VIX

VIX is the ticker symbol and the popular name for the Chicago Board Options Exchange's CBOE Volatility Index, a popular measure of the stock market's expectation of volatility based on S&P 500 index options. It is calculated and disseminated on a real-time basis by the CBOE, and is often referred to as the fear index or fear gauge.

CBOE Volatility Index (VIX) 2004–2020.

The VIX Index is a volatility index derived from S&P 500 options,[1] with the price of each option representing the market's expectation of 30-day forward-looking volatility.[1][2] The resulting VIX index formulation provides a measure of expected market volatility on which expectations of further stock market volatility in the near future might be based.[2]

Like conventional indexes, the VIX Index calculation employs rules for selecting component options and a formula to calculate index values.[2][3] Unlike other market products, VIX cannot be bought or sold directly.[4] Instead, VIX is traded and exchanged via derivative contracts (Futures contract, Option (finance)), or derived Exchange-traded fund (ETFs), and exchange-traded notes (ETNs) which most commonly track VIX futures indexes.[5]

In addition to VIX, CBOE uses the same methodology to compute the following related products:[2][3]

  • Cboe ShortTerm Volatility Index (VIX9DSM), which reflects 9-day expected volatility of the S&P 500 Index,
  • Cboe S&P 500® 3-Month Volatility Index (VIX3MSM),
  • Cboe S&P 500® 6-Month Volatility Index (VIX6MSM)
  • Cboe S&P 500 1-Year Volatility Index (VIX1YSM).

Cboe also calculates the Nasdaq-100® Volatility Index (VXNSM), Cboe DJIA® Volatility Index (VXDSM) and the Cboe Russell 2000® Volatility Index (RVXSM).[2]

Specifications

The concept of computing implied volatility or an implied volatility index dates back to the publication of the option valuation model by Black and Scholes in 1973. Just as a bond's implied yield to maturity can be computed by equating a bond's market price to its valuation formula, an option-implied volatility of a financial or physical asset can be computed by equating the asset option's market price to its valuation formula. In the case of VIX, the option prices are the S&P 500 index option prices.

The VIX takes as inputs the market prices of the call and put options on the S&P 500 index for near-term options with more than 23 days until expiration, next-term options with less than 37 days until expiration, and risk-free U.S. treasury bill interest rates. Options are ignored if their bid prices are zero or where their strike prices are outside the level where two consecutive bid prices are zero.[2] The goal is to estimate the implied volatility of S&P 500 index options at an average expiration of 30 days.

Monthly mean of VIX volatility index, 2004-2019

The VIX is the volatility of a variance swap and not that of a volatility swap, volatility being the square root of variance, or standard deviation. A variance swap can be perfectly statically replicated through vanilla puts and calls, whereas a volatility swap requires dynamic hedging. The VIX is the square root of the risk-neutral expectation of the S&P 500 variance over the next 30 calendar days and is quoted as an annualized standard deviation.

The VIX is calculated and disseminated in real-time by the Chicago Board Options Exchange. On March 26, 2004, trading in futures on the VIX began on CBOE Futures Exchange (CFE).

On February 24, 2006, it became possible to trade options on the VIX. Several exchange-traded funds hold mixtures of VIX futures that attempt to enable stock-like trading in those futures. The correlation between these ETFs and the actual VIX index is very poor, especially when the VIX is moving.[6]

VIX Formula

The VIX is a 30-day predictor of volatility given by a weighted portfolio of out-of-the-money European options on the S&P 500:[2]



where is the number of average days in a month (30 days), is the risk-free rate, is the 30-day forward price on the S&P 500, and and are prices for puts and calls with strike and 30 days to maturity.[2][7]

History

The following is a timeline of key events in the history of the VIX Index:

