# Simple Moving Average (SMA)

Table of Contents

- 1 Simple Moving Average (SMA)
- 2 Exponential Moving Average (EMA)
- 3 Weighted Moving Average (WMA)
- 4 Using of a Simple (arithmetic) moving average
- 5 Using of two Moving Averages
- 6 Using of three MAs
- 7 Sensitiveness and sequence of the technical indicators
- 8 Types of oscillators
- 9 Central and range oscillators
- 10 Momentum
- 11 Bases of the physic momentum
- 12 Conclusion
- 13 Momentum and Relative Strenght Index (RSI)
- 14 Relative Strenght Index (RSI)
- 15 Tactics of using indicators when taking up a position

The SMA is the easiest to construct. For its estimation, first the courses of closing for the last n periods are summed up and then the result is divided by n. In practice, the result is an average course for these n periods, which is plotted on the graphics. The course of every following period is added to the sum of the previous ones, and the course of the most distant period is subtracted. Then the new sum is divided by n. This method ensures the “movement” of the indicator.

For example, a SMA for five-day periods will be estimated after adding the courses of closing for the last 5 days and dividing the sum by 5.

### Exponential Moving Average (EMA)

In order to decrease the delay of the SMAs, the technical analysts sometimes use exponential (or exponential weighted) moving averages. They reduce the delay as they carry away more weight to the nearest in time courses. This weight depends on the magnitude of the moving average’s period. The shortest period we use, the bigger weight is given up to the nearest course.

Examples.

At a given EMA, estimated for 10 periods, the weight of the running course is 18.18%.

At a given EMA, estimated for 20 periods, the weight of the running course is 9.52%.

EMA = [K x (C – P)] + P, where:

EMA – an exponential moving average for the running period;

C – The course of closing of the running period;

P – The value of EMA of the previous period;

K – The smoothing constant (could be also meet as EMA %)

For estimation of the first value of the EMA a SMA is used. The smoothing constant applies the respective relative weight of the running course in relation to the value of EMA of the previous period. The formula for K is:

K = 2/(1 + N), where:

N – the number of periods, used for estimation of an EMA

At a given EMA, estimated for 5 periods, the weight of the running course is 33.33%.

### Weighted Moving Average (WMA)

The WMA gives away bigger weight to the nearer data. The weight is based on the number of periods for the estimation of the smoothing average and it uses the sum of the given periods.

Example: For estimation of the smoothing average for 5 periods at a day period:

The sum of the days = 1 + 2 + 3 + 4 + 5 = 15

The example is illustrated in the following table.

Characterization and application of the Moving Averages

The Moving Average (MA) is a trend indicator, which makes easier the analysis of the trends by smoothing the hesitations in the values of the serial course data.

For its estimation, it is used data of the previous periods and therefore it is known as a trend, falling behind indicator. The smooth averages do not predict change in the trend, but follow the running trend. For that reason, they are most appropriate for trends identification and their following.

Characterization

The MAs act best when there is a clearly definite trend of the course movements and they are inefficient when the currency trading courses hesitate within the bounds of a definite range.

Having this in mind, before analyzing with the help of a MA, every trader should first identify the currency couples, whose course hesitations have trend characterizations in the given time range.

Therefore, there is no need of a scientific research, but a simple visual judgement of the currency couple’s price graphics. Generally speaking, the currency course could do one of the following three things: to move up (a rising trend), to move down (a decreasing trend) or to hesitate in a definite range. A rising trend exists when a given currency course does a series of higher peaks and higher bottoms.

An established decreasing row is seen when the currency course forms a series of lower bottoms and lower peaks. There is a market range when there could not be established a presence of a rising or a decreasing trend. If the currency course is traded in range, for a beginning of a rising or a decreasing trend, we can count a respective break of the upper or lower border of the definite course range.

After we are sure that the course hesitations read the trend characterizations of the analyzed time period, the next step is to choose the type of the MA and the number of periods, needed for its estimation. The number of the periods will vary depending on the volatility of the analyzed currency, its trend characterizations and the personal preferences of the individual trader. A higher volatility requires a greater “smoothing” and therefore a bigger number of periods for the estimation of the MA. A bigger number of periods is used when analyzing currencies, which do not show clear trend characterizations of the analyzed period.

There are no definite ciphers for a number of periods, which could be used, but some of the most common periods include 21, 50, 89, 100 and 200 days, as well as, 10,30 and 40 weeks. Traders, who trade in a short-term, could use a 21-day MA for identification of a 2-3-weekly trend, while these, who trade in a long-term, could follow 3-4-monthly trends with the help of a 40-day MA.

