A weighted moving average is designed to put more weight on recent data and less weight on past data. A weighted moving average is calculated by multiplying each of the previous day's data by a weight. The following table shows the calculation of a 5-day weighted moving average.

The weight is based on the number of days in the moving average. In the above example, the weight on the first day is 1.0 while the value on the most recent day is 5.0. This gives five times more weight to today's price than the price five days ago.

The following chart displays 25-day moving averages using the simple, exponential, weighted, triangular, and variable methods of calculation.

A variable moving average is an exponential moving average that automatically adjusts the smoothing percentage based on the volatility of the data series. The more volatile the data, the more sensitive the smoothing constant used in the moving average calculation. Sensitivity is increased by giving more weight given to the current data.

Most moving average calculation methods are unable to compensate for trading range versus trending markets. During trading ranges (when prices move sideways in a narrow range) shorter term moving averages tend to produce numerous false signals. In trending markets (when prices move up or down over an extended period) longer term moving averages are slow to react to reversals in trend. By automatically adjusting the smoothing constant, a variable moving average is able to adjust its sensitivity, allowing it to perform better in both types of markets.

A variable moving average is calculated as follows:

Where:

Triangular

Triangular moving averages place the majority of the weight on the middle portion of the price series. They are actually double-smoothed simple moving averages. The periods used in the simple moving averages varies depending on if you specify an odd or even number of time periods.

The following steps explain how to calculate a 12-period triangular moving average.

1. Add 1 to the number of periods in the moving average (e.g., 12 plus 1 is 13).
2. Divide the sum from Step #1 by 2 (e.g., 13 divided by 2 is 6.5).
3. If the result of Step #2 contains a fractional portion, round the result up to the nearest integer (e.g., round 6.5 up to 7).
4. Using the value from Step #3 (i.e., 7), calculate a simple moving average of the closing prices (i.e., a 7-period simple moving average).
5. Again using the value from Step #3 (i.e., 7) calculate a simple moving average of the moving average calculated in Step #4 (i.e., a moving average of a moving average).

A simple, or arithmetic, moving average is calculated by adding the closing price of the security for a number of time periods (e.g., 12 days) and then dividing this total by the number of time periods. The result is the average price of the security over the time period. Simple moving averages give equal weight to each daily price.

For example, to calculate a 21-day moving average of IBM: First, you would add IBM's closing prices for the most recent 21 days. Next, you would divide that sum by 21; this would give you the average price of IBM over the preceding 21 days. You would plot this average price on the chart. You would perform the same calculation tomorrow: add up the previous 21 days' closing prices, divide by 21, and plot the resulting figure on the chart.

where

Overview

A Moving Average is an indicator that shows the average value of a security's price over a period of time. When calculating a moving average, a mathematical analysis of the security's average value over a predetermined time period is made. As the security's price changes, its average price moves up or down.

There are five popular types of moving averages: simple (also referred to as arithmetic), exponential, triangular, variable, and weighted. Moving averages can be calculated on any data series including a security's open, high, low, close, volume, or another indicator. A moving average of another moving average is also common.

The only significant difference between the various types of moving averages is the weight assigned to the most recent data. Simple moving averages apply equal weight to the prices. Exponential and weighted averages apply more weight to recent prices. Triangular averages apply more weight to prices in the middle of the time period. And variable moving averages change the weighting based on the volatility of prices.

Interpretation

The most popular method of interpreting a moving average is to compare the relationship between a moving average of the security's price with the security's price itself. A buy signal is generated when the security's price rises above its moving average and a sell signal is generated when the security's price falls below its moving average.

The following chart shows the Dow Jones Industrial Average ("DJIA") from 1970 through 1993.

This type of moving average trading system is not intended to get you in at the exact bottom nor out at the exact top. Rather, it is designed to keep you in line with the security's price trend by buying shortly after the security's price bottoms and selling shortly after it tops.

The critical element in a moving average is the number of time periods used in calculating the average. When using hindsight, you can always find a moving average that would have been profitable (using a computer, I found that the optimum number of months in the preceding chart would have been 43). The key is to find a moving average that will be consistently profitable. The most popular moving average is the 39-week (or 200-day) moving average. This moving average has an excellent track record in timing the major (long-term) market cycles.

