How Does SVXY Work?

Updated: Aug 23rd, 2016 | Vance Harwood

Just about anyone who’s looked at a multi-year chart for a long volatility fund like Barclays’ VXX has thought about taking the other side of the trade. ProShares’ SVXY is an Exchange Traded Fund (ETF) that allows you bet against funds like VXX while avoiding some of the issues associated with a direct short.

To have a good understanding of how SVXY works (full name: ProShares Short VIX Short-Term Futures ETF) you need to know how it trades, how its value is established, what it tracks, and how ProShares makes money with it.

How does SVXY trade?

  • SVXY trades like a stock.  It can be bought, sold, or sold short anytime the market is open, including pre-market and after-market time periods.  With an average daily volume of 8 million shares its liquidity is excellent and the bid/ask spreads are a few cents.
  • SVXY has options available on it, with five weeks’ worth of Weeklys and strikes in 50 cent increments.
  • Like a stock, SVXY’s shares can be split or reverse split—but unlike VXX (with 4 reverse splits since inception) SVXY has done two 1:2 splits to bring its price down into optimum trading levels. Unlike Barclays VXX, SVXY is not on a hell-ride to zero.
  • SVXY can be traded in most IRAs / Roth IRAs, although your broker will likely require you to electronically sign a waiver that documents the various risks with this security.  Shorting of any security is not allowed in an IRA.

How is SVXY’s value established?

  • Unlike stocks, owning SVXY does not give you a share of a corporation. There are no sales, no quarterly reports, no profit/loss, no PE ratio, and no prospect of ever getting dividends.  Forget about doing fundamental style analysis on SVXY. While you’re at it forget about technical style analysis too, the price of SVXY is not driven by its supply and demand—it is a small tail on the medium sized VIX futures dog, which itself is dominated by SPX options (notional value > $100 billion).
  • The value of SVXY is set by the market, but it’s closely tied to the daily percentage moves of the inverse of an index (S&P VIX Short-Term Futurestm) that manages a hypothetical portfolio containing VIX futures contracts with two different expirations. Every day the index methodology specifies a new mix of VIX futures in the portfolio. On a daily basis SVXY moves in the opposite direction of the index, so for example, if the index (ticker SPVXSPID) moves up 0.3%, then SVXY will move down precisely 0.3%. This post has more information on how the index itself works. The index is maintained by S&P Dow Jones Indices.
  • As is the case with all Exchange Traded Funds, SVXY’s theoretical share value is just the dollar value of the securities and cash that it currently holds divided by the number of shares outstanding. This theorectical value is published every 15 seconds as the “intraday indicative” (IV) value. Yahoo Finance publishes this quote using the ^SVXY-IV ticker. The end of day value is published as the Net Asset Value (NAV).  The NAV is computed at 4:15 ET, not the usual market close time of 4:00 ET, because VIX Futures don’t settle until 4:15.
  • If the trading value of SVXY diverges too much from its IV value wholesalers called Authorized Participants (APs) will normally intervene to reduce that difference. If SVXY is trading enough below the index they start buying large blocks of SVXY—which tends to drive the price up, and if it’s trading above they will short SVXY.  The APs have an agreement with ProShares that allows them to do these restorative maneuvers at a profit, so they are highly motivated to keep SVXY’s tracking in good shape.

What does SVXY track?

  • SVXY makes lemonade out of lemons.  The lemon in this case is the index S&P VIX Short-Term Futurestm that attempts to track the CBOE’s VIX® index—the market’s de facto volatility indicator. Unfortunately, it’s not possible to directly invest in the VIX, so the next best solution is to invest in VIX futures. This “next best” solution turns out to be truly horrible—with average losses of 5% per month. See this post for charts on how this decay factor has varied over time. For more on the cause of these losses see “The Cost of Contango”.
  • This situation sounds like a short sellers dream, but VIX futures occasionally go on a tear, turning the short sellers’ world into something Dante would appreciate.
  • Most of the time (75% to 80%) SVXY is a real money maker, and the rest of the time it is giving up much of its value in a few weeks—drawdowns of 80% are not unheard of. The chart below shows SVXY from 2004 using actual values from October 2011 forward and simulated values before that.