  • 1987 - The Sigma Index was introduced in an academic paper by Brenner and Galai, published in Financial Analysts Journal, July/August 1989.[8] Brenner and Galai wrote, "Our volatility index, to be named Sigma Index, would be updated frequently and used as the underlying asset for futures and options... A volatility index would play the same role as the market index play for options and futures on the index."
  • 1989 - Brenner and Galai's paper is published in Financial Analysts Journal. Brenner and Galai develop their research further in graduate symposia at The Hebrew University of Jerusalem and at the Leonard M. Stern School of Business at New York University.
  • 1992 - The American Stock Exchange announced it is conducting a feasibility study on a volatility index, proposed as the "Sigma Index."[9]
  • 1993 - On January 19, 1993, the Chicago Board Options Exchange held a press conference to announce the launch of real-time reporting of the CBOE Market Volatility Index or VIX. The formula that determines the VIX is tailored to the CBOE S&P 100 Index (OEX) option prices, and was developed by Professor Robert E. Whaley of Duke University (now at Vanderbilt University), whom the CBOE had commissioned.[10] This index, now known as the VXO, is a measure of implied volatility calculated using 30-day S&P 100 index at-the-money options.[11]
  • 1993 - Professors Brenner and Galai develop their 1989 proposal for a series of volatility index in their paper, "Hedging Volatility in Foreign Currencies," published in The Journal of Derivatives in the fall of 1993.
  • 2003 - The CBOE introduces a new methodology for the VIX. Working with Goldman Sachs, the CBOE developed further computational methodologies, and changed the underlying index the CBOE S&P 100 Index (OEX) to the CBOE S&P 500 Index (SPX). The old methodology was renamed the VXO.[2]
  • 2004 - On March 26, 2004, the first-ever trading in futures on the VIX Index began on the CBOE Futures Exchange (CFE). VIX is now proposed on different trading platforms, like XTB.
  • 2006 - VIX options were launched in February of this year.
  • 2008 - On October 24, 2008, the VIX reached an intraday high of 89.53.
  • 2008 - On November 21, 2008, the VIX closed at a record 80.74.[12]
  • 2018 - On February 5, 2018, the VIX closed 37.32 (up 103.99% from previous close).[13]
  • 2020 - On March 9, 2020, the VIX hit 62.12, the highest level since the 2008 financial crisis due to a combination of the 2020 Russia–Saudi Arabia oil price war and the COVID-19 pandemic.[14][15]
  • 2020 - During the COVID-19 pandemic, on March 12, 2020, the VIX hit and closed at 75.47, exceeding the previous Black Monday value, as a travel ban to the US from Europe was announced by President Trump.[16]
  • 2020 - On March 16, the VIX closed at 82.69, the highest level since its inception in 1990.[17]

Criticism
Performance of VIX (left) compared to past volatility (right) as 30-day volatility predictors, for the period of Jan 1990-Sep 2009. Volatility is measured as the standard deviation of S&P500 one-day returns over a month's period. The blue lines indicate linear regressions, resulting in the correlation coefficients r shown. Note that VIX has virtually the same predictive power as past volatility, insofar as the shown correlation coefficients are nearly identical.

VIX is sometimes criticized as a prediction of future volatility. Instead it is described as a measure of the current price of index options.

Critics claim that, despite a sophisticated formulation, the predictive power of most volatility forecasting models is similar to that of plain-vanilla measures, such as simple past volatility.[18][19][20] However, other works have countered that these critiques failed to correctly implement the more complicated models.[21]

Some practitioners and portfolio managers have questioned the depth of our understanding of the fundamental concept of volatility, itself. For example, Daniel Goldstein and Nassim Taleb famously titled one of their research articles, We Don't Quite Know What We are Talking About When We Talk About Volatility.[22] Relatedly, Emanuel Derman has expressed disillusion with empirical models that are unsupported by theory.[23] He argues that, while "theories are attempts to uncover the hidden principles underpinning the world around us... [we should remember that] models are metaphors—analogies that describe one thing relative to another."