The length of a moving average should fit the market cycle you wish to follow. For example if you determine that a security has a 40-day peak to peak cycle, the ideal moving average length would be 21 days calculated using the following formula:

Exponential

An exponential (or exponentially weighted) moving average is calculated by applying a percentage of today's closing price to yesterday's moving average value. Exponential moving averages place more weight on recent prices.

For example, to calculate a 9% exponential moving average of IBM, you would first take today's closing price and multiply it by 9%. Next, you would add this product to the value of yesterday's moving average multiplied by 91% (100% - 9% = 91%).

Because most investors feel more comfortable working with time periods, rather than with percentages, the exponential percentage can be converted into an approximate number of days. For example, a 9% moving average is equal to a 21.2 time period (rounded to 21) exponential moving average.

The formula for converting exponential percentages to time periods is:

You can use the above formula to determine that a 9% moving average is equivalent to a 21-day exponential moving average:

The formula for converting time periods to exponential percentages is:

You can use the above formula to determine that a 21-day exponential moving average is actually a 9% moving average:

Overview

An envelope is comprised of two moving averages. One moving average is shifted upward and the second moving average is shifted downward.

Interpretation

Envelopes define the upper and lower boundaries of a security's normal trading range. A sell signal is generated when the security reaches the upper band whereas a buy signal is generated at the lower band. The optimum percentage shift depends on the volatility of the security--the more volatile, the larger the percentage.

The logic behind envelopes is that overzealous buyers and sellers push the price to the extremes (i.e., the upper and lower bands), at which point the prices often stabilize by moving to more realistic levels. This is similar to the interpretation of Bollinger Bands.

Example

The following chart displays American Brands with a 6% envelope of a 25-day exponential moving average.

Calculation

Envelopes are calculated by shifted moving averages. In the above example, one 25-day exponential moving average was shifted up 6% and another 25-day moving average was shifted down 6%.

Overview

The Commodity Channel Index ("CCI") measures the variation of a security's price from its statistical mean. High values show that prices are unusually high compared to average prices whereas low values indicate that prices are unusually low. Contrary to its name, the CCI can be used effectively on any type of security, not just commodities.

The CCI was developed by Donald Lambert.

Interpretation

There are two basic methods of interpreting the CCI: looking for divergences and as an overbought/oversold indicator.

• A divergence occurs when the security's prices are making new highs while the CCI is failing to surpass its previous highs. This classic divergence is usually followed by a correction in the security's price.

• The CCI typically oscillates between ±100. To use the CCI as an overbought/oversold indicator, readings above +100 imply an overbought condition (and a pending price correction) while readings below -100 imply an oversold condition (and a pending rally).

Example

The following chart shows the British Pound and its 14-day CCI. A bullish divergence occurred at point "A" (prices were declining as the CCI was advancing). Prices subsequently rallied. A bearish divergence occurred at point "B" (prices were advancing while the CCI was declining). Prices corrected. Note too, that each of these divergences occurred at extreme levels (i.e., above +100 or below -100) making them even more significant.

Calculation

A complete explanation of the CCI calculation is beyond the scope of this book. The following are basic steps involved in the calculation:

1. Add each period's high, low, and close and divide this sum by 3. This is the typical price.

2. Calculate an n-period simple moving average of the typical prices computed in Step 1.

3. For each of the prior n-periods, subtract today's Step 2 value from Step 1's value n days ago. For example, if you were calculating a 5-day CCI, you would perform five subtractions using today's Step 2 value.

4. Calculate an n-period simple moving average of the absolute values of each of the results in Step 3.

5. Multiply the value in Step 4 by 0.015.

6. Subtract the value from Step 2 from the value in Step 1.

7. Divide the value in Step 6 by the value in Step 5.

Further details on the contents and interpretation of the CCI can be found in an article by Donald Lambert that appeared in the October 1980 issue of Commodities (now known as Futures) Magazine.

