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TECHNICAL ANALYSIS

ID’ING WHEN TO BUY AND SELL

USING THE STOCHASTIC OSCILLATOR

By Wayne A. Thorp

Stochastics work best

with those securities

that are currently

trading within a

particular range and

may prove useful in

identifying buying

and selling points.

But they can return

false signals,

especially during

periods when stocks

are in a strong

uptrend or

downtrend.

There is no such thing as a universal indicator. Rather, different conditions

dictate the use of different indicators.

Oscillators, which are indicators that move between zero and 100, are

useful in identifying conditions where a security may be overextended—

overbought or oversold. In the May issue of the AAII Journal , we took a

look at one popular oscillator, Wilder’s relative strength index. This article

focuses on another popular indicator, the stochastic oscillator.

THE CALCULATION

The word stochastic is defined in general as a process involving a random

variable. The stochastic oscillator was first introduced by George Lane in the

1970s. This indicator consists of two lines—the %K and %D lines—and

compares the most recent closing price of a security to the price range in

which it traded over a specified time period.

The following formula shows you how to calculate the latest point on the

%K line:

%K = [(Close – Lo) ÷ (Hi – Lo)] × 100

Where:

Close = Last closing price

Hi = Highest intraday price over the designated period

Lo = Lowest intraday price over the designated period

Therefore, if you were calculating a five-day %K line, the first point would

be calculated using the highest price over the last five trading days and the

lowest price over the last five trading days as well as the closing price for

day five (the last day of the five-day period).

The %D line typically is a three-point moving average of the %K line, and

serves as a “trigger” line for generating trading signals. In other words, you

add together the last three %K values, divide this sum by three, and continue

this over a rolling three-day period. You can use any type of moving average

you wish when calculating the %D line, including simple, weighted, or

exponential moving averages. [For more on how to use moving averages, see

“An Intro to Moving Averages: Popular Technical Indicators,” by Wayne A.

Thorp in the August 1999 AAII Journal .]

Like virtually all technical indicators, you can calculate stochastics over

any time period you wish, depending on your trading style. The shorter the

time period used to establish the high-low comparison, the more responsive

the indicator is to price changes which, in turn, will increase the number of

signals the indicator generates. Alternatively, as you increase the time period

used in calculating an indicator, you increase the time in which it takes to

respond to current price movements. This lowers the number of signals the

indicator generates. Also, keep in mind that you can use any time increment

as well—minute, hour, day, week, month, etc. The same principles apply no

matter the time period or increment you use.

Wayne A. Thorp is assistant financial analyst at AAII.

The figures in this article were produced using MetaStock by Equis.

AAII Journal /October 2000

TECHNICAL ANALYSIS

FIGURE 1. SLOW VS. FAST STOCHASTIC OSCILLATORS FOR GLOBAL MARINE

Fast Stochastic Oscillator

Slow Stochastic Oscillator

Open, High, Low and Closing Prices

FAST VS. SLOW STOCHASTICS

are taking the original %K line,

smoothing or averaging it over

three points, and then averaging

this line over three points once

more.

Figure 1 illustrates both the fast

(upper window) and slow (middle

window) stochastics for Global

Marine. In both instances, the %K

line is the solid line, and the %D

line is the dotted line. In both

stochastic windows, the two horizon-

tal lines mark the overbought

(indicator value above 80) and

oversold areas (indicator value

below 20) as defined by Lane. As we

will see later, the movements of the

%K and %D lines above and below

these levels are useful when timing

your buy and sell decisions.

The numbers in parentheses on the

chart indicate the number of points

used in calculating the moving

averages period used. Looking at the

slow stochastic in the middle win-

dow, you see (5,3) after the %K

label. This indicates that the points

on the %K line are calculated over

five points and then “smoothed,” or

averaged, over three points. The

%D lines in Figure 1 are a three-

point moving averages of their

respective %K lines.

When comparing the slow and fast

stochastics, you can immediately see

that the slow stochastic is more

rounded and less volatile than the

fast stochastic. Note, also, that there

are times when the fast stochastic

lines either cross above 80 or below

20, while the slow stochastic lines

do not. By slowing the lines, the

slow stochastic generates fewer

trading signals.

