How Does the CBOE’s VIX® Index Work?

Thursday, July 10th, 2014 | Vance Harwood

The CBOE did not create the VIX as an academic exercise, or as a service to stock market prognosticators everywhere.  They created it because they wanted to make money on volatility.  It took them two tries, but the CBOE succeeded in developing a volatility index that forms the backbone of a host of volatility products.  The CBOE offers some of these products, but other companies have built on the success of VIX to offer their own volatility based products.

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?

  • The VIX is a computed index, but unlike indexes such as the Dow Jones Industrial Average or the S&P 500 it’s not computed based on stock prices.  Instead it’s based on option prices.  Specifically the prices of options on the S&P 500 index (ticker SPX).
  • One component in the price of SPX options is an estimate of how volatile the S&P 500 will be between now and the option’s expiration date.  This estimate is not directly stated, but is implied in how much buyers are willing to pay.  If the market has been gyrating like mad option premiums will be high whereas in a quiet market they will be much cheaper.
  • There are various ways of extracting the volatility information from option prices.  The standard way is via the Black & Scholes model, but those equations assume that volatility will be the same for all available options—something that is definitely not the case and they also underestimate the risk of a market crash.
  • The CBOE’s approach combines the prices of many different SPX options (hundreds) to come up with an aggregate value of volatility. Their approach has some particular advantages—more on this later.
  • There are many good posts here, here, and here on the details of the actual VIX calculation, so I won’t reinvent the wheel.
  • The VIX is an estimate of volatility for the next 30 days, but by convention volatility measures in the stock market are reported in terms of annualized volatility.  Volatility doesn’t increase linearly with time, so the annualized number is not 12 times the 30 day estimate but rather ~3.5 times the monthly number. For example if the intermediate VIX calculation computes the expected 30 day volatility to be +-4.3%, the reported VIX will be 15%.  For more on this see Volatility and the Square Root of Time
  • There’s nothing magical about the 30 day estimate.  The CBOE uses the same methodology to compute 9 day (VXST), 93 day (VXV), and 180 day (VXMT) volatility indexes.


What does VIX track?

  • The moves of the VIX track prices on the SPX options market, not the general stock market—this is a key point.  The SPX options market is big, with a notional value greater than $100 billion, and is dominated by institutional investors. A single SPX put or call option has the leverage of around $200K in stock value—too big for most retail investors.
  • Generally options premiums move inversely to the market.  In a rising market, stock prices tend to be less volatile and option premiums low—hence a lower VIX.  Declining markets are volatile (the old saying is that the market takes the stairs up and the elevator down) and option premiums increase.  Much of this increase occurs when worried investors pay a large premium on puts to protect their positions.
  • While S&P 500 option premiums generally move opposite to the S&P 500 itself they sometimes go their own way.  For example, if the market has been on a long bull run without a pullback institutional investors will become increasingly concerned that a correction is overdue and start biding up the price of puts—leading to a rising VIX in spite of a rising S&P.   Historically 20% of the time the VIX moves in the same direction as the S&P 500—so please don’t claim the VIX is “broken” when you see the two markets move in tandem.
  • The daily percentage moves of the VIX tend to be around 4 times the percentage moves of the S&P 500, but unlike the stock market the VIX stays within a fairly limited range.  The all-time intraday high is 89.53 (24-Oct-2008) and the all-time intraday low is 9.39 (16-Dec-2006) with the current methodology.  Within this 10 to 1 range option premiums run from incredibly expensive to dirt cheap.  It’s unlikely that the VIX will go much below 9 because option market makers won’t receive enough premium to make it worth their while.  At the high end things go could go higher (if the VIX had been available in the October 1987 crash it would have peaked around 120), but at some point investors refuse to pay the premium and switch to alternatives (e.g., just selling their positions if they can).  The chart below shows the historical distribution of VIX values since 2002.


    Data Source: CBOE


  • Another way to look at the moves of the VIX is to recognize that it’s almost always a few percentage points higher than the recent historical volatility of the S&P 500.  In general it’s a good assumption that the future volatility of the market will be the same as recent volatility—but obviously this relationship doesn’t always hold.   Option market makers demand a premium to justify the risk they assume in buying / selling options in the face of this uncertainty—and this premium shows up as a VIX value greater than historical volatility.

How does VIX trade?