SVXY hist Aug16

 

  • Understand that SVXY does not implement a true short of its tracking index. Instead, it attempts to track the -1X percentage inverse of the index on a daily basis.  To maintain this -1X behaviour the fund must rebalance/reset its investments at the end of each day.  For a detailed example of how this rebalancing works see “How do Leveraged and Inverse ETFs Work?
  • There are some very good reasons for this rebalancing, for example, a true short can only deliver at most a 100% gain and the leverage of a true short is rarely -1X (for more on this see “Ten Questions About Short Selling”. SVXY, on the other hand, is up 600% since its inception and it faithfully delivers a daily percentage move very close to -1X of its index.
  • Detractors of the daily reset approach correctly note that SVXY and funds like it (XIV) can suffer from volatility drag. If the index moves around a lot and then ends up in the same place SVXY will lose value, whereas a true short would not, but as I mentioned earlier, true shorts have other problems.  Even with volatility drag daily reset funds don’t always underperform. If the underlying index is trending down, they can deliver better than -1X cumulative performance. The chart below shows the relative one-year performance of SVXY and a true short starting with $1K invested in January for 2011 through 2016.

SVXYvsShort

How does ProShares make money on SVXY?

  • An Exchange Trade Fund like SVXY must explicitly hold the appropriate securities or equivalent swaps matching the index it tracks. ProShares does a very nice job of providing visibility into those positions. The “Daily Holdings” tab of their website shows how many VIX futures contracts are being held. Because of the -1X nature of the fund, the face value of the VIX futures contracts will be very close to the negative of the net “Other asset / cash” value of the fund.
  • ProShares collects a daily investor fee on SVXY’s assets. The fee is stated as a 0.95 annual fee, but it’s implemented by subtracting 0.95/365 of a percent from each share’s value every calendar day. With current assets at $280 million this fee brings in around $2.5 million per year. That should be enough to be profitable, however I suspect the ProShares’ business model includes revenue from more than just the investor fee.
  • Exchange Traded Funds like SVXY recoup transaction costs in a non-transparent way. Transaction costs are deducted from the fund’s cash balance—resulting in a slow divergence of the fund’s IV value from the theoretical value of the index that it’s tied to. This differs from the approach that Exchange Traded Notes (ETN) use, their theoretical value is directly tied to the moves of the index itself, so the ETN issuers must pay for transaction costs other ways (e.g., out of the annual investor fee, or other explicit fees). In the case of SVXY, this hidden transaction fee has averaged around 0.28% per year.
  • One clue on ProShares’ business model might be contained in this sentence from SVXY’s prospectus:
    “A portion of each VIX Fund’s assets may be held in cash and/or U.S. Treasury securities, agency securities, or other high credit quality short-term fixed-income or similar securities (such as shares of money market funds and collateralized repurchase agreements).”  Agency securities are things like Fannie Mae bonds. The collateralized repurchase agreements category strikes me as a place where ProShares might be getting significantly better than money market rates. With SVXY currently able to invest around $250 million this could be a significant income stream.
  • I’m sure one aspect of SVXY is a headache for ProShares. Its daily reset construction requires its investments to be rebalanced at the end of each day, and the required investments are proportional to the percentage move of the day and the amount of assets held in the fund. SVXY currently holds $280 million in assets, and if SVXY moves down 10% in a day (the record negative daily move is -24%, positive move +18 %) then ProShares must commit an additional $28 million (10% of $280 million) of capital that evening. If SVXY goes down 10% the next day, then another $25 million capital infusion is required.

SVXY won’t be on any worst ETF lists like Barclays’ VXX, but its propensity for dramatic drawdowns (e.g. 69% in the 2015/2016 timeframe) will keep it out of most people’s portfolios. Not many of us can handle the emotional stress of holding on to a position with huge losses—even though the odds support an eventual rebound.

It’s interesting that an investment structurally a winner albeit with occasional setbacks is not as popular as a fund like VXX that’s structurally a loser, but holds out the promise of an occasional big win.

It seems that people would rather bet on a correction, rather than the slow grind of contango.

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Backtests for VelocityShares’ BSWN, LSVX, and XIVH Exchange Traded Notes

Updated: Aug 11th, 2016 | Vance Harwood

I have generated simulated end-of-day close indicative share values (4:15 PM ET) for VelocityShares’ BSWN, LSVX, and XIVH Exchange Traded Notes (ETNs) from March 31st, 2004 through July 14th, 2016.

  • BSWN VelocityShares VIX Tail Risk ETN
  • LSVX  VelocityShares VIX Variable Long/Short ETN
  • XIVH    VelocityShares VIX Short Volatility Hedged ETN

These simulated ETN histories are useful if you want to backtest various volatility strategies using these funds starting in 2004. The chart below show the simulated values with a logarithmic vertical axis so that you can see a reasonable amount of information for each fund.

