Volatility tools: standard deviation, Bollinger Bands, ATR and the VIX

🎯 In 30 seconds: Volatility is how much price moves, regardless of direction. Standard deviation measures how spread out closing prices are around their average. Bollinger Bands put lines 2 standard deviations above and below a 20-day average. Average True Range (ATR) measures the typical daily range, gaps included, and is the most practical tool for setting stops and sizing positions so each trade risks a similar dollar amount. Quiet periods (squeezes) often come before bigger moves, but they do not tell you the direction. The VIX measures the volatility that S&P 500 option prices expect.

Why volatility matters to a trader

Two stocks both trade at $50. One usually moves 50 cents a day; the other moves $3 a day. A $1.50 stop is generous for the first and almost certain to be hit by noise on the second.

Volatility is a measure of how much price tends to move. It does not say which way. Knowing it lets you:

place stops outside normal noise,
size positions so a volatile stock does not carry more risk than a calm one,
notice when a market goes unusually quiet or unusually wild.

Standard deviation, by hand

Standard deviation measures how far values typically sit from their average. Here is a 5-day example with hypothetical closes: $10, $11, $12, $11, $11.

Average: $55 / 5	$11.00
Differences from average: minus 1, 0, +1, 0, 0
Squared differences: 1, 0, 1, 0, 0. Sum	2
Variance: 2 / 5	0.40
Standard deviation: square root of 0.40	$0.63

Dividing by 5 (the number of values) gives the "population" standard deviation, which is what John Bollinger says he uses for his bands. Spreadsheets also offer a "sample" version that divides by 4 here; it gives a slightly larger number.

When traders talk about a stock's "historical volatility", they usually mean the standard deviation of daily percentage returns, scaled to a year by multiplying by the square root of about 252 trading days. A stock whose daily returns have a standard deviation of 1.5% has an annualized volatility of about 1.5% x 15.9 = 24%.

Bollinger Bands

Bollinger Bands, created by John Bollinger, have three lines:

Middle band: 20-day simple moving average of closes.
Upper band: middle band + 2 x the 20-day standard deviation of closes.
Lower band: middle band minus 2 x the same standard deviation.

The default is written (20, 2). If the 20-day average were $11.00 and the standard deviation $0.63, the bands would be $11.00 plus or minus $1.26: $9.74 and $12.26.

Because the bands are built from standard deviation, they widen when price swings more and narrow when it calms down. They adapt to each stock automatically.

Three ways to read them:

Touches are not signals. Bollinger himself describes moves that touch or exceed the bands as "tags", not signals. A close above the upper band in an uptrend is often a sign of strength.
Walking the band. In a strong trend, price can hug the upper (or lower) band for weeks.
The squeeze. When the bands get unusually narrow, volatility is unusually low. Low volatility periods tend to be followed by higher volatility. The squeeze tells you a bigger move may be coming, not which way.

Hypothetical daily chart. In the quiet middle stretch, the distance between the bands shrinks from about 11% of price to about 1.3%: a squeeze. Price then breaks out upward, the bands widen to about 16%, and price walks the upper band.

A common way to measure the squeeze is BandWidth: (upper band minus lower band) / middle band. Traders compare today's BandWidth with its range over the past six months or so. A reading near the low end of that range is a squeeze.

Average True Range (ATR)

ATR, introduced by J. Welles Wilder in 1978, measures the typical size of a day's move, including gaps. It starts with the true range (TR) for each day, which is the largest of:

today's high minus today's low,
the absolute value of today's high minus yesterday's close,
the absolute value of today's low minus yesterday's close.

Items 2 and 3 matter when the stock gaps. If a stock closed at $50.00 and opens the next day at $52.00, trading between $51.50 and $53.00, the high-low range is only $1.50. But the stock really moved $3.00 from yesterday's close to today's high. True range = max($1.50, $3.00, $1.50) = $3.00.

The ATR is a 14-day average of true range, smoothed Wilder's way:

ATR today = (ATR yesterday x 13 + TR today) / 14

The first ATR is the simple average of the first 14 true ranges. Continuing the example, if yesterday's ATR was $1.80 and today's TR is $3.00, today's ATR = ($1.80 x 13 + $3.00) / 14 = $26.40 / 14 = $1.89.

ATR is in dollars, so a $500 stock will have a bigger ATR than a $20 stock. To compare across stocks, divide ATR by price: $1.89 / $52 is about 3.6% a day.

Using ATR for stops and position size

This is where volatility tools earn their keep. Instead of a fixed $1 or 5% stop, you set the stop a multiple of ATR away, so it sits outside the stock's normal noise. Then you size the position so the dollar risk stays fixed.

Worked example (hypothetical): account $20,000, risking 1% per trade. Stock at $52.00, ATR $1.89. You use a 2 x ATR stop.