  • So far, no one has figured out a way to directly buy or sell the VIX index.  The CBOE offers VIX options, but they are based on the CBOE’s VIX Futures not the VIX index itself.  VIX futures usually trade at a significant premium to the VIX.  The only time they reliably come close to the VIX is at expiration, but even then they can settle up to +-5% different from the VIX level at the time.
  • There are 22 volatility Exchange Traded Products (ETPs) that allow you to go long, short, or shades in-between on volatility (see here for the complete list), but none of them do a good job of matching the VIX over any span of time.   For more on ways to trade volatility see  How to Go Long on the VIX, and How to Go Short on the VIX.

What does the VIX predict?

  • In my opinion nothing.  I think it does a good job of reflecting the current emotional state of the overall market (e.g., fearful, optimistic), but I don’t think the SPX options market is any better at forecasting the future than any other market.  We don’t take the value of the Dow Jones Industrial Average as a predictor of the future, so why should the value of the VIX be any different?

How does the CBOE make money on the VIX?

  • The “O” in CBOE stands for options.  In the early 90’s the CBOE wanted to sell options on volatility, but there was a problem—options need to be based on an underlying tradable security to function, and there wasn’t one.   To address that gap the CBOE decided to create an index that could form the basis of a volatility futures market.  Once that market was functioning then options could be introduced.
  • Version one  of the VIX index (now named VXO) was introduced in 1992, but futures based on it were never available.   For a futures market to function the market makers need to be able to cost effectively hedge their positions.  Hedging the 1992 version of the VIX required frequent rebalancing of SPX options that was too expensive to implement.
  • Undeterred the CBOE introduced version 2 in 2003.  The new methodology allowed market makers to hedge their positions with a static portfolio of SPX options that could be held until the VIX futures expired.  VIX Futures started trading in 2004 and in 2006 options on VIX futures were rolled out.
  • VIX futures and options have been very successful with recent daily volumes in the hundreds of thousands. The CBOE is generating hundreds of millions of dollars in annual revenues from these products—primarily from highly profitable transaction fees.

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 multi-decade  project and they were successful.

For more information:

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Volatility and the Square Root of Time

Thursday, June 12th, 2014 | Vance Harwood

It’s not obvious (at least to me) that volatility theoretically scales with the square root of time (sqrt[t]).  For example if the market’s daily volatility is 0.5%, then the volatility for two days should be the square root of 2 times the daily volatility (0.5% * 1.414 = 0.707%), or for a 5 day stretch 0.5% * sqrt(5) = 1.118%.

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 Monte-Carlo simulation1 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 Nth 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.



  1. Returns are expressed as the natural log of the current day’s close divided by the previous day’s close.  The specific daily return used is selected by randomly choosing a number between 0 and 16204 (Trunc(Rand()*16205)) and then using that number to index into the table of SPX returns.  The 16205 constant is the number of trading days from 3-Jan-1950 to 30-May-2014.  As mentioned in the post, the overall daily mean for that period (0.0286%) is subtracted from the result to compensate for the general upward bias of the market over that period.

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How Does XIV Work?

Tuesday, May 13th, 2014 | Vance Harwood

VelocityShares’ XIV and its sister fund ZIV are designed to go up when the volatility of the S&P 500 goes down.  XIV has a shorter time horizon (1 to 2 months) whereas ZIV has a 5 month timeframe

To have a good understanding of how XIV works (full name: VelocityShares Daily Inverse VIX Short-Term 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?

  • For the most part XIV 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 11 million shares its liquidity is excellent and the bid/ask spreads are a penny.
  • Unfortunately XIV does not have options available on it.  However its Exchange Traded Fund (ETF) equivalent, ProShare’s SVXY does, with five weeks’ worth of Weeklys with strikes in dollar increments.
  • Like a stock, XIV’s shares can be split or reverse split—but unlike VXX (with 3 splits since inception) XIV has only split once, a 10:1 split that took its price from  $160 down to $16. Unlike Barclays VXX, XIV is not on a hell-ride to zero.
  • XIV 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 XIV’s value established?