The method of try outs and faults is usually the best way for determination of the optimum number of periods. For that purpose, the MA is inscribed into the graphics. If there are many crossing between the indicators and the courses, the sensitiveness of the MA should be reduced by increasing the number of the used periods. If the MA reacts slowly, respectively we will reduce the number of the periods in order to increase its sensitiveness. In addition to this, we could choose between using a simple (arithmetic) or an exponential moving average. The EMA reacts faster to the market changes and is the most suitable for short-term movements’ analyses. The SMA reacts slowly and it s used for long-term prognoses.

Application

MAs are used basically for the following purposes:

- Identification/ Confirmation of the trends.
- Identification/ Confirmation of the support and resistance levels.
- Systematic design (trade systems developing).

Identification/ Confirmation of the trends

There are three ways for trade identification, using MAs:

- Determine the MA direction.
- Determine the course values’ position in relation to the MA.
- Mutual crossing of two moving averages.

The first method uses the direction of the MA for determination of the trend. The direction could be defined with a simple eye while observing the graphic image of the indicator. If the MA rises, we consider the trend for a rising one. If it decreases, then there is a decreasing trend. In both cases we would not like to react to every insignificant change, but only to the significant changes in the MA direction.

The second and most popular method compares the relation between the course values’ moving average and the course values themselves.

If the course values fall upon the MA, the trend is rising. And if the course values are under the MA, the trend is decreasing.

The third method for trend identification is based on the mutual position of the two moving averages. For that purpose, two MAs with a different number of periods are constructed on the course graphic. The trend is rising if the shortest (spanning the shorter time period) MA has crossed and is now situated over the longer (spanning the loner time period) MA. The trend is decreasing if the shorter MA has pierced and is now situated under the longer MA.

Identification/ Confirmation of the support and resistance levels

Other popular technique uses MAs for indication of eventual support and resistance levels. For that purpose, it is usually used one MA and its curve serves likewise to the support and resistance lines in the classic treatment of the technical analysis.

### Using of a Simple (arithmetic) moving average

This is the simplest system, using MA for signals generation. It is advisable for it to combine with other instruments of the technical analysis for market range identification. This aims avoiding loss in consequence of the frequent crossing of the course values with the MA’s curve.

Signals for trading

The signals are generated when the course values cross the MA.

Long positions reveal when the course crosses from below upwards the MA.

Short positions reveal when the course crosses from upwards below the MA.

Signal filtration

The filters are used for elimination of the insecure signals. They objectively show if the course crosses the MA.

Used filters:

- The course of closing – it is followed for the MA crossing from the course of closing for one, two or three consecutive periods.
- A crossing of the MA by a whole bar (at the histogram)
- Two or three consecutive bars must cross the MA.
- The MA direction.
- If we use the MA direction for signals’ filtration, the positioning of the market occurs itself if the slope of the MA coincide with the direction of the position.

Long positions are revealed if the course crosses from below upwards a rising MA. Short positions are revealed if the course crosses from upwards below a decreasing MA. Different combinations of these filters could be used.

## Using of two Moving Averages

Filtration alternative

There are used fast (for a shorter period) and slow (for a longer period) MAs as a measuring of the power and the direction of the trend. The fast MA is used for smoothing the course line and the number of periods at a fast MA conforms to the analyzed and traded cycle.

And this system, as well as the using of one MA, shows the same weakness – when there is a range, it generates faulty signals.

Trade Signals

They are generated when there is a mutual crossing of the two MAs.

Long positions are revealed when the fast MA crosses the slow MA from below upwards. Short positions are revealed when the fast MA crosses the slow MA from upwards below. The identification of the two MAs on the graphic happens as we compare the marked peaks and bottoms. The fast MA reads higher peaks and bottoms.

## Using of three MAs

This system is used for identification of markets without a trend, which are better to avoid because of the faulty signals, generated from the trend indicator.

Signals for trading

Three MAs are used: fast, intermediate and slow. The positioning levels are determined by the crossing of the slow MA by the intermediate one. And the going out from an open position takes place as it is followed for a crossing of the intermediate MA by the fast MA.

Necessary and sufficient conditions for opening of long positions:

- The intermediate MA has pierced from below upwards the slow MA.
- The fast MA is situated over the intermediate MA.

