Moving Averages
Introduction
Moving averages are one of the most popular and easy to use tools available to
the technical analyst. They smooth a data series and make it easier to spot
trends, something that is especially helpful in volatile markets. They also
form the building blocks for many other technical indicators and overlays.
The two most popular types of moving averages are the Simple Moving Average
(SMA) and the Exponential Moving Average (EMA). They are described in more
detail below.
Simple Moving Average (SMA)
(Click here for a live example of a Simple Moving Average)
A simple moving average is formed by computing the average (mean) price of a
security over a specified number of periods. While it is possible to create
moving averages from the Open, the High, and the Low data points, most moving
averages are created using the closing price. For example: a 5-day simple
moving average is calculated by adding the closing prices for the last 5 days
and dividing the total by 5.
10+ 11 + 12 + 13 + 14 = 60
(60 / 5) = 12
The calculation is repeated for each price bar on the chart. The averages are
then joined to form a smooth curving line - the moving average line. Continuing
our example, if the next closing price in the average is 15, then this new
period would be added and the oldest day, which is 10, would be dropped. The
new 5-day simple moving average would be calculated as follows:
11 + 12 + 13 + 14 +15 = 65
(65 / 5) = 13
Over the last 2 days, the SMA moved from 12 to 13. As new days are added, the
old days will be subtracted and the moving average will continue to move over
time.
In the example above, using closing prices from Eastman Kodak (EK), day 10 is
the first day possible to calculate a 10-day simple moving average. As the
calculation continues, the newest day is added and the oldest day is
subtracted. The 10-day SMA for day 11 is calculated by adding the prices of day
2 through day 11 and dividing by 10. The averaging process then moves on to the
next day where the 10-day SMA for day 12 is calculated by adding the prices of
day 3 through day 12 and dividing by 10.
The chart above is a plot that contains the data sequence in the table. The
simple moving average begins on day 10 and continues.
This simple illustration highlights the fact that all moving averages are
lagging indicators and will always be "behind" the price. The price of EK is
trending down, but the simple moving average, which is based on the previous 10
days of data, remains above the price. If the price were rising, the SMA would
most likely be below. Because moving averages are lagging indicators, they fit
in the category of trend following indicators. When prices are trending, moving
averages work well. However, when prices are not trending, moving averages can
give misleading signals.
Exponential Moving Average (EMA)
(Click here for a live example of an Exponential Moving Average)
In order to reduce the lag in simple moving averages, technicians often use
exponential moving averages (also called exponentially weighted moving
averages). EMA's reduce the lag by applying more weight to recent prices
relative to older prices. The weighting applied to the most recent price
depends on the specified period of the moving average. The shorter the EMA's
period, the more weight that will be applied to the most recent price. For
example: a 10-period exponential moving average weighs the most recent price
18.18% while a 20-period EMA weighs the most recent price 9.52%. As we'll see,
the calculating and EMA is much harder than calculating an SMA. The important
thing to remember is that the exponential moving average puts more weight on
recent prices. As such, it will react quicker to recent price changes than a
simple moving average. Here's the calculation formula.
Exponential Moving Average Calculation
Exponential Moving Averages can be specified in two ways - as a percent-based
EMA or as a period-based EMA. A percent-based EMA has a percentage as it's
single parameter while a period-based EMA has a parameter that represents the
duration of the EMA.
The formula for an exponential moving average is:
EMA(current) = ( (Price(current) - EMA(prev) ) x Multiplier) + EMA(prev)
For a percentage-based EMA, "Multiplier" is equal to the EMA's specified
percentage. For a period-based EMA, "Multiplier" is equal to 2 / (1 + N) where
N is the specified number of periods.
For example, a 10-period EMA's Multiplier is calculated like this:
(2 / (Time periods + 1) ) = (2 / (10 + 1) ) = 0.1818 (18.18%)
This means that a 10-period EMA is equivalent to an 18.18% EMA.
