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The Myth of Option Weekend Decay

 
Friday, January 13th, 2017 | 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 shorter term VXSTSM index—not surprising since this 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 implied 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.

Weekly Options Take Charge

 
Friday, September 18th, 2015 | Vance Harwood
 

The volume of CBOE’s Weeklyssm options has grown rapidly since they expanded their listings into equities and Exchange Traded Products in June 2010.  Now weekly options comprise almost 30% of the CBOE’s average daily option volume.  The list of available weekly options is available on the CBOE website.

http://www.cboe.com/micro/weeklys/introduction.aspx

http://www.cboe.com/micro/weeklys/introduction.aspx

Among other things option traders take advantage of the Weeklys to position themselves for earnings releases,  harvest rapid premium decay near expiration, and place low cost directional plays.

Three recent press releases suggest that the Options Clearing Corporation (OCC) and the CBOE are moving to the next phase—making up to 5 weeks of options available on popular securities and moving existing options to look more like the Weeklys.  The specific moves are:

  1. Five weeks of Weekly options for many securities (press release)
    •  Initially Weekly options were only made available 9 days before their expiration.  If you needed a later expiration date your only choices were monthly options with their 3rd Saturday of the month expiration, or in some cases quarterlies.    In 2013 the CBOE started making SPX options available with weekly expirations 5 weeks in advance.   Evidently encouraged, they rolled out additional weekly expirations for additional  indexes and stocks (e.g., SPY & AAPL).    Overall I think the advantages of a more regular set of dates will outweigh the  problems with spreading option volume across more option classes.
  2. Friday afternoon expiration for most monthly options
    • The OCC announced a plan to change the expiration date for monthly options—to align with the Weeklys.  Instead of expiring on Saturday, they would expire at the end of trading Friday.   The Saturday expiration always seemed awkward to me, causing confusion on theta calculations and exposing investors to weekend news events.  I suspect it’s a throwback to days when paper actually had to be shuffled to close things out.  This change, planned for February 2015, would render the 3rd Friday of the month options indestinguishable from Weeklys.
  3. Rationalizing ticker symbols with SPX options (press release)
    • There are  three different tickers for SPX options,  SPX, SPXW, and SPXPM. Unlike other options there are weekly options (PM settled) on the same week that the monthly (AM settled) expire.

In general the move to weekly options has been gradual and non-invasive.   One of the side benefits of the rise of the SPX weeklys is that now there are always options series that closely bracket the 30 day volatility window of the VIX calculation.  Using the monthly SPX options there were sometimes longish extrapolations required with suspect accuracy. In October 2014 the CBOE switched the VIX calculation methodology to take advantage of the SPX weeklys availability.   Ultimately this new VIX calculation was needed to support VIX Weekly futures and VIX Weekly options.

IVOP and XIV termination events

 
Monday, March 30th, 2015 | Vance Harwood
 

In the prospectuses for IVOP and XIV, there are some disconcerting discussions about termination events. In the case of IVOP, it occurs if its value drops below $10 and for XIV it is triggered if the daily percentage drop exceeds 80%. I did some digging into these events to try and figure out how likely they are to occur.  If you’d like to read a more general discussion about these two ETNs you can read this post.

First of all the IVOP and XIV provisions for termination/acceleration relate to volatility futures not the CBOE’s VIX index. The VIX relates to the instantaneous implied volatility of the S&P 500—which is a different thing. Volatility futures have contracts with different expiration dates. Typically the further out their expiration dates (e.g., 6 months from now), the slower they react to the day-to-day moves of the market. IVOP and XIV are based on the two futures contracts that are closest to expiration, the administrators for these funds adjust their positions in these contracts daily to achieve an effective average time till expiration of 30 days.

VXX does the same thing, except it is trying to be long volatility, not short/daily inverse % of volatility. When trying to understand IVOP or XIV you can view them as being a short position in VXX (IVOP), or tracking the opposite daily percentage move of VXX (XIV).

VXX is not as volatile as the VIX index. On a day with sharp market moves VXX will typically move about half the percentage move of what VIX does. VXX can still make big moves however—one day during the May 2010 Flash Crash, it jumped almost 25%—the VIX on that day jumped 46%.

