24 AAII Journal/October 2000

TECHNICAL ANALYSIS

There is no such thing as a universal indicator. Rather, different conditionsdictate the use of different indicators.

Oscillators, which are indicators that move between zero and 100, areuseful in identifying conditions where a security may be overextended—overbought or oversold. In the May issue of the AAII Journal, we took alook at one popular oscillator, Wilder’s relative strength index. This articlefocuses on another popular indicator, the stochastic oscillator.

THE CALCULATION

The word stochastic is defined in general as a process involving a randomvariable. The stochastic oscillator was first introduced by George Lane in the1970s. This indicator consists of two lines—the %K and %D lines—andcompares the most recent closing price of a security to the price range inwhich 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 priceHi = Highest intraday price over the designated periodLo = Lowest intraday price over the designated period

Therefore, if you were calculating a five-day %K line, the first point wouldbe calculated using the highest price over the last five trading days and thelowest price over the last five trading days as well as the closing price forday five (the last day of the five-day period).

The %D line typically is a three-point moving average of the %K line, andserves as a “trigger” line for generating trading signals. In other words, youadd together the last three %K values, divide this sum by three, and continuethis over a rolling three-day period. You can use any type of moving averageyou wish when calculating the %D line, including simple, weighted, orexponential 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 overany time period you wish, depending on your trading style. The shorter thetime period used to establish the high-low comparison, the more responsivethe indicator is to price changes which, in turn, will increase the number ofsignals the indicator generates. Alternatively, as you increase the time periodused in calculating an indicator, you increase the time in which it takes torespond to current price movements. This lowers the number of signals theindicator generates. Also, keep in mind that you can use any time incrementas well—minute, hour, day, week, month, etc. The same principles apply nomatter the time period or increment you use.

By Wayne A. Thorp

Stochastics work bestwith those securitiesthat are currentlytrading within aparticular range andmay prove useful inidentifying buyingand selling points.But they can returnfalse signals,especially duringperiods when stocksare in a stronguptrend ordowntrend.

Wayne A. Thorp is assistant financial analyst at AAII.The figures in this article were produced using MetaStock by Equis.

ID’ING WHEN TO BUY AND SELLUSING THE STOCHASTIC OSCILLATOR

AAII Journal/October 2000 25

TECHNICAL ANALYSIS

FAST VS. SLOW STOCHASTICS

The formula we provided on page24 to calculate points on the %Kline leads us to a stochastic oscilla-tor that is extremely volatile and,therefore, is often referred to as a“fast” stochastic. Lane realized thatdue to the fast stochastic’s volatility,it was not very useful as a tradingtool because it generated frequentand often inaccurate trading signals.In an attempt to create an indicatorthat 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 averagingover three points. In other words,the new %K line is a three-pointmoving average of the fast %Kline; and

• Using a three-point moving averageof the original %D line as the slowstochastic’s %D line. Therefore, we

are taking the original %K line,smoothing or averaging it overthree points, and then averagingthis line over three points oncemore.Figure 1 illustrates both the fast

(upper window) and slow (middlewindow) stochastics for GlobalMarine. In both instances, the %Kline is the solid line, and the %Dline is the dotted line. In bothstochastic windows, the two horizon-tal lines mark the overbought(indicator value above 80) andoversold areas (indicator valuebelow 20) as defined by Lane. As wewill see later, the movements of the%K and %D lines above and belowthese levels are useful when timingyour buy and sell decisions.

The numbers in parentheses on thechart indicate the number of pointsused in calculating the movingaverages period used. Looking at theslow stochastic in the middle win-dow, you see (5,3) after the %K

label. This indicates that the pointson the %K line are calculated overfive points and then “smoothed,” oraveraged, over three points. The%D lines in Figure 1 are a three-point moving averages of theirrespective %K lines.