The formula we provided on page

24 to calculate points on the %K

line leads us to a stochastic oscilla-

tor that is extremely volatile and,

therefore, is often referred to as a

“fast” stochastic. Lane realized that

due to the fast stochastic’s volatility,

it was not very useful as a trading

tool because it generated frequent

and often inaccurate trading signals.

In an attempt to create an indicator

that was less volatile and, therefore,

more useful, Lane created a “slow”

stochastic by:

• Making the original %D line the

new %K line—the stochastic is

“smoothed” or slowed by averaging

over three points. In other words,

the new %K line is a three-point

moving average of the fast %K

line; and

• Using a three-point moving average

of the original %D line as the slow

stochastic’s %D line. Therefore, we

INTERPRETATION

You can see in the figures that the

stochastic oscillator fluctuates

between zero and 100. A stochastic

value of 50 indicates that the closing

price is at the midpoint of the

AAII Journal /October 2000

TECHNICAL ANALYSIS

FIGURE 2. A BEARISH DIVERGENCE FOR PHOTON DYNAMICS

stochastic, reversed course,

and fell from a high of $85

to a low near $45 in less

than a month.

Bullish divergences occur

when the price is making

new lows while the oscillator

is making new highs—or

failing to make new lows—

below the 20 line. Here you

can expect prices to bottom

out and begin to rise, match-

ing the behavior of the

indicator.

Stochastic Oscillator

Open, High, Low, and Closing Prices

OVERBOUGHT &

OVERSOLD

The horizontal lines at 20

and 80 mark overbought and

oversold areas for a given

security. A security is consid-

ered overbought when the

stochastic lines rise above 80

as closing prices near

intraperiod highs. Likewise,

it is viewed as oversold when

they cross below 20 indicating

closing prices are near the intra-

period low. These levels represent

points where one would expect

prices to reverse—the extreme price

levels are not sustainable over time.

Note that either line—the %K line

or %D—may be used, although

most technicians consider the %D

line to be more accurate.

There are several strategies that

can be used based on overbought

and oversold levels.

The strictest rule would be to sell

when the %D line crosses above

80—in other words, when the stock

becomes overbought—and buy when

it crosses below 20 and becomes

oversold. This strategy, however,

has flaws. To begin with, there is no

indication as to how long the

security will remain at the price

extremes, meaning that the security

could become even more overbought

or oversold. Therefore, if you sold

when the %D line crossed above 80,

you run the risk of missing further

price gains, just as you run the risk

of buying prematurely before the

trading range for the specified

period. As values reach above 50, it

indicates that the price is moving up

into the higher trading-range for the

period. The opposite is true when

values fall below 50—the price is

moving into the lower levels of the

trading range for the period.

At the extreme, a value of 100

signals that the price closed at the

absolute highest point for the period,

while a value of zero means that the

price closed at the lowest point for

the period.

The three most common ways to

use the stochastic oscillator are

divergences, crossovers, and over-

sold/overbought.

indicator.

A bearish divergence, for example,

takes place when the prices are

making higher highs while the

stochastic is making new lows

(preferably below 20), or is failing

to also make new highs. This occurs

because, while prices are reaching

new intraperiod highs, the closing

prices are falling. When you see

this, you can reasonably expect the

price to fall in line with the indica-

tor—which means prices will reverse

course and begin to fall.

Figure 2 provides an example of a

bearish divergence between the daily

price of Photon Dynamics and five-

day stochastics (with three-day

slowing). As you can see, prices

moved in a generally upward

direction (higher highs and higher

lows) from late June through the

middle of July—creating three

successive peaks, each higher than

the previous. At the same time,

however, the stochastic oscillator

was moving in the opposite direc-

tion, creating two successively lower

peaks—both of which are above 80.

Eventually, prices followed the

DIVERGENCES

When Lane first introduced

stochastics, he believed that the only

valid signal occurred when a

divergence developed between the

price and the stochastic oscillator,

more specifically the %D line.

