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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.

How Much Should We Expect the VIX to Move?

 
Wednesday, November 4th, 2015 | Vance Harwood
 

Every couple of months it seems like there’s an uptick in articles about the CBOE’s VIX Index being broken or manipulated.   Generally I expect the percentage moves in the VIX to be around a factor of 4 in the opposite direction of SPX (S&P 500).  But there are significant eccentricities in the VIX that I factor in, for example Fridays tend to be down days, Mondays tend to be up.

The chart below shows the percentage moves at close for VIX (blue bars) and SPX (red line) for the first 12 trading days of November, 2012, along with my -4X rule of thumb (green bars).  The black ovals show 5 days where the VIX went opposite the expected direction. In addition, on two days, the 1st and the 16th the VIX moved far more than a -4X factor.


One of these days, the 12th, has at least a partial explanation.  That was the day that the VIX calculation shifted from using November / December SPX options to December / January options.   If you’re interested see Bill Luby’s post for more information on this phenomenon.

I did an analysis of SPX and VIX since 1990 to see the actual historical ratios between their percentage moves.   I excluded daily SPX percentage moves of less than +-0.1% because they often give very high, nonsensical ratio values.


The average ratio value was -4.77, but as you can see there is a wide spread.   About 20% of the time the ratio is positive (data to the right of the red line).

Each of the blue bars in the histogram shows how many days had a VIX% / SPX% ratio in each 0.25 wide bin.  For example there were 120 days where the ratio was between -3.25 and -3.5.   I also plotted a normal distribution—which shows this distribution is more concentrated and has wider tails than a Gaussian distribution.

While not broken, and probably not manipulated, the VIX as a fear gauge leaves a lot to be desired.   Given its past performance it’s not reasonable to expect it to negatively correlate with the S&P 500 every day.  However I think it does give us a very good feel for the mood of the SPX options market.  A single SPX option has the leverage of a $200K+ investment in the S&P 500, so it tends to be the domain of professional / institutional investors.  They aren’t always right, but they aren’t dummies, and they’re voting with their wallets.   Last week they were trading as if they thought the market decline was over, and at least for today, it looks like they were right.

A Covered Call That’s Long Volatility

 
Friday, January 11th, 2013 | Vance Harwood
 

Covered calls are an example of  positions that are short volatility.  I hadn’t thought of it that way until Sheldon Natenburg, the author of Option Volatility & Pricing  pointed that out in a fascinating interview in Expiring Monthly  (http://tinyurl.com/6wwplf9).   A covered call position is profitable if the underlying equity stays the same or goes up, but in a big market downswing, when volatility spikes up,  the modest potential profits from a covered call are more than wiped out by the losses in the underlying.

Unfortunately it is usually expensive to hedge a short volatility position.  The two most common strategies have problems:  VXX typically has roll yield losses, and VIX/VXX options have significant time decay.  Recently I started looking at Barclays’ VQT ETN, a fund that is intended to be long volatility.  The chart below compares $1000 invested in SPY and VQT starting in September 3rd, 2010—VQT inception date.

$1k investment in SPY and VQT

In bull market phases VQT underperformed the S&P 500  by about 50%,  but during the -19.5%  drawdown in August 2011 VQT only dropped 3% before going on a short term volatility fueled binge that lifted it 20%.    The next chart shows the day-to-day percentage moves of VQT vs SPY since June 2011.

Daily percentage moves SPY vs VQT

When times are volatile, VQT shifts its investments to include more short term volatility—which lowers its correlation to the S&P 500 to about 50% or 60%.  In very quiet times, like the end of December/January VQT shifts to a almost pure S&P play—giving it the nearly 100% correlation you see at the right side of the chart.   The next chart is from the VQT prospectus, showing the backtested, theoretical performance of VQT since 2005

VQT vs S&P500 backtest to 2005

VQT looks almost tailor-made for covered call writing.  Its low drawdown behavior limits capital risk while its volatility is similar to the S&P 500.  Unfortunately there are no options available on VQT, so we’ll have to get creative in developing a covered call style position.  Since much of VQT’s composition is direct exposure to the S&P 500 I will use SPY options as logical building blocks.  A covered call is a short call position hedged with a long equity position.    Since brokers won’t accept a long VQT position as a hedge for a short SPY call and I don’t want to have naked calls, I’ll protect my short call position with long out-of-the-money calls—creating a call spread.     I’m not too concerned about losses on these credit spreads, because VQT is a natural hedge for the position, so I’m comfortable with a $2 spread in the option strike prices.

Profitability analysis:

Market Action VQT action SPY call credit spread action Overall Profit
S&P 500 strongly up Up, but not as much as S&P Worst case loss.  Loss is premium received at creation minus $2/ option pair Neutral to small loss
S&P 500 up Up, but not as much as S&P  Neutral to profitable, with profit equal to premium received at creation minus any in-the-money intrinsic value. Modest profit
S&P 500 down Down, but not as much as S&P  Profitable, keep full premium received at creation Neutral to small loss
S&P 500 strongly down Strongly up as volatility portion kicks in  Profitable, keep full premium received at creation Very Profitable

 

The spreadsheet that provides the VQT backtest data from March 2004, including all formulas is available here.

 

The VIXs of Christmas Past

 
Tuesday, December 17th, 2013 | Vance Harwood
 

One of the persistent characteristics of the CBOE‘s VIX® index is the Christmas Effect—the tendency for VIX to drop down to relatively low levels during the Christmas holidays.  The CBOE’s VIX volatility December futures predict this drop for months in advance, and it has come to pass again this year.   I am aware of at least three possible explanations for this:

  1. Option market makers and others short options reduce their prices before the holidays so that they don’t get stuck with time decay (theta) during the multiple days off
  2. Traders in general go on vacation the end of December, volume drops, and the market becomes lethargic, reducing volatility
  3. People expect volatility to decrease, trade accordingly, and it becomes a self fulfilling prophecy

I am skeptical about calendar based trading strategies (e.g., “crash prone” October was +8.5%, -1.8%, +4%  2011 through 2013) but the Christmas effect has been persistent— perhaps because it’s not easy to profit from it.   The VIX index itself is not investable, and the December VIX futures already discount the effect.

I was curious  how the VIX behaved over the last few years in December and January, so I generated the chart below using VIX historical data from the CBOE.

Xmas-VIX



To make the chart more readable I carried over closing values over weekends / holidays and used a 3 day moving average.  I excluded 2008, even though it shows the Christmas effect, because the market that year was clearly in an unusual state.

There does seem to be a fairly consistent low around the 23rd of December and the VIX has consistently increased right after that—at least for a few days.   By mid January things seem to have settle back into their random ways.

I also wondered how VIX futures behaved around the holidays.     I used my VIX futures master spreadsheet  to generate the chart below showing the behavior of the front month VIX futures, the next ones to expire.

Xmas-VIX-Futures



With the VIX futures the December dip comes a few days earlier.

In my experience the future is often uncooperative in repeating the past, but this VIX Yet to Come, looks like a reasonable bet for a post Christmas boost.