 

The CBOE’s VIX index gets mainstream exposure as the “fear index”, but there’s a lot more to volatility watching than the VIX.   The VIX does a good job of measuring the current level of anxiety in the market, but it has some problems.  Among other things it’s:

  • Not a good predictor of the future
  • Often does not move in the direction people expect (opposite the S&P 500). Historically its average percentage move is -4.77x of the S&P 500, but around 20% of the time it moves in the same direction.
  • Not investable—it’s a measurement, not a security
  • Quirky around weekends and holidays
  • Prone to jumps/dips the Monday before the 3rd Friday of the month

There’s almost an overwhelming number of things to watch with volatility, but a few straightforward concepts can help you observe intelligently.

Option Implied Volatility (IV)

  • The market’s estimate of a security’s future volatility is reflected in the price of its options.  In practice the market isn’t always logical about this, for example out-of-the-money (OTM) puts usually have higher expected volatility than at-the-money (ATM) puts even though they are all based on the same security.
  • If an option expires in 60 days, we assume that its pricing reflects a 60 day expectation of volatility in the underlying security.

Implied Volatility Skew

  • When the market is especially fearful the IV of OTM puts goes way up because investors are buying options for portfolio insurance.  The difference between IVs at different options strike prices is called skew.  A partial measure of SPX (S&P 500) option skew is incorporated into the calculation of the VIX index.    The CBOE also does an explicit skew calculations.  Details of that calculation are given here, and a spreadsheet with historical daily values can be downloaded here.

Duration

  • Volatility measures are either variable or constant.  The VIX is a constant 30 day future estimate of volatility.   SPX options, VIX futures, and VIX options all have variable durations because they expire on specific dates.  While the volatility directly or indirectly expressed by these securities does not necessarily go up or down with the passage of time, they tend to get tweaky a few days before expiration.

Blends or Single Security

  • The VIX is an index that blends together the volatility characteristics of a wide range of SPX options.   Most measures (e.g,, VIX futures prices) give a volatility measure for a single security.

Term Structure

  • While the VIX has a 30 day duration, it’s useful to look further out in time for other volatility estimates.   The CBOE also provides VXV which is a 93 day estimate.  SPX options give estimates up to two years out, VIX futures 9 months, VIX options 6 months.  Different patterns (e.g., steadily rising estimates of volatility vs declining) over time indicate how nervous the market is, regardless of the absolute values of volatility.
  • When the term structure is climbing over time (positive slope) it is said to be in contango, if declining over time, backwardation.

http://www.cboe.com/data/volatilityindexes/volatilityindexes.aspx

http://www.cboe.com/data/volatilityindexes/volatilityindexes.aspx

vixcentral.com

vixcentral.com



Rolling Indexes

  • All exchange traded volatility funds (ETF/ETNs) rely on volatility rolling indexes that are blends of various VIX futures.  This blending achieves a constant duration estimate of volatility and is done in a way that can be physically traded.  Unfortunately the typical term structure of the VIX futures creates an erosion effect on this mix of futures.  The end result is that these indexes are only good at tracking volatility moves in the short term.    Long term these rolling indexes inexorably trend towards zero.
  • Examples:

 

The chart below summarizes the S&P 500 volatility measures that I monitor.  Click on the ticker for quotes (Yahoo! Finance) for more information.

Duration Securities

Term Structure

Short Term (1-2 month) 3 Month Mid-Term(4-7 month) Long Term
Constant Blend
VIX/VXV ratio (when below 1 indicates contango)
Single Historical Volatility (e.g., 22 day retrospective)
Variable Blend
  • VIN (23 day to 29 days)
  • VIF (30 to 37 days)
Per-expiration month SPX option volatility computed using the VIX’s option strike composite approach for months 3 through 10
Single

 

Notes

  • VVIX is an VIX-like index derived from the IV of VIX options—creating a mind bending volatility of volatility measure.
  • Historical or realized volatility is computed using past changes in the security.  The historical volatility is often compared to the implied volatility to determine the difference.  Implied volatility is almost always higher than historic volatility.
  • VIN and VIF are variable duration metrics created by the CBOE for use in calculating the VIX index.  The “N” in VIN stands for “near”, and the “F” in VIF stands for “far.”  The VIN is calculated from the set of SPX weekly and monthly options whoose expirations bracket the VIX’s 30 day expectation.   The VIF is calculated using the SPX options that expire the week after the VIN options.  See this post for calculation details.