Overview

Bollinger Bands are similar to moving average envelopes. The difference between Bollinger Bands and envelopes is envelopes are plotted at a fixed percentage above and below a moving average, whereas Bollinger Bands are plotted at standard deviation levels above and below a moving average. Since standard deviation is a measure of volatility, the bands are self-adjusting: widening during volatile markets and contracting during calmer periods.

Bollinger Bands were created by John Bollinger.

Interpretation

Bollinger Bands are usually displayed on top of security prices, but they can be displayed on an indicator. These comments refer to bands displayed on prices.

As with moving average envelopes, the basic interpretation of Bollinger Bands is that prices tend to stay within the upper- and lower-band. The distinctive characteristic of Bollinger Bands is that the spacing between the bands varies based on the volatility of the prices. During periods of extreme price changes (i.e., high volatility), the bands widen to become more forgiving. During periods of stagnant pricing (i.e., low volatility), the bands narrow to contain prices.

Mr. Bollinger notes the following characteristics of Bollinger Bands.

Example

The following chart shows Bollinger Bands on Exxon's prices.

Calculation

Bollinger Bands are displayed as three bands. The middle band is a normal moving average. In the following formula, "n" is the number of time periods in the moving average (e.g., 20 days).

The upper band is the same as the middle band, but it is shifted up by the number of standard deviations (e.g., two deviations). In this next formula, "D" is the number of standard deviations.

The lower band is the moving average shifted down by the same number of standard deviations (i.e., "D").

Mr. Bollinger recommends using "20" for the number of periods in the moving average, calculating the moving average using the "simple" method (as shown in the formula for the middle band), and using 2 standard deviations. He has also found that moving averages of less then 10 periods do not work very well.

Overview

The Average True Range ("ATR") is a measure of volatility. It was introduced by Welles Wilder in his book, New Concepts in Technical Trading Systems, and has since been used as a component of many indicators and trading systems.

Interpretation

Wilder has found that high ATR values often occur at market bottoms following a "panic" sell-off. Low Average True Range values are often found during extended sideways periods, such as those found at tops and after consolidation periods.

The Average True Range can be interpreted using the same techniques that are used with the other volatility indicators. Refer to the discussion on Standard Deviation for additional information on volatility interpretation.

Example

The following chart shows McDonald's and its Average True Range.

Calculation

The True Range indicator is the greatest of the following:

• The distance from today's high to today's low.

• The distance from yesterday's close to today's high.

• The distance from yesterday's close to today's low.

The Average True Range is a moving average (typically 14-days) of the True Ranges.

Overview

The Directional Movement System helps determine if a security is "trending." It was developed by Welles Wilder and is explained in his book, New Concepts in Technical Trading Systems.

Interpretation

The basic Directional Movement trading system involves comparing the 14-day +DI ("Directional Indicator") and the 14-day -DI. This can be done by plotting the two indicators on top of each other or by subtracting the +DI from the -DI. Wilder suggests buying when the +DI rises above the -DI and selling when the +DI falls below the -DI.

Wilder qualifies these simple trading rules with the "extreme point rule." This rule is designed to prevent whipsaws and reduce the number of trades. The extreme point rule requires that on the day that the +DI and -DI cross, you note the "extreme point." When the +DI rises above the -DI, the extreme price is the high price on the day the lines cross. When the +DI falls below the -DI, the extreme price is the low price on the day the lines cross.

The extreme point is then used as a trigger point at which you should implement the trade. For example, after receiving a buy signal (the +DI rose above the -DI), you should then wait until the security's price rises above the extreme point (the high price on the day that the +DI and -DI lines crossed) before buying. If the price fails to rise above the extreme point, you should continue to hold your short position.

In Wilder's book, he notes that this system works best on securities that have a high Commodity Selection Index. He says, "as a rule of thumb, the system will be profitable on commodities that have a CSI value above 25. When the CSI drops below 20, then do not use a trend-following system."

Example

The following chart shows Texaco and the +DI and -DI indicators. I drew "buy" arrows when the +DI rose above the -DI and "sell" arrows when the +DI fell below the -DI. I only labeled the significant crossings and did not label the many short-term crossings.