An open long position is closed when the fast MA pierces from below upwards the intermediate MA.

Necessary and sufficient conditions for opening of short positions:

- The intermediate MA has pierced from upwards below the slow MA.
- The fast MA is situated under the intermediate MA.

An open short position is closed when the fast MA pierces from upwards below the intermediate MA.

### Sensitiveness and sequence of the technical indicators

There is dependence between these two characteristics of a given indicator. In the perfect case, we would want the indicator to react often to the course movements and to give early, correct signals. If we increase the sensitiveness by reducing the number of periods, the indicator will generate more signals, but the number of the mistakes will rise.

If we reduce the sensitiveness by increasing the number of periods, the number of the faulty signals will decrease, but at the same time the signals will fall behind.

The longer the MA period is, the slower it will react to the market changes and the less signals will be generated. And vice versa, if we reduce the period, the curve of the MA will become more volative and quickly changeable, and that way the number of the generated faulty signals will increase.

The same thing applies to the different transitory indicators. RSI with period 14 will generate fewer signals than that with period 5, while the smaller period will presuppose bigger sensitiveness of the indicator and more overestimated/underestimated levels. All traders should choose themselves the appropriate time frame, conformable to their own trade style and the aims they have made.

### Types of oscillators

The oscillator is an indicator, whose values change as time goes by and fluctuates over or under the definite central line or between definite levels. The oscillators’ values can stay for a long time at extreme levels (overestimated or underestimated), but they can not maintain a trend for a long period of time. The movements are more restrained and the trends are limited, regardless to the period.

### Central and range oscillators

The central oscillators fluctuate round the central point or line. They are good for identification of the power or the direction of the course momentum. In its purest form, the momentum is positive (bullish), when the central oscilltors’ values are over the central line and negative (bearish), when the oscillators’ values are under the central line.

Central oscillators are: MACD, ROC, Momentum.

Range oscillators are: RSI, Stochastic.

### Momentum

The term “momentum” is frequently used in the market terminology when a reference is made to the market action. What actually do we have in mind when talking about momentum? The traders, using technical analysis for market prognosis, believe that if the course of a given financial instrument increases, it will continue its movement upward and back, if it falls, this direction will stay the same.

Martin Pring, a well-known trader and author of many books, devoted to the technical analysis, also shares the same opinion, adding that if there is a developing trend, it will continue to develop.

In that sense, when talking about momentum, we understand the market inclination to show constancy in its movement. This idea would be better expressed with words like “inertia” and “moment of inertia” from the physics.

According to John Murphy, also author of many books about the technical analysis, the term “momentum” can be defined as a technique, used for the construction of an oscillator that measures the overestimated and underestimated levels at time reading of the differences in the market courses. As there exists confusion between momentum and oscillator, Murphy gives the following definition for the oscillators: “Indicators which define when the market courses/prices are placed on overestimated or underestimated levels”.

From these definitions we can make the conclusion that “momentum” and “oscillator” are terms with a wide application. Despite the fact how simple and clear these definitions look, the market momentum could be better understood when compared with the physic momentum.

For that purpose, first we have to examine the characteristics of the physic momentum at the pendulum and after that we will compare it with the price momentum.

### Bases of the physic momentum

The pendulum, as well as the courses/prices at the market, have the following characteristics – a moment of inertia and oscillation.

In Physics – actually in theoretical mechanic – the term “momentum” is clearly defined. It is used at the physical bodies and it includes two classic conceptions – velocity and mass. It is defined as a calculation of these two.

The British philosopher and scientist Isaac Newton enunciate the principle of inertia, as follows: “Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.”

We call oscillation to the slow and periodic motions, vibrations round a constant point or round a constant axis, which the pendulum does under the influence of gravity. After each motion, the pendulum losses energy as a result of the friction of the thread into the swing axis and the air resistance. After each coming swing, the pendulum slows up its motion and eventually stops unless energy equal to the initial energy loss is applied. This energy is provided by the gravity increase and the needed energy is preserved as potential energy. When the gravity falls, because of the gravitation force, the potential energy is transferred to the pendulum motion, compensating the loss of energy caused by friction and air resistance.

With the made admissions in relation to the energy loss, the pendulum does simple harmonious motion (the swings are isochronic).

Let’s move the analogy with the pendulum to the theory of the course momentum.

When the course momentum reaches extreme levels, we say that the course is overestimated or underestimated. The extreme levels under the zero line indicate underestimated price levels, equivalent to the final point of the pendulum motion.

