VIX futures calendar spread strategy: a little data mining

Has anyone noticed a bit more volatility in markets these days?  That SNB shocker was something, indeed – it seems some FX retail brokerage houses have already declared insolvency.  Anyway, the increased volatility has had quite an impact on VIX in the year so far: after starting the year at an elevated, yet respectable 17-ish, the index has climbed to a panic-like 22.5.  For those stats-minded, that latter figure implies a daily move of around 1.4% for the SPX – not unusual recently, but pretty darn high compared to post-2008.

OK, let’s get to work.  The VIX is very elevated, but it can be a mug’s game to short (i.e. the VIX can get smashed a bit like the SNB smashed the Euro/CHF exchange rate yesterday).  Too risky for an outright short.  What to do?? A VIX calendar spread.

Mmm…spot the backwardation. Source: thinkorswim by TDAmeritrade

• Hypothesis: times of high volatility causes the VIX futures curve to go from contango (e.g. further months more expensive than near months) to backwardation (the opposite).  When the market returns to more normal conditions, the contango will return.
• Method: when the futures curve goes to backwardation, or very near it, go short a near-month future and hedge by going long a further-dated future.  Take off the trade when contango returns.
• Which contracts?  Note the curves in the picture.  The red line is today’s VIX futures curve – e.g. flat to backwardated.  The other lines are the month-end VIX futures curves for the past 6 months.  A couple observations:
  • In normal markets, there is a pretty smooth contango.  So the max return for any 1-month calendar spread is about the same going out 6 months.  You could choose, say, months 2/3, 3/4, etc.
  • However: notice how much extra movement occurs in months 1 & 2, say, relative to further months.  So, it’s a risk/return situation: if you want higher risk/return, go for earlier months.  I, being a chicken, will stick with a bit less risk – months 3/4, perhaps.  That means I choose to be short Apr 2015, hedged by long May 2015 futures.
• A bit of data mining to convince me: I downloaded the month 3 and 4 continuous contracts from Quandl, then did the following rough analysis:
  • Time range: 1 Jan 2008 through yesterday, daily data.
  • Metric: gross profit from Month 3 and 4 calendar spread, assuming a 1-month hold (i.e. mechanically holding the position 1 month).
  • Brief, dirty stats:
    • Unconditional (e.g. all daily observations)
      • Observations = 1740
      • Mean gross return = $0.006/spread
      • Expected return, using uniform probability distribution and decile returns (including min/max) = $0.033/spread
      • Z-test for mean different than 0 = 36.8%.  In sum, I can’t assume the expected return is positive.
    • Conditional (e.g. only enter trade when spread is $0.05 or less)
      • Observations = 454
      • Mean gross return = $0.341/spread
      • Expected return, same method = $0.320/spread
      • Z-test for mean different than 0 = less than 0.01%.  In sum, I can assume a positive return.
• Summary: I think this strategy will work in the current environment, so I’ve put on the trade in small size to test the waters.  Wish me luck!

A (slight) improvement on a terrible savings idea…lottery syndicates

Shark attack + lightning = MegaMillions? Source: http://www.onewhale.com via Google Images.

The season finale of Last Week Tonight with John Oliver had a great main story: the many fallacies associated with lotteries.  Among them:

• The probability of winning the ‘big one’ in the US, MegaMillions, is roughly the same as being stuck by lightning…while being eaten by a shark.  I’m not quite sure this is right, as the odds I see on the internet are the following:
  • MegaMillions jackpot: 1 in 258,890,850
  • Attacked (not necessarily killed) by shark: 1 in 3,700,000
  • Hit (not necessarily killed) by lightning: 1 in 300,000
  • Assuming independence (probably reasonable…?), odds of both at the same time are 1 in (3.7m * 0.3m) = 1.1 trillion.  So off by a factor of about 4,000 or so
  • Anyway, good TV
• Lotteries may not be so good for charity/education as one might think.  The program focuses on the replacement of education funds by lottery money; sometimes the shifted state funds are used elsewhere, and sometimes they’re just wasted.