Calculation

The calculations of the Directional Movement system are beyond the scope of this book. Wilder's book, New Concepts In Technical Trading, gives complete step-by-step instructions on the calculation and interpretation of these indicators.

Overview

The Accumulation/Distribution is a momentum indicator that associates changes in price and volume. The indicator is based on the premise that the more volume that accompanies a price move, the more significant the price move.

Interpretation

The Accumulation/Distribution is really a variation of the more popular On Balance Volume indicator. Both of these indicators attempt to confirm changes in prices by comparing the volume associated with prices.

When the Accumulation/Distribution moves up, it shows that the security is being accumulated, as most of the volume is associated with upward price movement. When the indicator moves down, it shows that the security is being distributed, as most of the volume is associated with downward price movement.

Divergences between the Accumulation/Distribution and the security's price imply a change is imminent. When a divergence does occur, prices usually change to confirm the Accumulation/Distribution. For example, if the indicator is moving up and the security's price is going down, prices will probably reverse.

Example

The following chart shows Battle Mountain Gold and its Accumulation/Distribution.

Battle Mountain's price diverged as it reached new highs in late July while the indicator was falling. Prices then corrected to confirm the indicator's trend.

Calculation

A portion of each day's volume is added or subtracted from a cumulative total. The nearer the closing price is to the high for the day, the more volume added to the cumulative total. The nearer the closing price is to the low for the day, the more volume subtracted from the cumulative total. If the close is exactly between the high and low prices, nothing is added to the cumulative total.

The first of the three advancing white soldiers is a reversal candle. It either ends a downtrend or signifies that the stock is moving out of a period of consolidation after a decline. The candle on day two may open within the real body of day one. The pattern is valid as long as the candle of day two opens in the upper half of day one's range. By the end of day two, the stock should close near its high, leaving a very small or non-existent upper shadow. The same pattern is then repeated on day three. Below you will find an illustration of the three white soldiers candlestick pattern.

In a downtrend, a black candlestick is followed by a small white candlestick with its close near the low of the black candlestick.

A bearish pattern where the market should move lower when the white candlestick's low is penetrated by the next bar.

Three long black candlesticks consecutively lower closes that close near their lows.

A top reversal signal.

A Long black body followed by several small body and ending in another long black body. The small bodys are usually contained within the first black body's range.

The Unique Three River Bottom is a bullish pattern, somewhat characteristic of
the Morning Star Pattern. It is formed with three candles. At the end of a
downtrend, a long black body is produced. The second day opens higher, drops
down to new lows, then closes near the top of the trading range. This is a
Hammer-type formation. The third day opens lower but not below the low of the
previous day. It closes higher, producing a white candle. But it doesn’t close
higher than the previous day’s close. This pattern is a rare pattern.

Criteria


1. The candlestick body of the first day is a long black candle, consistent
with the prevailing trend.
2. The second day does a harami/hammer. It also has a black body.
3. The second day’s shadow has set a new low.
4. The third day opens lower, but not below the lowest point of the previous
day. It closes higher but below yesterday’s close.

Signal Enhancements


1. The longer the shadow of the second day, the probability of a successful
reversal becomes greater.

Meeting Lines (or Counterattack Lines) are formed when opposite colored bodies
have the same closing price. The first Candlestick body is the same color as the
current trend. The second body is formed by a gap open in the same direction as
the trend. However, by the close, it has come back to the previous day's close.
The Bullish Meeting Line has the same criteria as the Piercing Line except that is
closes the same close as the previous day and not up into the body. Likewise,
the Bearish Meeting Line is the same as the Dark Cloud pattern, but it does not
close down into the body of the previous day.

Criteria


1. The first candlestick body should continue the prevailing trend.
2. The second candlestick gaps open continuing the trend.
3. The real body of the second day closes at the close of the first day.
4. The body of the second day is opposite color of the first day
5. Both days should be long candle days.

