When we experience market jolts like those on Feb. 2nd (Friday) and Feb. 5th (Monday), with the S&P 500 dropping 2% and 4% in subsequent trading sessions, one of the most cited indicators of what is going on-and what is likely to happen-is the VIX. On Monday alone, VIX jumped by almost 120%. To the extent that we follow VIX, it is important to understand exactly what VIX means and what information can usefully be drawn from VIX.

To begin, the term volatility, as it is used in finance, is the standard deviation of returns. The simplest measure of volatility is to directly calculate the standard deviation of actual returns in the market. This is referred to as realized volatility-what has actually happened. The VIX is a measure of *implied* volatility derived from the prices of call options and put options on the S&P 500 that will expire over the next thirty days. The prices of options are largely determined by the assumed future volatility of the underlying asset or index (the S&P 500 in this case). Using an option pricing model, you can back out what the market assumption for the volatility needs to be to explain the prices of the options-and this is the implied volatility. If more options traders are increasingly seeking to buy options-and thus to benefit from an increase in volatility-the prices of options increase, thereby driving up the implied volatility. When the markets turn down, investors are long equities seek to buy put options to protect their downside. Note that investors may also short the market and buy call options to achieve the same end-protection if the market declines at a fixed price (the price of the put or call). The VIX is quoted as 100 times the implied annualized volatility. A VIX of 20 corresponds to 20% annualized volatility for the S&P 500. The long-term average volatility for the S&P 500 is around 15%, to provide a reference.

Over most of the last twelve months, VIX has been hovering around 10 (implied volatility of 10%) but started to creep up in the start of 2018. On Jan. 2nd, VIX closed at 9.8 and then rose fairly steadily to close at 14.8 on Jan. 30th. Even though this was a fairly large percentage rise, 15 or so (15% annualized volatility) is normal for the S&P 500. By the close of Feb. 2nd, VIX closed at 17.3. On Monday, Feb. 5th, VIX really spiked, closing at 37.3, a jump of almost 120%. VIX has since started to decline, but still closed at 27.7 on Wednesday, Feb. 7th, almost twice its value at the end of January. What can be taken away from these numbers?

First and foremost, it is important to understand what a short-term indicator VIX is. VIX is implied volatility only for the nearest-expiring options-those which expire within the next thirty days. VIX is not a long-term outlook for volatility. If you want a longer-term outlook, you need to look at the implied volatility for longer-dated options. I have an analytic model that inverts options prices not simply to provide the volatility (the standard deviation of returns) but the entire distribution of future returns. This is my own flavor or model but the general process is described here and here. Using a set of call and put options on SPY, an S&P 500 ETF with very liquid options, which expire on June 15, 2018, I have created an implied distribution of returns using option prices after the close on Feb. 5th, when VIX closed at 37.3.

*Option implied distribution of future returns for the period Feb. 5-June 15, 2018*

This distribution of expected returns for the period from Feb. 6th to June 15th 2018, about 1/3rd of a year into the future, has a mode (the highest-probability outcome) of 5.6% in price return over this period. The distribution is highly negatively skewed, with a long and fat downside tail. The standard deviation of this distribution is 14.4%, which annualizes up to 24%. And here is the crucially important fact. On the same day that VIX jumped to an implied volatility of 37%, the implied volatility for the returns over the next 4 months was at 24%, far lower. Even in the midst of a major upheaval in the short-term, the longer-dated options provide a calmer outlook. To be certain, if the implied volatility of 24% turned out to be a decent forecast over the next four months or so, it would be a bumpy ride-but this outlook suggests that the very high near-term volatility outlook descends rather quickly towards more reasonable levels.

As the panic subsided, implied volatilities dropped dramatically, with VIX closing at 27.7 on Feb. 6th and the June 15th 2018 option implied volatility falling to 20.1%.

After the close on Feb. 5th, with VIX at 37, the option-implied distribution (shown above) contained an important signal that I have not yet discussed. The mode of the distribution, the most probable return over the next 0.36 years, was 5.6% after market close. If we add 0.6% in dividend yield (1.7% annual yield x 0.36 years), we get a most probable return of 6.2% over the next 0.36 years. This is a substantial return for a period of just over 1/3rd of a year. Even though the implied volatility and downside risk was elevated, the most likely outcome implied by the options prices was for a high return.

In summary, the VIX is a useful measure of the market's consensus view on near-term volatility. It is potentially highly misleading to infer anything beyond a truly near-term period however. Even as the near-term options implied a serious spike in risk, the longer-dated options on SPY were telling a far more nuanced story.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **I am long U.S. equities but I do not own SPY, IVV, etc.