First things first. The stock market volatility that appeared during the first full week of February might be normal.
With a bit of math that is presented at the end of this article, it is reasonable to envision the Dow Jones Industrial Average (“DJIA”) fluctuating above and below the current price level by about 300 points or more on one or two days every week.
The same math says it should not surprise us to see it move by 1,000 points or more one or two days in a year.
Repeat. 300-point-plus days are not unusual and 1,000-point days should not surprise anyone with a memory. The comparable figures for the Standard & Poor’s 500 (“S&P 500”) are close to 30 points and 100 points, respectively.
What should surprise us is a year like 2017, when the S&P 500 moved up or down more than 30 points on only six trading days. “Normal” volatility would have been something closer to 80 days. It’s the comparison to a long period of well-below-average volatility that makes recent “normal” volatility seem, well, abnormal.
The cluster of volatile trading days – four of the first seven in the month – also gets everyone’s attention. As Shakespeare wrote more than 500 years ago, “When sorrows come, they come not single spies. But in battalions.” Volatility only hibernates, but never goes away. And when it wakes, it shakes.
Investment researchers often use a statistical concept called variance to measure volatility. All we need to know about variance for this article is that it gives a useful way of expressing the size of the ups and downs as a number.
It can be calculated using historical data. But that can be misleading because the chosen time period can bias the result. For example, anyone relying only on trading data in 2017 would have seriously underestimated volatility going into 2018. If the past is not necessarily a guide to the future, then is there a way to estimate volatility that has not happened yet?
It cannot be measured directly, but in theory there is a way to infer it from the trading prices of options. An option price is what an investor pays to gain a degree of certainty about the future price of an unpredictable asset, such as a stock. Since volatility relates to uncertainty, options effectively put a price on volatility.
With a bit of math, based on a theory developed in the 1970s that won a Nobel Prize in economics, four other variables combine with volatility to form the option price. These other four can be measured directly. They include the present stock price, the so-called exercise price of the option, the length of time before the option expires, and an interest rate. Knowing those four items, it is possible to calculate what’s called “implied volatility”. In theory, this result gives the volatility investors expect in the future.
The popular Volatility Index (“VIX”) measure developed by the Chicago Board Options Exchange (“CBOE”) has its roots in this type of calculation. As described on the CBOE’s web site, the VIX takes into account a wide range of options prices on the S&P 500, then develops a number that says, in effect, “Investors expect volatility over the next 30 days to be about this much.”
A low VIX reading indicates low expected risk, and vice versa. For all of 2017, the average VIX was about 11. Through the first week of February, the average was above 26. On the close February 8th, it was above 33, three times the average for all of 2017. All we need to know about these numbers is that they tie back to investor expectations for risk, according to a generally accepted theory about options prices.
By the way, the average volatility expectation based on the VIX since 1990 has been about 19, according to daily price data obtained from from the CBOE as presented by Yahoo! Finance. This 28-year average tells us that, as often as not, investors have expected the S&P 500 to fluctuate, in one year’s time, by 19 percentage points or more, above or below its long-term rate of return.
The VIX has been much in the news as a result of market tumult in early February. It has risen sharply from a below-average level in 2017, to an above-average level in recent days. On these occasions, news media like to portray the VIX as some kind of “fear index”, as if it gauged widely shared investor sentiment. Is that so?
VIX is just a number that emerges from a math process relating to the trading prices of options. By this math, holding all else equal, a sudden jump in the VIX could result from a minority of excitable investors rushing to pay high prices to buy options.
It may be that a greater number of investors simply expect market volatility in the future to resemble the long-run average level in the past. That would be more volatile than we saw in 2017, but not as volatile as the VIX currently implies. In that case we may see the VIX settle down after the excitable options buyers finish spending their money.
This article discusses the VIX only as an analytical tool, and not as a trading vehicle. We do not express an opinion about trading based on the VIX, and this article cannot be used for that purpose.
Now for a very general overview on the math that started this article.
We used the average VIX level since 1990 – 19.3% — as an estimate for the expected annual standard deviation of returns on a broad market index. Standard deviation is just the variance, the risk measure, converted in a way that describes equally-likely moves up or down. Converting it to a daily value involves dividing by the square root of 252, the typical number of trading days in a year. This gives approximately 1.2% for daily volatility, which is a bit more than 300 points up or down from a DJIA price level of 26,000.
The standard deviation gives a way to estimate the likelihood of such a move occurring purely at random, for no reason at all. We can do this using probability theory, if we assume that the frequency of different stock market returns follows the familiar, bell-shaped, so-called normal distribution. In this analysis, a random move of more than one standard deviation has a probability of about 1 chance in 3. Translation: a DJIA move exceeding 300 points could occur randomly on more than 80 trading days in a year, or 1 to 2 days a week.
A larger move of 3 times the standard deviation would have a probability of about 1 chance in 100. That works out to about 1,000 points on a couple of days each year. Even larger gains or losses remain possible, though theoretically less often.
Investing involves risk, including the chance of losing money. If the VIX truly does indicate the level of risk investors expect to encounter in the future, then it’s telling us to get used to market moves of 300 to 1,000 points, or more, both up and down.
Indexes are unmanaged and you cannot invest directly in an index. The S&P 500 Index is a market capitalization–weighted index of 500 common stocks chosen for market size, liquidity, and industry group representation to represent U.S. equity performance.
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