Sim shr BSWN-LSVX-XIVH

For a description of how these funds work, see this post.

The algorithms for generating these ETN’s values are documented in their combined prospectus and the underlying S&P 500 VIX Futures Long/Short Strategy Index methodology.  The short term VIX futures index SPVXSP is used as the base index and all the specific fund indexes are calculated using it.  The respective fund underlying indexes are:

ETN Ticker Underlying Index
BSWN SPVXTRST
LSVX SPVXVST
XIVH SPVXVHST

I calculate my version of SPVXSP directly from historic VIX futures settlement data. This futures data is available on this CBOE website—in the form of 100+ separate spreadsheets.  To make the calculation of this index tractable I created a master spreadsheet that integrates the futures settlement data into a single sheet.  See this post for more information about that spreadsheet.

My simulated values very closely track the published values of the underlying indexes (less than +-0.01% error) from the December 20, 2005 index inception date through the present, so I have very high confidence in the accuracy of these simulations.

These ETN prices reflect the contribution of 91-day treasury bills on their overall performance.   Thirteen-week Treasuries annualized yields are running around 0.30% in 2016, but in February 2007 they yielded over 5%— things have changed a bit…

I am making these 3 simulation spreadsheets available for purchase, individually, or as a single spreadsheet with all three funds. These spreadsheets do not include the index calculations themselves. The only formulas included are the ones required to go from the underlying index of each fund (e.g. SPVXVHST for XIVH) to the final ETN values including fees.

In addition to the 1.3% annual fee, these funds charge a “Futures Spread Fee” that can change on a daily basis.  There is no historical data available for the fee before the funds’ inception and I have not provided for changing the fee on a daily basis in the spreadsheet.  I have made a guess that this fee will effectively add 0.3% to the overall annual fees.  This guess can be changed for each fund at an overall level in the spreadsheet, however changing it will require regenerating a “seed” value to re calibrate the simulation to the actual IV levels.  Details on how to do that will be included in the readme sheet.

For more information on the spreadsheets see this readme.

If you can’t see the pricing/ purchasing information at the bottom of this post please click this link.

If you purchase the spreadsheet you will 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 can download the spreadsheet.  Please email me [email protected] if you have problems, questions, or requests.  It’s easy to miss the “Return to Six Figure Investing” link.  If you don’t get it / can’t find it please email me and I will reply with the spreadsheets you purchased attached.

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How Do VelocityShares’ BSWN, LSVX, & XIVH Work?

Updated: Aug 7th, 2016 | Vance Harwood

Not Just Long or Short and No Signals

The indexes that power VelocityShares new BSWN, LSVX, and XIVH funds have been live since 2011, but they haven’t been directly accessible via exchange traded products until July 2016.  The goals of these new funds are pretty straightforward, on the long side BSWN & LSVX track upside volatility with some fidelity while minimizing decay costs, while XIVH captures the premium typically available by being short volatility, but with a hedging component to reduce drawdowns during corrections and bear markets.

The technology backbone of these VelocityShares funds is quite simple—and counter-intuitive. Each of these Exchange Traded Notes (ETNs) tracks a mix of both long and short VIX futures. You’d think that the short and long positions would just cancel each other out—but they don’t.

The long positions are managed as a 2X leveraged fund (similar to TVIX), and the short positions as a –1X inverse fund (similar to XIV). Both long and short positions use daily end-of-day rebalancing to keep their daily percentage moves consistent with the moves of their underlying index (short term VIX Futures—SPVXSP) and their leverage factors. By selecting the weights of the long and short positions in these funds VelocityShares positioned them at three different points on the volatility spectrum—ranging from volatility spike catcher all the way to hedged inverse volatility.

The baseline allocations / strategies for these three funds are shown below:

Ticker  2X long % -1X short % Strategy
BSWN 45% 55% Tail Risk  (strong long bias)
LSVX 33.33% 66.67% Long / Short (long bias)
XIVH 10% 90% Hedged short volatility   (strong short bias)

The chart below shows the simulated behavior of the two longish funds against the popular VXX and 2X leveraged UVXY / TVIX.

BSWN LSVX Dec05

This simulation shows that the BSWN and LSVX portfolios managed to retain an impressive amount of value ($368 & $1724 respectively) over an eleven year period while the VXX and UVXY/TVIX portfolios withered away to nothing ($2.86, $0.00008) respectively).