Divergences between price and an

indicator occur when the behavior

in the price is not mirrored by the

AAII Journal /October 2000

TECHNICAL ANALYSIS

FIGURE 3. A STOCHASTIC OSCILLATOR “BREAKDOWN” FOR PSINET

swings. In addition, the

indicator is most reliable

when used with a security

whose price moves within a

trading range. On the other

hand, problems tend to arise

when you attempt to use the

stochastic oscillator in

trending markets.

Oscillators in general

perform poorly during strong,

prolonged trends—either

upward or downward.

During strong uptrends, the

stochastics tend to move into

the overbought range (above

80) and can stay there for an

extended period of time.

Furthermore, during such

trends, movements by the

indicator below 80 tend not

to be indicative of a reversal

in the overall trend. The

same is true for divergences

that occur in trending

markets, which also tend to

generate false signals.

One way to avoid trading on these

false signals is to only trade on

those signals that are in the direc-

tion of the overall trend. In other

words, sell when the price is over-

bought only when there is a con-

firmed downtrend, and buy when

the price is oversold only if the

trend is up.

Figure 3 is an example of how the

stochastic oscillator “breaks down”

during a prolonged trend. Here,

PsiNet experienced a steady decline

from early March through late

April. During this time, the

stochastics fell from above the 80

line to below the 20 line. Subse-

quently, it rose above 20 four other

times during this period. If you had

purchased the stock on any of these

crossovers above the 20 line, you

would have seen three of the four

trades lose money as the price fell

from $60 to below $20, eventually

staging a small rally.

Stochastic Oscillator

Open, High, Low, and Closing Prices

price bottoms if you buy when the

line crosses below 20.

A more conservative approach is

to allow the oscillator to cross either

above 80 or below 20 and wait until

it reverses itself—in other words,

wait until it crosses back below 80

before selling and wait until it rises

above 20 before buying. While you

risk giving up some of your price

gains or missing out on some or all

of the upward movement, over time

this strategy tends to perform better.

a sell or short signal occurs when

the %K line crosses below the %D

line.

For the most reliable signals,

technicians typically wait to act on

crossovers until the %K and %D

lines are in the overbought or

oversold zones—above 80 and below

20, respectively. Therefore, a

stronger sell signal would be when

the %K line crosses below the %D

line when both are above 80, and a

stronger buy signal would be when

the %K rises above the %D line

when both are below 20.

Further study has shown that the

side of the %D line on which the

crossover by the %K line takes

place can also be a factor in how

profitable the trade may be. “Right-

side” crossings, which tend to be

more profitable than “left-side “

crossings, take place when the %K

line crosses after the %D line has

reached an extreme.

CROSSOVERS

The stochastic oscillator is unique

compared to other oscillators, such

as Wilder’s relative strength indica-

tor, because it is composed of two

lines instead of just one. Therefore,

as with indicators such as multiple

moving averages and the MACD

(moving average convergence/

divergence), potential trading signals

arise when the %K line crosses the

%D.

Generally speaking, a buy signal

is generated whenever the %K line

moves above the %D line. Likewise,

BREAKDOWNS

CONCLUSION

Stochastics are most useful in

identifying short(er)-term price

Stochastics, like any technical

AAII Journal /October 2000

TECHNICAL ANALYSIS

indicator, can be a useful tool in

implementing your trading strategy

as long as you understand both its

strengths and weaknesses.

Stochastics work best with those

securities that are in a trading range

or are non-trending. Under these

conditions, the stochastic indicator

may prove useful in identifying

buying and selling points based on

divergences between the indicator

and the security’s price, the interac-

tion between the %K and %D lines

that make up the oscillator, as well

as when a security

may be overbought

or oversold.

But stochastics can

return false signals,

especially during

strong up- and

downtrends. Using

stochastics with other

indicators can help

reduce the risk of

entering a trade

against the overall

trend.

RESOURCES

Articles

Luisi, Joe “The Stochastic Oscillator,” Technical

Analysis of Stocks and Commodities, December 1997.

Evens, Stuart “Stochastics,” Technical Analysis of

Stocks and Commodities, September 1999.

“Indicator Insight: Stochastics,” Active Trader

Magazine, August 2000.

W eb Sites

BigCharts, www . bigchar t s.com

Meta Stock, www . metastock.com

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