To have a good understanding of how the VIX works you need to know how its value is established, what it tracks, what it predicts, and how the CBOE makes money with it.
How is VIX’s value established?
What does VIX track?
How does VIX trade?
What does the VIX predict?
How does the CBOE make money on the VIX?
The VIX frustrates a lot of investors. It’s complicated, you can’t directly trade it, and it’s not useful for predicting future moves of the market. In spite of that, the investment community has adopted it, both as a useful second opinion on the markets, and as the backbone for a growing suite of volatility based products.
But what impresses me is the vision and persistence of the people at the CBOE in advancing the highly theoretical concept of stock market volatility from an academic exercise to an effective commercial product. It was a multidecade project and they were successful.
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This relationship holds for option prices too. With the Black and Scholes model if an option due to expire in 30 days has a price of $1, then the 60 day option with the same strike price and implied volatility should be priced at sqrt (60/30) = $1 * 1.4142 = $1.4142 (assuming zero interest rates and no dividends).
Underlying the sqrt[t] relationship of time and volatility is the assumption that stock market returns follow a Gaussian distribution (lognormal to be precise). This assumption is flawed (Taleb, Derman, and Mandelbrot lecture us on this), but general practice is to assume that the sqrt[t] relationship is close enough.
I decided to test this relationship using actual S&P 500 data. Using an Excel based MonteCarlo simulation^{1} I modeled 700 independent stock markets, each starting with their index at 100 and trading continuously for 252 days (the typical number of USA trading days in a year). For each day and for each market I randomly picked an S&P 500 return for a day somewhere between Jan 2, 1950 and May 30, 2014 and multiplied that return plus one times the previous day’s market result. I then made a small correction by subtracting the average daily return for the entire 1950 to 2014 period (0.0286%) to compensate for the upward climb of the market over that time span. Plotting 100 of those markets on a chart looks like this:
Notice the outliers above 160 and below 60.
Volatility is usually defined as being one standard deviation of the data set, which translates into a plus/minus percentage range that includes 68% of the cases. I used two handy Excel functions: large(array,count) and small(array,count) to return the boundary result between the upper 16% and the rest of the results and the lowest 16% for the full 700 markets being simulated. The 16% comes from splitting the remaining 32% outside the boundaries into a symmetrical upper and lower half. Those results are plotted as the black lines below.
The next chart compares those two lines to the theoretical result which takes the annualized standard deviation of the S&P 500 daily returns from 1950 to 2014 and divides it by the square root of time.
Standard Deviation (N) = Annualized Standard Deviation/ sqrt (252/N)
Where N is the N^{th }day of the simulation.
Impressively close.
Since the simulated boundaries vary some from run to run I collected 32 runs and determined the mean
Very, very close.
So, in spite of the S&P 500’s distribution of results not being particularly normally distributed (see chart below), the general assumption that volatility scales with the square root of time is very appropriate.
Notes:
To have a good understanding of how XIV works (full name: VelocityShares Daily Inverse VIX ShortTerm ETN) you need to know how it trades, how its value is established, what it tracks, and how VelocityShares (and the issuer— Credit Suisse) make money running it.
How does XIV trade?
How is XIV’s value established?
What does XIV track?
How do VelocityShares and Credit Suisse make money on XIV?
XIV won’t be on any worst ETF lists like Barclays’ VXX, but its propensity to dramatic drawdowns will keep it out of most people’s portfolios. Not many of us can sit tight with big loses on the hope that this time will not be different.
It’s interesting that an investment structurally a winner albeit with occasional setbacks is normally not as popular as a fund like VXX that is structurally a loser, but holds out the promise of an occasional big win.
Slow and unsteady is trumped by a lotto ticket.
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It turns out the 21% gain is there, it’s just on such a low basis ($815), that it’s dwarfed by the other curves on the chart (one of the dangers of a chart with linear vertical axis).
My analysis didn’t include dividends nor did I factor in interest that could have been earned while out of the market. I think these two factors would roughly offset each other with the in/out strategies, and including dividends would have boosted the gains of the “always in” strategy.