The next chart shows the simulated behavior of XIVH compared to the popular XIV and SVXY -1X inverse volatility funds.

 

XIVH XIV Dec05

Wow, quite a ride—including a peak value of more than $12K for the XIVH portfolio followed by a drawdown to half of that in less than 2 years.

Over this time span, the 2008/2009 bear market was the key differentiator between these two funds. The 2X long allocation of XIVH’s portfolio beautifully protected it during the financial crisis.

The chart below compares the two funds starting immediately after the 2008/2009 bear market.

XIV vs XIVH apr09

 

When starting in April 2009 XIV/SVXY has better absolute performance, but XIVH’s volatility and drawdown percentages are better. XIVH’s drawdown percentage during the 2011 correction was half of XIV/SVXY’s.

The Trend is Their Friend

 Leveraged funds actually perform better than their leverage factors in trending markets. Consider the example of a hypothetical 2X leveraged fund where the underlying fund goes up 10% a day for three days:

Day Underlying % Underlying Underlying Cumulative % gain 2X leveraged

With daily reset

2X fund

Cumulative % gain

Day 0 100 100
Day 1 +10% 110 10% 120 +20%
Day 2 +10% 121 21% 144 +44%
Day 3 +10% 133.1 33.1% 172.8 +72.8%

 

Instead of the 66.2% gain you might have expected from the 2X leveraged fund, it went up 72.8%—a 6% bonus. See this post for a real world example of how the 2X long TVIX overachieved in this fashion.

Leveraged funds can also lose less than you’d expect in markets that are moving against them—if the underlying is strongly trending against them the percentage losses in the leveraged funds will be less than the leverage factor would indicate.

Winner Take All

The other key attribute of these funds is a “winner take all” characteristic. If there is a volatility spike the 2X long portion of the portfolio grows rapidly and the inverse portion shrinks rapidly.  Fund allocations (e.g., initially 45% long, 55% short) dynamically shift towards the long side of things during a volatility spike –exactly what you’d like to see happen. Conversely, if volatility is slumping the funds dynamically shift their allocations towards the short side.

Some Reset Required

 There are some downsides to using this long / short technology.  With an unconstrained “winner take all” strategy the losing side of the portfolio shrinks to the point where there’s nothing to build on when the trend reverses—and the trend will always reverse. To address this issue the funds do periodic resets back to their initial weighting factors. However, this resetting introduces another problem—path dependency. Not only does it matter how much VIX futures move in price, it also matters when the VIX futures move relative to the reset schedule of the funds. For example, if a volatility spike occurs right before a reset it can have a significantly different impact on the fund’s value compared to a spike right after a reset.

The funds take a two-tiered approach to mitigate path dependency. Each of the funds is rebalanced back to its target weighting quarterly and there’s a weekly rebalance of a rotating subset of assets within the funds.

Volatility of Volatility is a Drag

Another downside of these funds is that they don’t do well if the values of the underlying VIX Futures are choppy. If VIX futures are up strongly one day, and down sharply the next these funds will suffer—both their trend compounding and their “winner-take-all” strategies take multiple days of trending action to work well. When volatility of volatility is high it drags down the performance of all leveraged funds—both long and short.

Not Great at Black Swans

Volatility spikes that ramp up quickly (e.g., flash crashes, overnight geopolitical / economic surprises) are not captured particularly well by the longish funds (BSWN, LSVX). If these funds are operating close to their target weights then the short side will significantly drag down the performance of the 2X long side during quick volatility jumps.

The short volatility oriented fund, XIVH would be at some risk of termination if a historically unprecedented volatility spike (e.g., VIX spike of >70%) occurred.  These funds terminate if the intraday indicative value drops 80% or more from the previous day’s close.  If this situation occurs the holder would likely receive somewhere between 0% and 20% of their previous day’s holdings in cash (no lower than zero). XIVH would be significantly less likely to terminate than standard inverse volatility funds (e.g., XIV/SVXY) because it maintains a 2X long position also.

No Signals Need Apply

Most volatility funds that aren’t just pure long or short plays rely on algorithms to monitor market parameters (e.g., VIX moving averages) and then generate signals that cause allocations to be shifted.  I’ve listed some of these funds and the parameters they monitor.