Michael Harris, the trader, programmer, price pattern theorist, and author, has argued that VIX just tracks the inverse of price and has no predictive power.[24][25]

According to some, VIX should have predictive power as long as the prices computed by the Black-Scholes equation are valid assumptions about the volatility predicted for the future lead time (the remaining time to maturity). Robert J. Shiller has argued that it would be circular reasoning to consider VIX to be proof of Black-Scholes, because they both express the same implied volatility, and has found that calculating VIX retrospectively in 1929 did not predict the surpassing volatility of the Great Depression—suggesting that in the case of anomalous conditions, VIX cannot even weakly predict future severe events.[26]

An academic study from the University of Texas at Austin and Ohio State University examined potential methods of VIX manipulation.[27] On February 12, 2018, a letter was sent to the Commodity Futures Trading Commission and Securities and Exchange Commission by a law firm representing an anonymous whistleblower alleging manipulation of the VIX.[28]

Interpretation

The VIX is quoted in percentage points and represents the expected range of movement in the S&P 500 index over the next month, at a 68% confidence level (i.e. one standard deviation of the normal probability curve). For example, if the VIX is 15, this represents an expected annualized change, with a 68% probability, of less than 15% up or down. The expected volatility range for a single month can be calculated from this figure by dividing the VIX figure of 15 not by 12, but by √12 which would imply a range of +/- 4.33% over the next 30-day period.[29] Similarly, expected volatility for a week would be 15 divided by √52, or +/- 2.08%. The VIX uses calendar day annualization so the conversion of 15% is 15 divided by √365, or +/- 0.79% per day. The calendar day approach does not account for the number trading days in a calendar year (that is, the fact that markets are not open on weekends or holidays). Trading days typically amount to 252 days out of a given calendar year.

The price of call and put options can be used to calculate implied volatility, because volatility is one of the factors used to calculate the value of these options. Higher volatility of the underlying security makes an option more valuable, because there is a greater probability that the option will expire in the money (i.e., with a market value above zero). Thus, a higher option price implies greater volatility, other things being equal.

Even though the VIX is quoted as a percentage rather than a dollar amount, multiple VIX-based derivative instruments are in existence (totaling roughly $4 Billion in AUM),[30] including:

  • VIX futures contracts, which began trading in 2004
  • exchange-listed VIX options, which began trading in February 2006.
  • VIX futures based exchange-traded notes and exchange-traded funds, such as:
    • S&P 500 VIX Short-Term Futures ETN and S&P 500 VIX Mid-Term Futures ETN launched by Barclays iPath in February 2009.
    • S&P 500 VIX ETF launched by Source UK Services in June 2010.
    • VIX Short-Term Futures ETF and VIX Mid-Term Futures ETF launched by ProShares in January 2011.
    • Daily 2x VIX Short-Term ETN and Inverse VIX Medium-Term ETN launched by VelocityShares in November 2010.

Similar indices for bonds include the MOVE and LBPX indices.

Although the VIX is often called the "fear index", a high VIX is not necessarily bearish for stocks.[31] Instead, the VIX is a measure of market perceived volatility in either direction, including to the upside. In practical terms, when investors anticipate large upside volatility, they are unwilling to sell upside call stock options unless they receive a large premium. Option buyers are willing to pay such high premiums only if similarly anticipating a large upside move. The resulting aggregate of increases in upside stock option call prices raises the VIX just as the aggregate growth in downside stock put option premiums that occurs when option buyers and sellers anticipate a likely sharp move to the downside. When the market is believed as likely to soar as to plummet, writing any option that will cost the writer in the event of a sudden large move in either direction may look equally risky.

Hence high VIX readings mean investors see significant risk that the market will move sharply, whether downward or upward. The highest VIX readings occur when investors anticipate that huge moves in either direction are likely. Only when investors perceive neither significant downside risk nor significant upside potential will the VIX be low.

The Black–Scholes formula uses a model of stock price dynamics to estimate how an option's value depends on the volatility of the underlying assets.

Volatility of Volatility

In 2012, the CBOE introduced the "VVIX index" (also referred to as "vol of vol"), a measure of the VIX's expected volatility.[32] VVIX is calculated the same as VIX, except the inputs are market prices for VIX options, instead of stock market options.