I also wondered about the choice of 1994 as a starting point. A 20 year time frame is reasonable, and 1994 wasn’t a particularly eventful year, but I repeated the analysis with 63 years of S&P 500 data to see if it made a difference.
Over this timespan the “Sell in May” strategy significantly lagged in the bull markets of the late nineties and 2002 to 2007, and catches up during the depths of the bear markets.
The hold May through September strategy is still a flatliner. It’s hard to see how being in the market during that period helps the buy & hold strategy. A closer look at the yearly distributions yields the answer.
The chart below shows the distribution of the percentage gains/losses by year being invested only May through September.
The average of all the returns is low—a paltry 0.33% yearly gain, but the number of up years out numbers the down years by almost two to one, 40 up years vs 23 down years.
The next chart adds the results (green bars) of being invested except for May through September.
There were only 10 years during this 63 year period where losses during the May through September period weren’t more than offset by the returns from the rest of the year. And in 33 of those years both periods had gains—dramatically compounding the results. It’s this compounding effect that rewards the buy and hold investors.
This final chart shows the performance of the “Sell in May and Go Away” strategy with taxes included, assuming a 28% marginal tax rate.
Since the strategy is never invested for a full year taxes on profits will always be at short term capital gains rates—typically the same as your marginal tax on income. Since you don’t have to pay taxes on gains until the year after you sell the security I assumed that the money earmarked to pay taxes was used for ongoing investment until early April of the next year. Losses were carried forward and used to reduce/ eliminate tax on latter gains.
Including taxes the results of the 63 year “Sell in May” strategy were hammered down 70%—from $100K down to $30K and the 20 year period takes a 30% haircut. So, unless your investments are in a tax protected account the historical performance of this strategy would have been abysmal. Even in nontaxable accounts the long term performance of “Sell in May” would have been inferior.
I think it’s best to stay away from “Sell in May”.
]]>The other half of the portfolio, initiated in July 2009, is still long with a 57% open gain—market breadth has not diverged enough to trigger an exit.
]]>Regarding VXST options:
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The method is still 100% long after the last buy on 11/30/12 when the Russell 2000 closed at 821.92. Since then the ETF that tracks the Russell 2000 (IWM) is up more than 42% with dividends reinvested.
The following chart illustrates the method’s computed potential exit points since the Buy on 11/30/12. The upper line is the weekly close of the Russell 2000 index; the lower line depicts the exit points each week. The method has remained 100% long in the Russell 2000, despite several pullbacks and the usual plethora of predictions that the market is overvalued and cannot go much higher.
Additionally, the original 4% method would have exited and reentered 3 times during this rally, greatly reducing the gain compared to remaining 100% long. Searching for thresholds other than 4% and employing the dynamicallyadjusted trend line have payed off handsomely this time.
The stop was just barely missed on 02/07/14. Since then, the stop has risen more than 23 points and is still rising. The method’s use of breadth suggests that the final top has not been reached. But, sooner or later an exit point will be breached, and soon thereafter, it will be reported here.
]]>For most of 2009 through 2012 the monthly roll cost between the two front month VIX futures used by VXX averaged around 10% when the market was flat or rising (in contango). In 2013 this average cost dropped to around 5% and is headed even lower in 2014.
The monthly roll costs of the longer term VIX futures used by VXZ and ZIV have been declining also, dropping from historic 5%+ highs during 2012 to average slightly above 2% in 2013 and 2014.
This change was driven by a flattening of the VIX Futures term structure. In spite of the front month’s future being about the same value, the later dated futures values have dropped considerably since early 2013.
Why has the curve shifted?
First of all it’s important to remember that VIX futures are ultimately tied to the prices of SPX options of the appropriate month (e.g., August VIX futures are settled to September SPX options). So the real driver is the much larger SPX options market. Not surprising the SPX options premiums have shown the same shift in term structure over this timeframe.
I think this big shift in longer dated volatility is due to two factors:
Both of these factors would tend to depress longer term SPX option prices—and VIX futures prices. It’s possible that this trend will continue, leading to the flattened term structure we saw in 2007 and early 2008 —at the end of the last bull market. But I doubt it; instead I expect the term structure to stabilize until we see another real VIX spike (into the 40’s).