Tickers Parameters Monitored
VQT, PHDG S&P 500 volatility, VIX 5 & 20-day moving averages, Fund losses
VQTS S&P 500 volatility, VIX Futures Term Structure
XVZ VIX term structure (VIX/VXV)
VIXH VIX Future absolute prices

BSWN, LSVX, and XIVH and two other VelocityShares funds (TRSK and SPXH) do not make allocations based on signals, nor do they rely on any characteristics outside the underlying short term futures themselves. They don’t shift allocations based on the term structure between short and medium-term VIX Futures, VIX term structure, VIX volatility or S&P 500 historic volatility.

I think this self-sufficiency is a significant advantage.  The volatility landscape is relatively young, with VIX futures only trading since 2004. The interplay between VIX futures of various expirations, the VIX, and equity markets has evolved over time and I don’t see any indication those relationships have stopped shifting.  By avoiding linkages to these factors BSWN, LSVX, and XIVH should exhibit more consistent behavior over time compared to the other strategy funds.  But to be clear, they do have their dependencies—specifically the trendiness and volatility of the underlying short term VIX futures index.

Complicated Fee Structure 

The issuer of these ETNs, the Swiss bank UBS, has levied a complex transaction fee in addition to the annual fee (1.3%).  The “Futures Spread Fee” captures some of the costs associated with the daily rebalancing of the funds’ long and short positions.  I’m guessing this fee will increase the annual costs associated with owning these funds by around 0.3%.

Low Volume and Low Asset Base 

Initially these funds will have low volumes and relatively low asset levels.  This naturally leads to concerns about liquidity.  In reality, the liquidity of all Exchange Traded Products is critically dependent on the nature of the underlying securities they track.  If the underlying index of an ETP is based on small-cap stocks in a 3rd world country then great care is required for all but the smallest trades, however in the case of these VelocityShares ETPs, their underlying is short term VIX futures—which are high volume, very liquid securities. As a result, traders will find that with a little care they can make large purchases or sales without significantly shifting the prices of these funds. For more information and suggestions on trading low volume funds see Evaluating ETP liquidity and Trading Low Volume ETPs.

Hedging Hurdle—How Much Decay?

Funds that are effectively long volatility are attractive candidates for hedging equity portfolios because volatility reliably spikes up when stocks plummet. Unfortunately when the market isn’t panicking long volatility positions often decay quickly. One approach to get around this decay is to apply these hedges only during high-risk times. However, corrections / bear markets are notoriously difficult to predict—if crystal balls were that good there’d be no need for hedging. Since BSWN and LSVX’s decay rates are relatively low holding them all the time becomes a viable option.

The chart below shows historical monthly decay rates.

This simulation shows that the decay of VelocityShares’ BSWN and LSVX would have been dramatically lower than TVIX/UVXY and VXX during relatively quiet markets—BSWN decaying mostly in the 1% to 2% per month range and LSVX running in the -1% to +1%  range.

How Much Oomph do BSWN and LSVX Have?

While low ongoing losses are very important for any potential hedge strategy it’s also important to know how much these funds will likely jump when a volatility event occurs.  This jump data helps establish the required “hedge ratio”—the percentage of a portfolio’s assets that should be held in a long volatility fund to compensate for the losses in the rest of the portfolio during a market correction / crash.

The chart below shows the peak percentage increases in VIX, UVXY, VXX, BSWN, and LSVX during some historical volatility spikes—some of which lasted months, others a day or two.

Multi-day Vol Bumps

 

Not surprisingly, in the jump category UVXY is the top performer for investible securities, with VXX coming in second most of the time. BSWN and LSVX perform very well during longer, more severe events—not a bad characteristic to have.

Traversing the Volatility Landscape 

Volatility investing has been a minefield for investors. If you’re long volatility you expose yourself to devastating decay losses if your timing isn’t perfect. Alternately if you’re short volatility you risk being blown up by vicious volatility spikes.

VelocityShares’ long/short strategy funds allow us to mitigate risk on both sides of the spectrum using a technology that doesn’t rely on backtested volatility signals or VIX future term structure assumptions. The indexes the BSWN, LSVX, and XIVH funds are based on have been published since 2011 and have performed appropriately through a wide range of market conditions.  I expect them to continue doing their jobs well.

 

Resources

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High Sigma Events—They’re Not All Black Swans

Updated: Jul 27th, 2016 | Vance Harwood

After every crash or major geopolitical event that roils the market we are exposed to graphics like this one containing sigma numbers:

Black Swan

 

The message associated with these charts is usually, “We should be very worried because the events that just occurred were really unlikely.”