OK, back on point.  The program got me thinking about the humble lottery syndicate: suppose a group of 5 or so co-workers pool $1 each, on a weekly basis, to buy MegaMillions tickets.  The jackpot would be shared equally.  I’m sure many folks just do this as a way to build camaraderie, but there are indeed many people who honestly believe the lottery will help fund retirement. So let’s discuss a very slight improvement for this group of folks.

• Objective: a better payout ratio than MegaMillions, while keeping similar ideas of a lottery (e.g. small investment with big potential payout).  So I would like a higher expectancy, which is defined as
  • Prob(win) * Win$ – Prob(not win) * Cost$
  • For MegaMillions, the average jackpot is $105 million.  So the expectancy is:
    • (1/259 million) * ($105 million) – (1- 1/259 million) * ($1) = $(0.60).  I expect to lose $0.60 of my $1 invested each week, on average.
    • NB: I don’t include the other prizes, to simplify analysis.  Take a look here for more rigorous computations.
• Strategy:  purchase of deep out-of-the-money put options on the S&P500.  Similar to lottery tickets, they will almost always expire worthless, but will sometimes have some value and very infrequently have a very large value.
• Method: choose a near-dated, highest-strike put option on the S&P500 (SPX) which can be purchased for $5 – the ‘nickel option’.  To give perspective, here are the best value nickel puts on the SPX (current value = 2040) this morning:
  • 2 days to expiry (DTE): 1795 strike.  The S&P would need to ‘crash’ 12% over the next couple days for this to close in the money.  I choose this one.
  • 8 DTE: 1605 strike.  A 20% crash needed.
  • 16 DTE: 1450 strike.  A 29% crash needed.
• Scenarios:
  • Under most conditions, the 2 DTE 1795 put will expire worthless.  The syndicate has lost its $5 this week.
  • The probability of reaching 1795 in two days can be very roughly modelled as the probability of a 12% move given the S&P’s current 13% annualised volatility.  That is a roughly 11-standard deviation move, meaning 0% probability given a normal distribution of returns.  So conventional stats don’t really help us.
  • Going to our friend Quandl, we can calculate all the 2-day (overlapping) returns for the S&P 500 going back to 1950.  It turns out our 12% OTM Put would have ‘come good’ a few times in that period:
    • 20 Nov 2008 (-12.4%)
    • 20 Oct 1987 (-16.2%)
    • 19 Oct 1987 (-24.6%)
  • So: out of 16,318 overlapping observations, we’ve found 3 that would result in a win for the nickel option.  That’s a historical probability of 3/16318, or around 1 in 5,500.
  • What do you win?  That’s a good question.  With only 3 observations where this has occurred, the expected move given the 12% loss is difficult to estimate.  Just averaging the 3 gives -17.7%, or today’s S&P crashing to around 1678.  Our option would then be worth $11,700 at expiration.
    • Extension: what about volatility? If we are indeed down 17% on the S&P, we can’t expect implied volatility to remain 13% annualised.  Though the VIX wasn’t around in 1987, estimates of implied volatility around Black Monday were about 170% annualised.  Suppose we assumed we bought the nickel option today, then the crash happened; suppose further the volatility expanded to 170% annualised.  Our option would now be worth about $17,500 with the extra vol.  If we’re playing for this scenario, we might actually prefer the options with greater DTE…but I’m getting too complicated.
  • Our expectancy, then: (1/5500) * ($11,700) – (1 – (1/5500)) * ($5) = $(2.87), or $(0.57) for each $1 invested.  I expect to lose slightly less than the lottery.

In sum, this fun little exercise has taught me a few things:

1. Lotteries are still terrible ways to make money.  The expectation is horrible.
2. Buying deep OTM options is also a pretty terrible way to make money.  The expectation is nearly as bad.
3. Statistics are fun when the numbers involved are ludicrous.  I reckon almost every one of the stats mentioned above is dubious in one way or another.  So fun for a thought experiment, but never for creating an actual investment strategy.