Note: StockCharts.com only support period-based EMA's.
Below is a table with the results of an exponential moving average calculation
for Eastman Kodak. For the first period's exponential moving average, the
simple moving average was used as the previous period's exponential moving
average (yellow highlight for the 10th period). From period 11 onward, the
previous period's EMA was used. The calculation in period 11 breaks down as
follows:
(C - P) = (57.15 - 59.439) = -2.289
(C - P) x K = -2.289 x .181818 = -0.4162
( (C - P) x K) + P = -0.4162 + 59.439 = 59.023
*The 10-period simple moving average is used for the first calculation only.
After that the previous period's EMA is used.
(Download this table as an Excel spreadsheet)
Note that, in theory, every previous closing price in the data set is used in
the calculation of each EMA that makes up the EMA line. While the impact of
older data points diminishes over time, it never fully disappears. This is true
regardless of the EMA's specified period. The effects of older data diminish
rapidly for shorter EMA's. than for longer ones but, again, they never
completely disappear.
Simple Versus Exponential
>From afar, it would appear that the difference between an exponential moving
>average and a simple moving average is minimal. For this example, which uses
>only 20 trading days, the difference is minimal, but a difference nonetheless.
>The exponential moving average is consistently closer to the actual price. On
>average, the EMA is 3/8 of a point closer to the actual price than the SMA.
>From day 10 to day 20, the EMA was closer to the price than the SMA 8 out of
>11 times. The average absolute difference between the exponential moving
>average and the current price was 1.52 and the simple moving average had an
>average absolute difference of 1.69. This means that on average, the
>exponential moving average was 1.52 point above or below the current price and
>the simple moving average was 1.69 points above or below the current price.
When Kodak stopped falling and started to trade flat, the SMA kept on
declining. During this period, the SMA was closer to the actual price than the
EMA. The EMA began to level out with the actual price, and remain further away.
This was because the actual price started to level out. Because of its lag, the
SMA continued to decline and nearly touched the actual price on 13-Dec.
A comparison of a 50-day EMA and a 50-day SMA for IBM also shows that the EMA
picks up on the trend quicker than the SMA. The blue arrows mark points when
the stock started a strong trend. By giving more weight to recent prices, the
EMA reacted quicker than the SMA and remained closer to the actual price. The
gray circle shows when the trend began to slow and a trading range developed.
When the change from trend to trading began, the SMA was closer to the price.
As the trading range continued into 2001, both moving averages converged. In
early 2001, CPQ started to trend up and the EMA was quicker to pick up on the
recent price change and remain closer to the price.
Which is better?
Which moving average you use will depend on your trading and investing style
and preferences. The simple moving average obviously has a lag, but the
exponential moving average may be prone to quicker breaks. Some traders prefer
to use exponential moving averages for shorter time periods to capture changes
quicker. Some investors prefer simple moving averages over long time periods to
identify long-term trend changes. In addition, much will depend on the
individual security in question. A 50-day SMA might work great for identifying
support levels in the NASDAQ, but a 100-day EMA may work better for the Dow
Transports. Moving average type and length of time will depend greatly on the
individual security and how it has reacted in the past.
The initial thought for some is that greater sensitivity and quicker signals
are bound to be beneficial. This is not always true and brings up a great
dilemma for the technical analyst: the trade off between sensitivity and
reliability. The more sensitive an indicator is, the more signals that will be
given. These signals may prove timely, but with increased sensitivity comes an
increase in false signals. The less sensitive an indicator is, the fewer
signals that will be given. However, less sensitivity leads to fewer and more
reliable signals. Sometimes these signals can be late as well.
For moving averages, the same dilemma applies. Shorter moving averages will be
more sensitive and generate more signals. The EMA, which is generally more
sensitive than the SMA, will also be likely to generate more signals. However,
there will also be an increase in the number of false signals and whipsaws.