The reader, on the other hand, should be thinking: the person that wrote this really doesn’t understand statistics or Black Swans.

What is Sigma?

The common usage of the term “sigma” in statistics stems from the use of the lower-case Greek letter sigma to denote volatility.  A standard deviation calculation is usually used to compute volatility, so sigma and one standard deviation have become interchangeable.  A standard deviation is an always positive measure of how much variation there is in a data set. If the data doesn’t move around much (e.g., daily high temperature in Hawaii) the standard deviation will be low.  If the data moves around a lot (e.g., the CBOE’s VIX), then the standard deviation will be higher.

The calculation (slightly simplified) of the standard deviation is not all that scary:

  1. Compute the average of the data set
  2. Subtract the average from every data point (which will give you both positive and negative differences) and then square it.
  3. Average the squared differences for all the data points, and then take the square root

Once computed the standard deviation provides a succinct way to describing how widely a specific data point differs from the average. For example, if the standard deviation of daily high temperatures in Hawaii is 4 degrees, then a cold day with a high 12 degrees below average would be a 3 standard deviation, or “3 Sigma” event.

Sigma and the Normal Distribution—Not Siamese Twins

The standard deviation calculation makes NO assumptions about how the data points are arranged around the average—what statisticians call the distribution. The standard deviation calculation does not assume, or require, that the distribution is normal (Gaussian) or any one of the many other different possible distributions (e.g., Laplace, Cauchy, Parabolic Fractal).

Unfortunately, even though there’s no mathematical linkage between the standard deviation and the normal distribution, most people assume the two are locked together.  For example, you may have heard of “6-sigma quality”, which strives to achieve quality levels of fewer than 3.4 defective features per million opportunities. This percentage assumes a normal distribution—not a bad assumption for flaws in a complex manufacturing process. However if the distribution of failures happens to be Laplacian, then 6-sigma quality might exhibit 860 defective features per million–not such a great achievement.

Nassim Taleb in his book “The Black Swan” calls this tendency to assume the normal distribution the Ludic Fallacy.  He suggests this belief stems from people inappropriately extending the structured randomness of games and gambling into the real world processes where complexity and human psychology reign.

Financial Indexes are Typically Not Normally Distributed

Most of the time variations in financial markets look like what you’d expect from a normal distribution.  The chart below shows returns of the S&P 500 since 1950 compared to what the normal distribution predicts.

LP-ActualsvsNorm-linear

Although the central peak of the historic data is higher than the normal distribution, and the shoulders are a bit narrower, the match is usually considered good enough. Financial analysts usually assume the normal distribution because they are familiar with it and there’s a rich tool set for it (e.g., Excel supports it directly with built-in functions).  For typical situations it works well enough.

The Devil is in the Assumptions

 If a process has 30 or more sub-processes or components within it and these components are independent from each other then it’s very likely the distribution of that process will be normal.

While it’s common for financial markets or metrics to have 30 or more components it’s incorrect to assume they’re independent—especially when emotions are running high.  In very stressful times market participants abandon any pretense of independence and start moving in lockstep. The chart below shows the correlation (a statistical measure of independence) between two exchange traded funds that track sectors in the S&P 500. A correlation of one means the sectors are in lockstep, a correlation of zero indicates they’re independent.

XLI-XLP-correl histo

As you can see the sectors are usually not independent.  And as a result of these correlations, the S&P’s returns are not normally distributed. Not only is the central peak too high, and the shoulders too narrow, but the tails of the distribution on both the positive and negative side (impossible to see on most histograms) are much fatter than the normal distribution.

So if the normal distribution is not a good match to financial returns which one should we be using?

Using the Laplace Distribution to Assess Probabilities

Mathematically it’s pretty easy to come up with distributions that are better matched to the S&P’s distribution than the normal, but it’s not possible to prove which one is best—there’s just not enough data to settle the matter.

One distribution that works well is the Laplace distribution (which I describe here). It has a good match to historical data and it serves to illustrate how different some distributions are from the normal. The chart below shows how the classic Laplace distribution is a better fit to the central peak of the historic S&P 500 data.

Act vs Normal vs Classic Laplace

 

The big disconnects between the historic data and the normal distribution are in the tails.  The table below shows the differences for a range of sigma levels. The “Matched Laplace” distribution used is one that’s tuned to better match the tails of the S&P 500 distribution.