References
  1. Kuepper, Justin. "CBOE Volatility Index (VIX) Definition". Investopedia. Retrieved 2020-04-10.
  2. CBOE Staff (2019). "Whitepaper: Cboe Volatility Index" (PDF). CBOE.com. Retrieved 26 February 2020.
  3. "How Does the Cboe's VIX® Index Work? | Six Figure Investing". sixfigureinvesting.com. Retrieved 2020-04-10.
  4. Iachini, Michael. "VIX ETFs: The Facts and Risks". Schwab Brokerage. Retrieved 2020-04-10.
  5. Reiff, Nathan. "How to Use a VIX ETF in Your Portfolio". Investopedia. Retrieved 2020-04-10.
  6. Conway, Brendan (17 June 2014). "No, Your ETF Doesn't Track the VIX Volatility Index—and Here are the Numbers". Barrons.com. Retrieved 26 February 2020.
  7. Papanicolaou, Andrew. "Identifying Links Between the S&P500 and VIX Derivatives". Institute for Pure & Applied Mathematics. UCLA. Retrieved 10 April 2020.
  8. "Volatility" (PDF). people.stern.nyu.edu. Retrieved 2020-02-26.
  9. "IFR report" (PDF). people.stern.nyu.edu. 1992. Retrieved 2020-02-26.
  10. "Derivatives on market volatility" (PDF). rewconsulting.files.wordpress.com. 2012. Retrieved 2020-02-26.
  11. Mehta, Salil (July 2015). "Volatility in motion" (blog). Statistical Ideas. Retrieved 26 February 2020 – via Statisticalideas.blogspot.com.
  12. Yun Li (March 16, 2020). "Wall Street's fear gauge closes at highest level ever, surpassing even financial crisis peak". MSNBC. Retrieved March 17, 2020.
  14. Yakob Peterseil (March 9, 2020). "VIX Spikes to Highest Since 2008 in Manic Monday Trading". Bloomburg. Retrieved March 9, 2020.
  15. Pete Evans (March 9, 2020). "'This is basically panic selling': Stock markets plunge as coronavirus fear spreads". CBC. Retrieved March 9, 2020.
  16. Nicholas Jasinski (March 12, 2020). "The VIX Fear Gauge Is Soaring. It's Unlikely to Come Down Anytime Soon". Barron's. Retrieved March 12, 2020.
  17. Li, Yun (March 16, 2020). "Wall Street's fear gauge closes at highest level ever, surpassing even financial crisis peak". cnbc.com. Retrieved March 19, 2020.
  18. Cumby, R.; Figlewski, S.; Hasbrouck, J. (1993). "Forecasting Volatility and Correlations with EGARCH models". Journal of Derivatives. 1 (2): 51–63. doi:10.3905/jod.1993.407877.
  19. Jorion, P. (1995). "Predicting Volatility in Foreign Exchange Market". Journal of Finance. 50 (2): 507–528. doi:10.1111/j.1540-6261.1995.tb04793.x. JSTOR 2329417.
  20. Adhikari, B.; Hilliard, J. (2014). "The VIX, VXO and realised volatility: a test of lagged and contemporaneous relationships". International Journal of Financial Markets and Derivatives. 3 (3): 222–240. doi:10.1504/IJFMD.2014.059637.
  21. Andersen, Torben G.; Bollerslev, Tim (1998). "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts". International Economic Review. 39 (4): 885–905. doi:10.2307/2527343. JSTOR 2527343.
  22. Goldstein, Daniel G.; Taleb, Nassim Nicholas (28 March 2007). "We Don't Quite Know What We are Talking About When We Talk About Volatility". Journal of Portfolio Management. 33 (4). doi:10.3905/jpm.2007.690609. SSRN 970480.
  23. Derman, Emanuel (2011). Models Behaving Badly: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life. New York, NY: Simon and Schuster. pp. unknown page nos. ISBN 9781439165010. Retrieved 25 February 2020.
  24. Harris, Michael (21 August 2012). "On the Zero Predictive Capacity of VIX—Price Action Lab Blog" (self-published blog). PriceActionLab.com. Retrieved 25 February 2020.
  25. Harris, Michael (25 August 2012). "Further Analytical Evidence that VIX Just Tracks the Inverse of Price" (self-published blog). PriceActionLab.com. Retrieved 25 February 2020.
  26. Shiller, Robert (30 March 2011). "Econ 252-11: Financial Markets [Lecture 17—Options Markets]". New Haven, CT: Yale University. Archived from the original (college course content) on 22 September 2016. Retrieved 26 February 2020 – via OYC.Yale.edu.
  27. Griffin, John M.; Shams, Amin (May 23, 2017). "Manipulation in the VIX?". SSRN.com. doi:10.2139/ssrn.2972979. SSRN 2972979. Retrieved 25 February 2020.
  28. Cornish, Chloe (13 February 2018). "Anonymous 'Whistleblower' Claims 'Rampant Manipulation' of Vix Index". Financial Times. Retrieved 26 February 2020 – via FT.com.
  29. Note that the divisor for a single month is √12, and not 12. See the definition volatility for a discussion of computing inter-period volatility.
  30. "Seller Beware: Everybody's Short VIX These Days". RCM Alternatives. 2017-05-09. Retrieved 2017-09-18.
  32. BBOE Staff (March 13, 2012). "Double the Fun with CBOE's VVIX Index" (PDF). CBOE.com. Retrieved November 19, 2019.