When comparing the slow and faststochastics, you can immediately seethat the slow stochastic is morerounded and less volatile than thefast stochastic. Note, also, that thereare times when the fast stochasticlines either cross above 80 or below20, while the slow stochastic linesdo not. By slowing the lines, theslow stochastic generates fewertrading signals.

INTERPRETATION

You can see in the figures that thestochastic oscillator fluctuatesbetween zero and 100. A stochasticvalue of 50 indicates that the closingprice is at the midpoint of the

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

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Open, High, Low and Closing Prices

Fast Stochastic Oscillator

Slow Stochastic Oscillator

26 AAII Journal/October 2000

TECHNICAL ANALYSIS

trading range for the specifiedperiod. As values reach above 50, itindicates that the price is moving upinto the higher trading-range for theperiod. The opposite is true whenvalues fall below 50—the price ismoving into the lower levels of thetrading range for the period.

At the extreme, a value of 100signals that the price closed at theabsolute highest point for the period,while a value of zero means that theprice closed at the lowest point forthe period.

The three most common ways touse the stochastic oscillator aredivergences, crossovers, and over-sold/overbought.

DIVERGENCES

When Lane first introducedstochastics, he believed that the onlyvalid signal occurred when adivergence developed between theprice and the stochastic oscillator,more specifically the %D line.Divergences between price and anindicator occur when the behaviorin the price is not mirrored by the

indicator.A bearish divergence, for example,

takes place when the prices aremaking higher highs while thestochastic is making new lows(preferably below 20), or is failingto also make new highs. This occursbecause, while prices are reachingnew intraperiod highs, the closingprices are falling. When you seethis, you can reasonably expect theprice to fall in line with the indica-tor—which means prices will reversecourse and begin to fall.

Figure 2 provides an example of abearish divergence between the dailyprice of Photon Dynamics and five-day stochastics (with three-dayslowing). As you can see, pricesmoved in a generally upwarddirection (higher highs and higherlows) from late June through themiddle of July—creating threesuccessive peaks, each higher thanthe previous. At the same time,however, the stochastic oscillatorwas moving in the opposite direc-tion, creating two successively lowerpeaks—both of which are above 80.Eventually, prices followed the

stochastic, reversed course,and fell from a high of $85to a low near $45 in lessthan a month.

Bullish divergences occurwhen the price is makingnew lows while the oscillatoris making new highs—orfailing to make new lows—below the 20 line. Here youcan expect prices to bottomout and begin to rise, match-ing the behavior of theindicator.

OVERBOUGHT &OVERSOLD

The horizontal lines at 20and 80 mark overbought andoversold areas for a givensecurity. A security is consid-ered overbought when thestochastic lines rise above 80as closing prices nearintraperiod highs. Likewise,it is viewed as oversold when

they cross below 20 indicatingclosing prices are near the intra-period low. These levels representpoints where one would expectprices to reverse—the extreme pricelevels are not sustainable over time.Note that either line—the %K lineor %D—may be used, althoughmost technicians consider the %Dline to be more accurate.

There are several strategies thatcan be used based on overboughtand oversold levels.

The strictest rule would be to sellwhen the %D line crosses above80—in other words, when the stockbecomes overbought—and buy whenit crosses below 20 and becomesoversold. This strategy, however,has flaws. To begin with, there is noindication as to how long thesecurity will remain at the priceextremes, meaning that the securitycould become even more overboughtor oversold. Therefore, if you soldwhen the %D line crossed above 80,you run the risk of missing furtherprice gains, just as you run the riskof buying prematurely before the

FIGURE 2. A BEARISH DIVERGENCE FOR PHOTON DYNAMICS

Open, High, Low, and Closing Prices

Stochastic Oscillator

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$

AAII Journal/October 2000 27

TECHNICAL ANALYSIS

price bottoms if you buy when theline crosses below 20.

A more conservative approach isto allow the oscillator to cross eitherabove 80 or below 20 and wait untilit reverses itself—in other words,wait until it crosses back below 80before selling and wait until it risesabove 20 before buying. While yourisk giving up some of your pricegains or missing out on some or allof the upward movement, over timethis strategy tends to perform better.