Greater Than
Plus / Minus
Sigma Levels
Expected Frequency

S&P 500

Matched Laplace

Expected Frequency

Normal

Distribution

>+-1 76 events per year 80 events per year
>+-2 23 events per year 12 events per year
>+-3 7 events per year 0.7 trading events per year
>+-4 2.2 events per year 0.016 events per year
>+5 7 events in 10 years 0.0014 events in 10 years
>+-6 2 events in 10 years 5×10-6 times in 10 years
>+-7 6  events in 100 years 6×10-8 times in 100 years
>+-8 2 events in 100 years 3×10-11 times in 100 years
>+-9 6 events in 1000 years 6×10-14 times in 1000 years
>+-10 2 events in 1000 years 4×10-18 times in 1000 years
>+-11 5 events in 10,000 years 9×10-22 times in 10,000 years
>+-12 2  events in 10,000 years 9×10-27 times in 10,000 years

 

For sigma levels lower than four the normal and Laplacian distributions aren’t dramatically different, but the expected frequencies diverge rapidly as we evaluate higher sigma levels. For events with sigmas as low as six or seven, the normal distribution predicts their odds of occurrence as incredibly low. Even with the Laplace distribution the probability of a sigma event higher than seven or eight is unlikely in a lifetime.

 Interpreting Sigma Events Above Seven

Common probability distributions predict that events with sigma levels above seven are very unlikely—and yet we see lots of them.   I think the potential causes of these events fall into the following four categories:

  • System Failures
  • Externally Driven
  • Low Liquidity Metrics
  • Stuff Happens

System Failures (e.g., Flash Crashes)

 The 2010 Flash Crash and the 1987 Black Monday Crash (21 sigma) were both system failures where the combination of flawed technology and run-away human emotion triggered unprecedented downswings.  In both cases the market makers stepped away from the market during the worst times—exacerbating an already bad situation.

Everyday variations in markets can’t be used to predict system failures—there’s no connection between those variations and the things (e.g., software defects, unanticipated interactions between subsystems) that cause system crashes. When systems do crash the obvious questions are how much damage was done, what was the root cause, and what can be done to prevent future failures.  While huge amounts of money are lost during these failures (at least on paper), some people benefit (e.g., Taleb made his first fortune from the 1987 crash) and the long-term effects are often minor. Despite the 22% drop during the October 19th crash the 1987 market ended up with a small overall gain for the year.

Externally driven (e.g., Forex shocks, Bank Rates)

In 2015 when the Swiss National Bank stopped trying to cap the Swiss Franc exchange rate to the Euro the Franc jumped 19% (180 sigma) essentially instantaneously relative to the Euro. The British Pound dropped 8.1% (15 sigma) in the confusion after the Brexit vote.  The everyday volatility of foreign exchange rate or an overnight interbank lending rate is clearly not a good predictor of the macroeconomic forces that ultimately drive those rates.  It’s like trying to use daily vibration levels in a car to predict auto accidents.

Low Liquidity Metrics (e.g., VIX, PE ratios)

The CBOE’s VIX index is fertile ground for producing high sigma events. Prognosticators pore over single and multiple day increases looking and often finding high sigma events useful for supporting their oft-repeated contention that the system is about to collapse.  Not only does the VIX spike up frequently, it often collapses after emotions subside—offering even more high sigma events to work with.

A key characteristic of the VIX is that unlike stocks or currencies it impossible to invest in it directly.  The best you can do to follow the VIX is trade large quantities of SPX options spread over dozens, or even hundreds of strike prices.  Things are further complicated by the fact that the VIX is calculated using mid prices, halfway between ask and bid prices, but real trades aren’t constrained to trade at that point.  Especially during times of market stress buyers must pay significantly more, and sellers get significantly less than the midpoint price.

Because there’s not an easy way to hedge or monetize it, the VIX acts like a market with low liquidity.  High demand during fearful times (usually for S&P 500 puts) rapidly drives up the index, and when the crisis has passed it collapses.

It hasn’t happened yet, but I wouldn’t be surprised to see a daily +100% move in the VIX (15 sigma).  The index can get as low as 10 or 12 when the market is quiet and has averaged around 20 over the long term.   A major geopolitical event / disaster after the VIX closes at a low level could quite conceivably result in the VIX opening in the 20 to 24 range—doubling in value and yet very close to its long-term average.

The VIX generates high sigma events when people rush to insure their portfolios, and also when they lose interest and wander off.  This behavior offers entertainment value but is not particularly informative, and definitely not predictive.