Description

The Upside Gap Two Crows is a three-day pattern. The upside-gap is created
between the long white candle at the top of an uptrend and the small black
candle of the second day. The black candle gaps open and pulls back before the
end of the day. Even though it has pulled back, it did not fill the gap. The third
day opens above where the first black candle opened. It can not hold at these
levels and pulls back before the end of the day. Closing lower than the previous
day, it has engulfed the small black candle's body. However, it still did not close
the gap from the white candle.

Criteria


1. A long white candle continues the uptrend.
2. The real body of the next day is black while gapping up and not filling the gap.
3. The third day opens higher than the second day's open and closes below
the second day's close. This produces a black candle that completelyengulfs the small black candle.
4. The close of the third day is stil above the close of the last white candle

Bullish Abandoned Baby Bearish Abandoned Baby


Abandoned Baby pattern is similar to the family of Morning Star and Evening Star patterns. It is almost the
same as Morning Doji and Evening Doji Star. The difference is the shadows on the Doji must gap below the
shadows of the first and third days for the Abandoned Baby bottom.

Recognition Criteria:

The first day shal indicates the prior trend.
The second day is a Doji which gaps above or below the previous day's range.
The third day is the opposite color of the first day and gaps in the opposite direction.
There is no shadows overlapping between the Doji and other two days.

(Confirmation is suggested.)

An Evening Doji Star is when a Doji Star is in an uptrend fol owed by a long black body. Like the regular
Evening Star, the third day will support the reversal of the trend. It is more significant than the regular
Evening Star pattern.

Recognition Criteria:

The first day is a white day which indicates the trend of the market.
The second day is a Doji day.
The third day is black day which supports the reversal of the trend.

(Confirmation is suggested.)

When a downtrend market is in place, fol owing by a Doji Star. Like the regular Morning Star, the third day
will support the reversal of the trend. It is more significant than the regular Morning Star pattern.

Recognition Criteria:

The first day is a black day which indicates the trend of the market.
The second day must be a Doji day.
The third day is a white day and supports the reversal of the trend.

(Confirmation is suggested.)

Evening Star (Bearish)--a top reversal pattern where the first is a tall
real body, the second is a small real body (green or red) which gaps
high to form a star. The third is a red candlestick which closes well
into the first session's green real body.

A Doji Star is a trend reversal pattern which is composed of a long black body fol owed by a doji(a pattern
with the same opening and closing price).

Recognition Criteria:

Long black day fol owed by a doji.
The doji gaps down from the prior black body.

(Confirmation is suggested.)

Recognition

The market is in uptrend
1st day is a long white body
2nd day is a black body which opens above the previous day’s high

2nd day closes within, but below the midpoint of the 1st day's body

In a downtrend the market gaps open, but rallies strong to close above the previous days
midpoint. This pattern suggests an opportunity for the bulls to enter the market and support the
trend reversal. The Piercing Line pattern is the opposite of the Dark Cloud Cover.


A long black body followed by a white body.
The white body pierces the midpoint of the prior white body.

Occurs in a downtrend.

If you are a regular Swing Trader reader, then the inverted hammer should seem very
familiar. However, you may not be able to put your finger on exactly why it looks so
familiar.

The reason is that the inverted hammer is identical in appearance to the shooting star,
which we discussed in our December 8th, 2003 Swing Trader issue. The difference is
that the shooting star occurs at the end of a long uptrend. The inverted hammer, on the
other hand, occurs after a significant decline has taken place.

If you examine the inverted hammer carefully, it hardly looks like a bullish candle. Prices
opened low and then rallied strongly. By the close of trading, however, the stock has
given back almost all of the day's gains. That leaves a small real body and a very large
upper shadow. If anything, the candle looks bearish. The bulls could not sustain a rally,
so the bears took the stock back toward its lows for the day.

So, why should this candle potentially set up an important reversal? My theory is that the
inverted hammer is a signal that shorts are beginning to cover their positions.

Here is my reasoning. Since the inverted hammer can only occur after a sustained
downtrend, the stock is in all probability already oversold. Therefore, the inverted
hammer may signify that shorts are beginning to cover. In addition, traders who have
held long positions in the security, most of whom are now showing large losses, are often
quick to dump their shares by selling into strength. This will also serve to drive the stock
back down.