CROSSOVERS

The stochastic oscillator is uniquecompared to other oscillators, suchas Wilder’s relative strength indica-tor, because it is composed of twolines instead of just one. Therefore,as with indicators such as multiplemoving averages and the MACD(moving average convergence/divergence), potential trading signalsarise when the %K line crosses the%D.

Generally speaking, a buy signalis generated whenever the %K linemoves above the %D line. Likewise,

a sell or short signal occurs whenthe %K line crosses below the %Dline.

For the most reliable signals,technicians typically wait to act oncrossovers until the %K and %Dlines are in the overbought oroversold zones—above 80 and below20, respectively. Therefore, astronger sell signal would be whenthe %K line crosses below the %Dline when both are above 80, and astronger buy signal would be whenthe %K rises above the %D linewhen both are below 20.

Further study has shown that theside of the %D line on which thecrossover by the %K line takesplace can also be a factor in howprofitable the trade may be. “Right-side” crossings, which tend to bemore profitable than “left-side “crossings, take place when the %Kline crosses after the %D line hasreached an extreme.

BREAKDOWNS

Stochastics are most useful inidentifying short(er)-term price

swings. In addition, theindicator is most reliablewhen used with a securitywhose price moves within atrading range. On the otherhand, problems tend to arisewhen you attempt to use thestochastic oscillator intrending markets.

Oscillators in generalperform poorly during strong,prolonged trends—eitherupward or downward.During strong uptrends, thestochastics tend to move intothe overbought range (above80) and can stay there for anextended period of time.Furthermore, during suchtrends, movements by theindicator below 80 tend notto be indicative of a reversalin the overall trend. Thesame is true for divergencesthat occur in trendingmarkets, which also tend to

generate false signals.One way to avoid trading on these

false signals is to only trade onthose signals that are in the direc-tion of the overall trend. In otherwords, sell when the price is over-bought only when there is a con-firmed downtrend, and buy whenthe price is oversold only if thetrend is up.

Figure 3 is an example of how thestochastic oscillator “breaks down”during a prolonged trend. Here,PsiNet experienced a steady declinefrom early March through lateApril. During this time, thestochastics fell from above the 80line to below the 20 line. Subse-quently, it rose above 20 four othertimes during this period. If you hadpurchased the stock on any of thesecrossovers above the 20 line, youwould have seen three of the fourtrades lose money as the price fellfrom $60 to below $20, eventuallystaging a small rally.

CONCLUSION

Stochastics, like any technical

FIGURE 3. A STOCHASTIC OSCILLATOR “BREAKDOWN” FOR PSINET

Open, High, Low, and Closing Prices

Stochastic Oscillator

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28 AAII Journal/October 2000

TECHNICAL ANALYSIS

indicator, can be a useful tool inimplementing your trading strategyas long as you understand both itsstrengths and weaknesses.

Stochastics work best with thosesecurities that are in a trading rangeor are non-trending. Under theseconditions, the stochastic indicatormay prove useful in identifyingbuying and selling points based ondivergences between the indicatorand the security’s price, the interac-tion between the %K and %D linesthat make up the oscillator, as well

RESOURCES

ArticlesLuisi, Joe “The Stochastic Oscillator,” TechnicalAnalysis of Stocks and Commodities, December 1997.

Evens, Stuart “Stochastics,” Technical Analysis ofStocks and Commodities, September 1999.

“Indicator Insight: Stochastics,” Active TraderMagazine, August 2000.

W eb SitesBigCharts, www.bigcharts.comMeta Stock, www.metastock.com

as when a securitymay be overboughtor oversold.

But stochastics canreturn false signals,especially duringstrong up- anddowntrends. Usingstochastics with otherindicators can helpreduce the risk ofentering a tradeagainst the overalltrend. ✦

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