Longer moving averages will move slower and generate fewer signals. These
signals will likely prove more reliable, but they also may come late. Each
investor or trader should experiment with different moving average lengths and
types to examine the trade-off between sensitivity and signal reliability.
Trend-Following Indicator
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Moving averages smooth out a data series and make it easier to identify the
direction of the trend. Because past price data is used to form moving
averages, they are considered lagging, or trend following, indicators. Moving
averages will not predict a change in trend, but rather follow behind the
current trend. Therefore, they are best suited for trend identification and
trend following purposes, not for prediction.
When to Use
Because moving averages follow the trend, they work best when a security is
trending and are ineffective when a security moves in a trading range. With
this in mind, investors and traders should first identify securities that
display some trending characteristics before attempting to analyze with moving
averages. This process does not have to be a scientific examination. Usually, a
simple visual assessment of the price chart can determine if a security
exhibits characteristics of trend.
In its simplest form, a security's price can be doing only one of three things:
trending up, trending down or trading in a range. An uptrend is established
when a security forms a series of higher highs and higher lows. A downtrend is
established when a security forms a series of lower lows and lower highs. A
trading range is established if a security cannot establish an uptrend or
downtrend. If a security is in a trading range, an uptrend is started when the
upper boundary of the range is broken and a downtrend begins when the lower
boundary is broken.
In the Ford (F) example, it is evident that a stock can go through both
trending and trading phases. The red circles indicate trading range phases that
are interspersed among trending periods. It is sometimes difficult to determine
when a trend will stop and a trading range will begin or when a trading range
will stop and a trend will begin. The basic rules for trends and trading ranges
laid out above can be applied to Ford. Notice the trading range periods, the
breakouts (both up and down) and the trending periods. The moving average
worked well in times of trend, but faired poorly in times of trading. Also note
how the moving average lags behind the trend: it is always under the price
during an uptrend and above the price during a downtrend. A 50-day simple
moving average was used for this example. However, the number of periods is
optional and much will depend on the characteristics of the security as well as
an individual's trading and investing
style.
If price movements are choppy and erratic over an extended period of time, then
a moving average is probably not the best choice for analysis. The chart for
Coca-Cola (KO) shows a security that moved from 60 to 40 in a couple months in
2001. Prior to this decline, the price gyrated above and below its moving
average. After the decline, the stock continued its erratic behavior without
developing much of a trend. Trying to analyze this security based on a moving
average is likely to be a lesson in futility.
A quick look at the chart for Time Warner (TWX) shows a different picture. Over
the same time period, Time Warner has shown the ability to trend. There are 3
distinct trends or price movements that extend for a number of months. Once the
stock moves above or below the 70-day SMA, it usually continues in that
direction for a little while longer. Coca-Cola, on the other hand, broke above
and below its 70-day SMA numerous times and would have been prone to numerous
whipsaws. A longer moving average might work better, but it is clear that the
Time Warner chart had better trending characteristics.
Moving Average Settings
Once a security has been deemed to have enough characteristics of trend, the
next task will be to select the number of moving average periods and type of
moving average. The number of periods used in a moving average will vary
according to the security's volatility, trendiness and personal preferences.
The more volatility there is, the more smoothing that will be required and
hence the longer the moving average. Stocks that do not exhibit strong
characteristics of trend may also require longer moving averages. There is no
one set length, but some of the more popular lengths include 21, 50, 89, 150
and 200 days as well as 10, 30 and 40 weeks. Short-term traders may look for
evidence of 2-3 week trends with a 21-day moving average, while longer-term
investors may look for evidence of 3-4 month trends with a 40-week moving
average. Trial and error is usually the best means for finding the best length.
Examine how the moving average fits with the price data.
If there are too many breaks, lengthen the moving average to decrease its
sensitivity. If the moving average is slow to react, shorten the moving average
to increase its sensitivity. In addition, you may want to try using both simple
and exponential moving averages. Exponential moving averages are usually best
for short-term situations that require a responsive moving average. Simple
moving averages work well for longer-term situations that do not require a lot
of sensitivity.