With this candle, it is imperative to watch the next day's trading action. If the stock opens
strongly and remains strong during the day, then a key reversal is likely in progress.

Bullish Harami Cross Pattern is a doji preceded by a long black real body. The Bullish
Harami Cross Pattern is a major bullish reversal pattern. It is more significant than a
regular Bullish Harami Pattern.

Recognition Criteria:

1. Market is characterized by downtrend.
2. Then we see a long black candlestick.
3. Long black candlestick is followed by a doji completely engulfed by the real body
of the first day. The shadows (high/low) of the doji may not be necessarily contained
within the first black body, though it's preferable if they are.

Explanation:

The Bullish Harami Cross Pattern is a strong signal of disparity about the market’s
health. During a downtrend, the heavy selling reflected by a long, black real body; is
followed by a doji next day. This shows that the market is starting to severe itself
from the prior downtrend.

Important Factors:

The Bullish Harami Pattern is not a major reversal pattern, however the Bullish
Harami Cross Pattern is a major upside reversal pattern. Short traders will not be
wise to ignore the significance of a harami cross just after a long black candlestick.
Harami crosses point out to the bottoms.


A third day confirmation of the reversal is recommended (though not required) to
judge that the downtrend has reversed. The confirmation may be in the form of a
white candlestick, a large gap up or a higher close on the next trading day.

Bearish Harami Pattern is a two-candlestick pattern composed of a small black real
body contained within a prior relatively long white real body. “Harami” is an old
Japanese word for “pregnant”. The long white candlestick is “the mother” and the
small candlestick is “the baby”.

Recognition Criteria:

1. Market is characterized by an uptrend.
2. We see a long white candlestick on the first day.
3. Then we see a black candlestick on the second day whose real body is completely
engulfed by the real body of the first day. The shadows (high/low) of the second
candlestick do not have to be contained within the first body, though it's preferable if
they are.



Explanation:

The Bearish Harami Pattern is a sign of a disparity about the market’s health. Bull
market continues further confirmed by the long white real body’s vitality but then we
see the small black real body which shows some uncertainty. This shows the bulls’
upward drive has weakened and now a trend reversal is possible.

Important Factors:

It is important that the second day black candlestick has a minute real body relative
to the prior candlestick and that this small body is inside the larger one. The Bearish
Harami Pattern does not necessarily mean a market reversal. It rather predicts that
the market may not continue with its previous uptrend. There are however some
instances in which the Bearish Harami Pattern can warn of a significant trend change
- especially at market tops.

A confirmation of the reversal on the third day is required to be sure that the
uptrend has reversed. This confirmation may be in the form of a black candlestick, a
large gap down or a lower close on the next trading day (the third day).

A bullish engulfing candle occurs after a significant downtrend. Note that the engulfing
candle must encompass the real body of the previous candle, but need not surround the
shadows. Below you will find an illustration of a bullish engulfing candle:



A bearish engulfing candle occurs after a significant uptrend. Again, the shadows need
not be surrounded. Below you will find an illustration of a bearish engulfing candle:
The power of the engulfing candle is increased by two factors -- the size of the candle
and the volume on the day it occurs. The bigger the engulfing candle, the more



significant it is likely to be. A large bullish engulfing candle says the bulls have seized
control of the market after a downtrend. Meanwhile, a large bearish engulfing says the
bears have taken command after an uptrend. Also, if volume is above normal on the day
when the signal is given, this increases the power of the message.

In a Hammer, during a downtrend, there is an initial sharp sell off to new lows. However, by the
end of the day, the market rallies to close at or near its high for the day.



The sharp recovery suggests that the bearish sentiment may be beginning to wane and if a move
above the high of the Hammer days occurs during the next day's trading there is a stronger risk of
complete trend reversal.

In a Hanging man, during an uptrend there is a sharp sell off after the market. By the end of the
day, the market rallies to close at or near the high for the day.

This pattern definitely requires confirmation. The recovery in price over the day could mean the
bulls are still in control. However, a break to new highs on the next trading day is required to
confirm. Alternately, a decline to test the low of the Hanging Man day will suggest a trend reversal