Stuff Happens

Physicists have a saying: “If something can happen it will.”  Given enough time low probability events will happen.  Thirty-two consecutive reds occurred on a roulette table in 1943—the odds of that happening are around 24 billion to one.   However, I’m not aware of any high sigma financial event that is best explained as a truly random event.  All the ones I’ve looked at appear to be explained best by one or more of the first three causes mentioned.

Are High Sigma Events Ever Predictive?

At least one high sigma event did foreshadow the 2008 meltdown—the 2007 jump in the 3-Month LIBOR OIS spread (6-sigma).  In Jack Schwager’s book Hedge Fund Market Wizards there’s a fascinating interview with Colm O’Shea. When the LIBOR spike occurred (more than a year before the 2008 travails) O’Shea saw it as a clear signal of the beginning of the end for the housing / financial bubble and shifted his investments.

It’s prudent to evaluate high sigma events as possible leading indicators of troubles ahead but recognize that virtually all these events reflect disruptions that have just occurred or are meaningless noise.

High Sigma Exhaustion

It’s an inherent survival skill to notice unusual events. For a savanna dweller, an atypical movement in the savanna grass might be a snake or a lion—well worth some focused attention. In the same way, investors should be monitoring their financial environment for threats. But focused attention requires a lot of energy—always a scare resource.

In the financial world attending to too many cries of “Wolf!!” will just leave us exhausted, paranoid, and vulnerable. We need to filter the cacophony of alerts/alarms we receive to determine real significance.

Specifically:

  • Are probabilities being assessed correctly? Most financial processes are not normally distributed.
  • Is the event a reasonable response to a system failure or a macroeconomic development?
  • Is the new value extreme, or is it within historic ranges? If values remain within historic ranges it’s likely that the damage isn’t that severe.
  • Is there an informed analysis showing the linkage between the event and real economic factors? If not, then you should suspect there’s an ideology being pushed, often unaccompanied by any coherent economic analysis or any accountability on why an oft-repeated prediction is being rolled out once again.

Being Antifragile

Saving some energy by filtering will allow us to focus on what Taleb recommends relative to Black Swans—rather than try to predict them, figure out how to prevent them, or mitigate their effects.  Build systems/portfolios that are tolerant of failures/unexpected events (Taleb calls systems with this attribute “antifragile”).

And probably most importantly, don’t assume something won’t happen because the computed probabilities are very low.  Those computations often severely underestimate the true risk.  We only need to look the failures of Long-Term Capital Management and the collapse of the Mortgage Backed Security market in 2008 to see the impact of underestimating risk.



Monthly and Yearly Decay Rates for Long Volatility Funds

Updated: Jul 31st, 2016 | Vance Harwood

While it’s certain that short-term volatility exchange traded products (ETPs) like VXX, TVIX, and UVXY are doomed to march towards zero, their decay rates are not consistent. Things like bear markets and big corrections can cause big upward swings. On the downside, the term structure of VIX futures and the volatility of volatility can significantly impact decay rates in monthly and yearly time frames.

The charts below give a graphical history of their decay rates. With each of them I’m making trade-offs between reducing noise (averaging out normal market action) and the ability to see medium term trends. Each data point on the first chart is computed using the cumulative gain or loss over the previous six months and a monthly compounding period.

 

1 + 2X vol monthly

None of these ETPs existed before 2009 (the first one, VXX started in January 2009), so I used my simulations based on historical VIX futures data to generate the pre-inception data.

The yearly percentage chart below uses a monthly moving average for all the price points and then uses the result for each date and the price a year prior to compute the simple percentage increase or decrease.

Vol Yearly Percent Loss

 

Despite eye-watering decay rates these funds are increasing in popularity.  I’m not sure why (except for the possibility of shorting them).

They are one of the few investments that will reliably go up when the market has a significant drop, but unless your timing is exquisite the decay rates on these ETPs will make you wish you never laid eyes on them.

 

Quant Corner

  1. The formula used in the first chart is the classic compounding equation:   Compounded Growth = ((End Price/ Start Price)^(1/Period))-1   To obtain monthly compounded returns I use a start price 6 months prior to the end price.  The start price I use is the average of the prices 21 days prior to and including the start date.  The period used in the formula is, of course, six. I negated the results in order to make decay rates show up as positive numbers.
  2. The second chart uses moving average prices (22 trading days) and computes the percentages using End Price / Start Price -1, with the start price one year previous to the end price.  I negated the results in order to make decay rates show up as positive numbers.