Dollar risk: 1% of $20,000	$200
Stop distance: 2 x $1.89	$3.78
Stop price: $52.00 minus $3.78	$48.22
Shares: $200 / $3.78, rounded down	52 shares
Position size: 52 x $52.00	$2,704

Now a calmer stock, also at $52, with an ATR of $0.80. Stop distance is $1.60, and $200 / $1.60 = 125 shares ($6,500). The calmer stock gets a bigger position, but both trades risk the same $200 if the stops fill at their prices.

That last condition matters. A stop order becomes a market order when triggered. If the stock gaps below your stop overnight, you get the next available price, which can be much worse. ATR sizing controls normal risk, not gap risk. See Stop losses and Position sizing.

Hypothetical example. The red dashed trailing stop sits 2 ATRs below the close and only ratchets up. When the market turned choppy, ATR nearly tripled and the stop, set during the calm phase, was hit on the first big drop, even though price later rose further. A wider multiple survives more noise but risks more per share.

Common mistake: same stop distance for every stock

A $2 stop on a stock with a $0.50 ATR is four days of normal movement. The same $2 stop on a stock with a $4 ATR is half a normal day, so you will be stopped out by noise again and again. Check ATR before you set any stop, and if the right stop means too few shares to bother with, skip the trade.

Volatility clusters

Calm periods tend to follow calm periods, and wild periods tend to follow wild ones. This is called volatility clustering and is one of the more reliable patterns in market data. It is why yesterday's ATR is a reasonable guess for tomorrow's range, and why a sudden jump in ATR, as in the figure, should make you rethink stops and size.

Practical tip: put ATR on every chart

Add ATR(14) under your price chart and write its value in your trade plan before every entry. Stop distance, share count and profit target can all be expressed in ATRs. After 30 trades, look at how far your winners ran and your losers went, in ATRs. That tells you more about your stops than any rule of thumb.

The VIX, briefly

Cboe builds the Cboe Volatility Index (VIX®) from the prices of S&P 500 index options, as an estimate of how far traders expect the index to swing in the near term. Cboe labels it a one-month measure. It is quoted as an annualized percentage.

A rough way to read it: divide by the square root of 12 (about 3.46) to get a one-month figure. A VIX of 20 suggests option prices imply S&P 500 moves of roughly 5.8% over a month, at one standard deviation. A VIX of 40 implies about twice that.

Two cautions. The VIX is an index, not something you can buy directly; products linked to it, like VIX futures and exchange-traded products, behave very differently from the index and some lose value steadily over time. And the VIX describes the expected size of moves for the broad index, not for your stock. More in Implied volatility.

What the evidence says

Volatility tools are on firmer ground than most indicators in one respect: volatility really does cluster, so measuring it helps with stops and sizing. Using bands or squeezes to predict direction is a different claim, and there is little reliable evidence that a band touch or a squeeze alone predicts which way price goes. Treat a squeeze as "get ready", and let price structure, such as a breakout from a range, tell you the direction.

Try it

Pick two stocks at similar prices from the stock screener, one calm and one volatile. Find each one's ATR(14) and divide by price.
Using the worked example, compute share counts for a $10,000 paper account risking 1% with a 2 x ATR stop. Place both trades in the paper portfolio.
Look back at a year of daily charts for one stock and mark every Bollinger squeeze. Write down which way price broke out afterward. Count ups and downs.
Check the VIX level on the market dashboard and convert it to an approximate one-month move.

Check yourself

What are the default Bollinger Band settings? Answer: (20, 2): a 20-day simple moving average in the middle, with bands 2 standard deviations above and below it.
A stock closed at $50.00 and today trades between $51.50 and $53.00. What is today’s true range? Answer: $3.00, the move from yesterday’s close to today’s high, which is larger than the $1.50 high-low range.
Your account is $20,000 and you risk 1%. A $52 stock has an ATR of $1.89 and you use a 2 x ATR stop. Where is the stop, and how many shares do you buy? Answer: The stop is $48.22 ($52.00 - $3.78), and you buy 52 shares ($200 / $3.78, rounded down).
The Bollinger Bands are in a tight squeeze. Does that tell you which way price will break? Answer: No. A squeeze says a bigger move may be coming, not its direction. Let price structure, such as a breakout from a range, show the direction.

Sources

BollingerBands.com: Bollinger Bands
VIX® is a registered trademark of Cboe Exchange, Inc., and Bollinger Bands® is a registered trademark of John Bollinger. The names are used here only to describe the indicators; neither owner is affiliated with this course.
StockCharts ChartSchool: Bollinger Bands
StockCharts ChartSchool: Average True Range (ATR)
Cboe: VIX Index