Coincident with the drop in contango, there has been a leveling off of the open interest in VIX futures. I don’t think either of these changes caused the other—but perhaps I’m missing a linkage.
Up until 2013 the open interest had been growing 40% per year, but since then the shorter term open interest has stabilized and the medium term open interest has pulled back around 20%. VIX futures volume on the other hand has continued to set records. Volatility ETP asset growth was a big driver in VIX futures starting in 2009, but currently the total assets in those funds have hit a plateau.
VXX will probably set some new lows in the next month or two, but expect it to moderate its losing ways for a while.
]]>But in real life people rarely borrow something, immediately sell it, and hope to buy it back at a cheaper price. Since we aren’t familiar with selling short many of its characteristics are counterintuitive.
Below I’ve listed some common questions and answers—hopefully they’ll make short selling a little easier to understand.
How do you measure the returns on a short sale?
Return = (Initial Cash flow + Final Cash flow) / Initial Cash flow
So for example if I short 100 shares of XYZ corp at $10, I will see $1000 deposited in my margin account. If I close the position after the stock climbs to $11 my percentage loss is:
(10001100)/1000 = 0.1 A 10% loss.
What is the maximum percentage gain possible on a short sale?
What’s the leverage of a short sale position?
Can I short securities in my IRA?
What happens if I’m short a security when it goes exdividend?
My short sale won’t go through because my broker says shares aren’t available to borrow. What should I do?
What is a short squeeze? Should I worry about it?
What does it mean that the shares I borrow can be recalled at any time?
What is a margin call?
What are the tradeoffs between short selling and buying a resetting inverse exchange traded fund/note (ETF/ETN) on the same security?
On October 1^{st}, 2013 the CBOE introduced the VXST index. VXST uses the same methodology as the CBOE’s VIX® index except that it gives the market’s 9 day expectation of volatility rather than the 30 day. VXST options on VXST futures started trading April 10, 2014.
Some of the tickers related to the VXST are:

The CBOE publishes two intermediate calculations (VSTN & VSTF) that are used to the compute the VXST index. These two indexes do a VIX style calculation with just the nearest SPX weekly options (VSTN) and the next available set of SPX weekly options (VSTF). The VXST is a variance (not linear) interpolation between these two indexes that gives a 9 day expectation of volatility.
At expiration the VXST calculation uses the same option series utilized in the VSTF—the SPX weekly options that will expire in 9 days. These indexes are analogous to the VIN and VIF used in the VIX calculation. For more on this see Calculating the VIX index—the “easy” part.
VXST Futures
On February 13th, 2014 the CBOE started trading futures on their new VXST based index.
Currently the CBOE has opened up futures trading up to 5 sequential weeks of VXST. The futures typically expire on Wednesday morning.
The full ticker symbology for VXST futures is given here. For CBOE delayed quotes the symbol is constructed with one of the 5 preambles: 1VSW, 2VSW, 3VSW, 4VSW 5VSW followed by a “/” and then the futures month and year code (see below for details). So for example the VXST futures expiring 26Feb2014 will have the symbol: 4VSW/G4. The futures are numbered by the week of the month that they expire, so the futures expiring the first week of the month will have the 1VSW preamble, 2^{nd} week 2VSW, and so on.
The settlement price at expiration for VXST futures and options will be computed using the CBOE’s Special Opening Quotation (SOQ) process and will be distributed under the SVRO symbol. This price is not the same as the VXST opening quote on the day of expiration, the SVRO print will occur at least a few minutes after market open. The SVRO price is derived from actual option trade prices, not the split bid/ask price that the index calculation uses.
VXST Options
VXST options started trading April 10, 2014. The most important thing to remember with VXST (and VIX) options is that the underlying is not the index, but rather the future that expires on the same day as the options. As with VIX options the last day of trading is the day before settlement, which is typically a Wednesday. For more on trading VXST options see 13 Things You Should Know About VXST options.
The futures month codes are:
Code 
Month 
F 
January 
G 
February 
H 
March 
J 
April 
K 
May 
M 
June 
N 
July 
Q 
August 
U 
September 
V 
October 
X 
November 
Z 
December 
The year code is just the last digit of the year (e.g., 4 for 2014).