Uses for Moving Averages
There are many uses for moving averages, but three basic uses stand out:
* Trend identification/confirmation
* Support and Resistance level identification/confirmation
* Trading Systems
Trend Identification/Confirmation
There are three ways to identify the direction of the trend with moving
averages: direction, location and crossovers.
The first trend identification technique uses the direction of the moving
average to determine the trend. If the moving average is rising, the trend is
considered up. If the moving average is declining, the trend is considered
down. The direction of a moving average can be determined simply by looking at
a plot of the moving average or by applying an indicator to the moving average.
In either case, we would not want to act on every subtle change, but rather
look at general directional movement and changes.
In the case of Disney (DIS), a 100-day exponential moving average (EMA) has
been used to determine the trend. We do not want to act on every little change
in the moving average, but rather significant upturns and downturns. This is
not a scientific study, but a number of significant turning points can be
spotted just based on visual observation (red circles). A few good signals were
rendered, but also a few whipsaws and late signals. Much of the performance
would depend on your entry and exit points. The length of the moving average
influences the number of signals and their timeliness. Moving averages are
lagging indicators. Therefore, the longer the moving average is, the further
behind the price movement it will be. For quicker signals, a 50-day EMA could
have been used.
The second technique for trend identification is price location. The location
of the price relative to the moving average can be used to determine the basic
trend. If the price is above the moving average, the trend is considered up. If
the price is below the moving average, the trend is considered down.
This example is pretty straightforward. The long-term for Cisco (CSCO) is
determined by the location of the stock relative to its 100-day SMA. When CSCO
is above its 100-day SMA, the trend is considered bullish. When the stock is
below the 100-day SMA, the trend is considered bearish. Buy and sell signals
are generated by crosses above and below the moving average. There was a brief
sell signal generated in Aug-99 and a false buy signal in July-00. Both of
these signals occurred when Cisco's trend began to weaken. For the most part
though, this simple method would have kept an investor in throughout most of
the bull move.
The third technique for trend identification is based on the location of the
shorter moving average relative to the longer moving average. If the shorter
moving average is above the longer moving average, the trend is considered up.
If the shorter moving average is below the longer moving average, the trend is
considered down.
For Inter-Tel (INTL), a 30/100 moving average crossover was used to determine
the trend. When the 30-day moving average moves above the 100-day moving
average, the trend is considered bullish. When the 30-day moving average
declines below the 100-day moving average, the trend is considered bearish. A
plot of the 30/100 differential is plotted below the price chart by using the
Percentage Price Oscillator (PPO) set to (30,100,1). When the differential is
positive the trend is considered up – when it is negative the trend is
considered down. As with all trend-following systems, the signals work well
when the stock develops a strong trend, but are ineffective when the stock is
in a trading range. Also notice that the signals tend to be late and after the
move has begun. Again, trend following indicators are best for identification
and following, not predicting.
Support and Resistance Levels
Another use of moving averages is to identify support and resistance levels.
This is usually accomplished with one moving average and is based on historical
precedent. As with trend identification, support and resistance level
identification through moving averages works best in trending markets.
After breaking out of a trading range, Sun Microsystems (SUNW) successfully
tested moving average support in late July and early August. Also notice that
the June resistance breakout near 18 turned into support. Therefore, the moving
average acted as a confirmation of resistance-turned-support. After this first
test, the 50-day moving average went on to 4 more successful support tests over
the next several months. A break of support from the 50-day moving average
would serve as a warning that the stock may move into a trading range or may be
about to change the direction of the trend. Such a break occurred in Apr-00 and
the 50-day SMA turned into resistance later that month. When the stock broke
above the 50-day SMA in early Jun-00, it returned to a support level until the
Oct-00 break. In Oct-00, the 50-day SMA became a resistance level and that held
for many months.
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