  • Unlike stocks, owning XIV 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 XIV.  While you’re at it forget about technical style analysis too, the price of XIV 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 XIV is set by the market, but it’s tied to the inverse of an index (S&P VIX Short-Term Futurestm) that manages a hypothetical portfolio of the two nearest to expiration VIX futures contracts.  Every day the index specifies a new mix of VIX futures in that portfolio.  For more information on how the index itself works see this post or the XIV prospectus.
  • The index is maintained by the S&P Dow Jones Indices and the theoretical value of XIV if it were perfectly tracking the inverse of the index is published every 15 seconds as the “intraday indicative” (IV) value.  Yahoo Finance publishes this quote using the ^XIV-IV ticker.
  • Wholesalers called “Authorized Participants” (APs) will at times intervene in the market if the trading value of XIV diverges too much from its IV value.  If XIV is trading enough below the index they start buying large blocks of XIV—which tends to drive the price up, and if it’s trading above they will short XIV.  The APs have an agreement with Credit Suisse that allows them to do these restorative maneuvers at a profit, so they are highly motivated to keep XIV’s tracking in good shape.

What does XIV track?

  • XIV makes lemonade out of lemons.  The lemon in this case is an 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.   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%) XIV 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 XIV from 2004 using actual values from November 2010 forward and simulated values before that.


  • To be specific XIV does not implement a true short of its tracking index.   Instead it attempts to track the -1X inverse of the index on a daily basis, and then rebalances investments at the end of each day.  For a detailed example of what this rebalancing looks like see “How do Leveraged and Inverse ETFs Work?
  • There are some very good reasons for this rebalancing, for example a true short can only produce 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”.  XIV on the other hand is up almost 200% since its inception and it faithfully delivers a daily move very close to -1X of its index.
  • Detractors of the daily reset approach correctly note that XIV and funds like it can suffer from volatility drag.  If the index moves around a lot and then ends up in the same place XIV will lose value, whereas a true short would not, but as I mentioned earlier, true shorts have other problems.  However daily reset funds don’t always underperform.   If the underlying index is trending down, they can deliver better than -1X cumulative performance.  For more see “A Hat Trick for Inverse / Leveraged Volatility Funds

How do VelocityShares and Credit Suisse make money on XIV?

  • Credit Suisse collects a daily investor fee on XIV’s assets—on an annualized basis it’s 1.35%.  With current assets at $600 million this fee brings in around $8 million per year.  That should be enough to cover Credit Suisse’ XIV costs and be profitable.  But even if it was all profit it would be a tiny 0.3% of Credit Suisse’s overall net income—$2.6 billion in 2013.  My understanding is that a portion of this fee is passed onto to VelocityShares for their technical and marketing activities.
  • I’m sure one aspect of XIV is a headache for Credit Suisse.  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.   XIV currently holds $600 million in assets, and if XIV moves down 10% in a day (the record negative daily move is -24%, positive move +18 %) then Credit Suisse has to commit an additional $60 million (10% of $600 million) of capital that evening.  If XIV goes down 10% the next day, then another $60 million infusion is required.
  • Unlike an Exchange Trade Fund (ETF), XIV’s Exchange Traded Note structure does not require Credit Suisse to report what they are doing with the cash it receives for creating shares.  The note is carried as senior debt on Credit Suisse’s balance sheet but they don’t pay out any interest on this debt.  Instead they promise to redeem shares that the APs return to them based on the value of XIV’s index.
  • Credit Suisse could hedge their liabilities by shorting VIX futures in the appropriate amounts, but they almost certainly don’t because there are cheaper ways (e.g., swaps) to accomplish that hedge.  ETFs like ProShare’s SVXY can use swaps also, but they often just deal with the futures.  The picture below is a snapshot of their holdings on May 13th,2014.  The parenthesis indicate a short position in the futures.

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.


 For more information 

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Sell in May and Go Away—Not Good for Taxable Accounts

Tuesday, May 6th, 2014 | Vance Harwood

When I first saw a chart similar to the one below in Business Insider I was immediately suspicious.  For example I knew that May through September of 2009 was a period of rapid growth (21%) yet that surge did not seem to show up on the bottom curve (green)—which shows the performance of staying in the market only May through September.  

SIM 20yr-no-tax

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.

SIM 50yr-no-tax

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 flat-liner.  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.

SIM 50yr-rtns-IMS

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.

SIM 50yr-rtns-both

 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.

SIM 50yr-w-tax

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 non-taxable 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”.

Modified Davis Method Moves to 50% Cash

Sunday, April 13th, 2014 | Vance Harwood

The market stumble the end of last week dropped the Russell 2000 enough for Frank Roellinger’s Modified Davis Method to signal a 50% sell.  That portion of the portfolio gained 17.6% since being opened 30-November-2012.  This exit was foreshadowed in the Modified David Method-March 2014 Update 

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.  

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