Further reading
  • Black, Fischer and Myron Scholes. "The Pricing of Options and Corporate Liabilities." Journal of Political Economy (May/June 1973), pp. 637–659.
  • Brenner, Menachem; Galai, Dan (July–August 1989). "New Financial Instruments for Hedging Changes in Volatility" (PDF). Financial Analysts Journal. Unknown volume (unknown issue): unknown page nos.
  • Brenner, Menachem; Galai, Dan (Fall 1993). "Hedging Volatility in Foreign Currencies" (PDF). The Journal of Derivatives. Unknown volume (unknown issue): unknown page nos.
  • "Amex Explores Volatility Options," International Financing Review, August 8, 1992.
  • Black, Keith H. "Improving Hedge Fund Risk Exposures by Hedging Equity Market Volatility, or How the VIX Ate My Kurtosis." The Journal of Trading. (Spring 2006).
  • Connors, Larry. "A Volatile Idea." Futures (July 1999): p. 36—37.
  • Connors, Larry. "Timing Your S&P Trades with the VIX." Futures (June 2002): pp. 46–47.
  • Copeland, Maggie. "Market Timing: Style and Size Rotation Using the VIX." Financial Analysts Journal, (Mar/Apr 1999); pp. 73–82.
  • Daigler, Robert T., and Laura Rossi. "A Portfolio of Stocks and Volatility." The Journal of Investing. (Summer 2006).
  • Fleming, Jeff, Barbara Ostdiek, and Robert E. Whaley, "Predicting Stock Market Volatility: A New Measure," The Journal of Futures Markets 15 (May 1995), pp. 265–302.
  • Hulbert, Mark, "The Misuse of the Stock Market's Fear Index," Barron's, October 7, 2011.
  • Mele, Antonio and Yoshiki Obayashi. "The Price of Fixed Income Market Volatility." Springer Verlag: Springer Finance Series, New York (2015).
  • Moran, Matthew T., "Review of the VIX Index and VIX Futures.," Journal of Indexes, (October/November 2004). pp. 16–19.
  • Moran, Matthew T. and Srikant Dash. "VIX Futures and Options: Pricing and Using Volatility Products to Manage Downside Risk and Improve Efficiency in Equity Portfolios." The Journal of Trading. (Summer 2007).
  • Szado, Ed. "VIX Futures and Options—A Case Study of Portfolio Diversification During the 2008 Financial Crisis." (June 2009).
  • Tan, Kopin. "The ABCs of VIX." Barron's (Mar 15, 2004): p. MW16.
  • Tracy, Tennille. "Trading Soars on Financials As Volatility Index Hits Record." Wall Street Journal. (Sept. 30, 2008) pg. C6.
  • Whaley, Robert E., "Derivatives on Market Volatility: Hedging Tools Long Overdue," The Journal of Derivatives 1 (Fall 1993), pp. 71–84.
  • Whaley, Robert E., "The Investor Fear Gauge," The Journal of Portfolio Management 26 (Spring 2000), pp. 12–17.
  • Whaley, Robert E., "Understanding the VIX." The Journal of Portfolio Management 35 (Spring 2009), pp. 98–105.

See also
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