Now we can talk about termination / acceleration. I think it is reasonable to assume that the goals of the ETN providers in including these measures are to:

  • Prevent the ETN value from going negative (they specify in these prospectuses that the value will stay positive)
  • Protect the provider from undue market risk in hedging these products during volatile times

IVOP is essentially a short position in VXX, and Barclays doesn’t want to ever lose more than was put into it, so they liquidate the fund if it drops below $10 on the market. This termination would occur if VXX climbs 50% above its value when IVOP was created—jumping from $41.55 to approximately $63.

With XIV termination (or “acceleration” in marketing speak) relates to daily percentage moves. If VXX jumped more than 100% in a day, then if VelocityShares didn’t terminate XIV its notational value could go to zero.   They avoid this particular unhappy situation by terminating the fund if the daily move of VXX is 80% or more—although losing 80% in one day would still be plenty traumatic.

Just to be clear, these funds aren’t tied directly to VXX, but rather the underlying futures contracts, but I believe VXX is a good proxy for the situation.

The termination risk for XIV appears to be limited to market crashes worse than the Flash crash. Two examples that come to mind are the 2009 crash and the October 1987 crash. VXX didn’t exist for either of these. I have analyzed VIX data (or simulated data) since 1992—there were 20 days with VIX jumping over 30% (previous day close to intraday high) during that period. The highest percentage jump over that period was 70.5% on February 27, 2007. There were three days with VIX jumps over 30% in the 2008/2009 crash, and during the Flash Crash.

If VXX had existed during this time span, and held to its typical behavior of 50% of VIX’s move it looks like the XIV termination event would not have occurred, but obviously it would have taken heavy losses on those days.

The termination risks for IVOP (and its fallen sibling IVO) are obviously higher.   All it takes is an absolute 50% rise in the SPXVSTR index from its value at IVOP’s inception to kill the fund.

In IVO and IVOP’s case it matters when the fund was initiated, because VXX going up 50% over the case of a correction/crash is common.  IVO started January 20th, 2011, when the VIX index was a relatively low 18.   The VIX index at IVOP’s inception was at 31,  so the timing seems to be better—assuming we don’t go into a 2009 style crash in the next 6 months or so.

If you are investing significant amounts of money in these products it looks prudent to at least hold some OTM VIX or VXX  calls. These would provide some insurance against these infrequent, but dramatic events.

Thanks to Steve, who commented on the first version of this post pointing out that the ETN providers were probably not looking out for the investor, but rather for their own hides in incorporating these termination events.

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April Condor

 
Monday, January 17th, 2011 | Vance Harwood
 

Put a condor in place on S&P 500 April futures.   The call spread was at S1350 (sell-to-0pen) and S1370 (buy), while the put spread was at S1140 (sell-to-open) and S1100(buy).  The net credit on each set of four options before commissions was 6.15 points.   With S&P 500 futures each point is worth $250, on the futures as well as the options on the futures.

With the S&P 500 at 1290 there is a 4.6% upside margin  before the short call goes in-the-money, and 11.6% downside before the short call goes in-the-money.  The worst case loss would be 33.85 points per contract set.  Currently this position pretty close to delta neutral, and the plan is to close out, or roll this position in 30 to 45 days.

Option spreads, early exercise and other wrinkles

 
Thursday, January 6th, 2011 | Vance Harwood
 

A week ago Monday I created an IEF (iShares Lehman 7-10 Yr Treas Bond) bear spread in my Schwab margin account—with the short calls deep in the money at S90.   Several of the calls were assigned that night when IEF went ex-dividend ($0.248/share).  Since I wasn’t long IEF, this assignment resulted in a short position being created in my account.   I was surprised the calls were assigned since they don’t expire until January 22nd, but not unhappy collecting a small amount of premium early,  being shifted into a position with no more risk (the paired long calls were still in place), and more profit potential if IEF really drops.

On Wednesday I received a call from Schwab regarding the short position.   Evidently they had no IEF shares to loan to create the short position, so I was politely informed that I had two choices:

  • Work with them to try to borrow IEF shares from other brokers (some additional cost involved)
  • Close out the short position by the end of the week (which seemed like a generous amount of time)

I think it’s odd that a big player like Schwab doesn’t have a couple hundred shares of IEF available to short (overall short interest about 4.5%), but previously when I’ve checked, Schwab has always shown IEF in the “Hard to Borrow” category.

Rather than pay extra, I sold-to-open a couple S91 calls at 2.05 to collect a little bit more premium and bought IEF shares to cover the short.

An analogous situation can happen with option spreads in an IRA account if short calls are assigned or expire in the money, however in an IRA you can’t maintain a short position indefinitely, even if there were shares available to borrow—you have to cover the short.