A common momentum oscillator with clearly established values for indication of the overestimated and underestimated conditions is the Relative Strenght Index (RSI). RSI, introduced by Wells Wilder, oscillates around the line of the number 50, instead of 0 and the scale is limited from 0 in its bottom end to 100 in the upper. Wilder determines that 70 indicates overestimated levels, while 30 – underestimated. Actually, we have a momentum oscillator with all the three characteristics – it oscillates around an equilibrium line (at value 50), indicates over\underestimated levels at values 70/30 and has a direction (its values increase or decrease with time). Let’s have a look at the behavior of the currency courses, in relation to the indicator line. The zones on the graphic, marked with OS (oversold) are related with values under 30.

In order to get more concrete quantitative ratings for this how the RSI works, systematic functions are used for simulation of historic deals. That is why, for instance, two separate tests are done using different criteria for entering and going out of the market.

The first method uses only the break of the equilibrium line as a signal of a deal. An indicator increase over that line signals of a purchase and closing of the open short positions, whereas the indicator decrease under the line is a signal of a sale and closing of the long positions.

The second method keeps the line at value of 50, adding criterion for the overestimated and underestimated levels at value of 70/30.

### Conclusion

The momentum oscillator is a conception, which is used for prediction of turning points by measuring the change speed of the currency courses and identification of the indicator’s extreme values. The currency course, which increases quickly, is likely to keep its motion’s direction, while the decreasing course is likely to keep decreasing.

The market is close to its turning point when the moment of inertia of the increase or the decrease reaches definite maximum or minimum values. The passing from the one side to the other side of the equilibrium line usually indicates that the turning of the course direction is a fact.

### Momentum and Relative Strenght Index (RSI)

A “momentum oscillator” is a generic term, used for different indicators, two of which are the momentum indicator and the RSI.

Wells Wilder presents them in his book “New conceptions about the trade systems”, which has turned into classical literature and since then the two indicators become popular instruments for the technical analysis. Both indicators can be used for entering and going out to the market. In order to see how in practice these two indicators can be used in real situations, we will expose two simple methods, which are used by both indicators and a combined method, which uses the two indicators at the same time. For each of the indicators, we will use a period of 14 days.

### Relative Strenght Index (RSI)

A momentum oscillator is the developed one by Wells Wilder, also using the course of closing for its estimation. The indicator compares the average rising prices of closing with the average decreasing prices of closing for a definite historic period.

The oscillator oscillates around the line 50 and has a value, equal to 50, when the average rising course of closing is equal to the average decreasing course of closing. The maximum theoretical value is 100, while the minimum is 0. Horizontal lines are drawn up at the values of 30 and 70, corresponding with the determined by Wilder levels, preceding respective market bottom or peak. From the five factors, associated with the using of the indicator, the criterion for over\underestimation at the values of 70/30 is the most common one.

Wilder comes to the conclusion that when the index of a given market exceeds the value of 70, then there is a premise for a significant reaction or change of the trend with a direction, pointing below. Likewise, when the indicator falls under 30, a significant reaction or change of the direction upward is expected. Not rarely, the indicator indicates over/underestimated market levels and at the same time the course keeps increasing/decreasing.

In order to avoid this, techniques for filtration of the signals are used, i.e. confirmation of other indicators, conformity to the support and resistance levels and so on. The application of a strategy for limiting the loss, as a part of an adequate plan for managing the risk, also could lead to limiting the negative consequences.

In addition to the condition for over/underestimated levels, some traders use also the value of 50 of the indicator to indicate deals.

As an addition, in his book “Technical analysis of the financial markets”, John Murphy mentions that this line is often used as a reference point for the discovery of support and resistance levels in the market courses movement. Repulsion from the value of 50 could be used for discovery of a new position or doubling of an already made deal in the same direction.

**Momentum**

It expresses the quantity, with which the course of a given currency changes in a given time period. Or simply said, “Momentum” is the difference in the course of a given currency for a definite period of time. The indicator expresses the level of change as a coefficient. It is defined as a difference between the course of closing of a running period and the course of closing of n – periods back.

The produced positive or negative value is depicted graphically around the zero line.

Mn = P – Pn, where:

P – the course of closing for the last period;

Pn – the course of closing for n – periods back.

The behaviout of the indicator line is the following:

When the indicator’s values are over 0 :

– a rising line means that the rising trend becomes stronger;

– a horizontal line means a stable trend;

– a falling line means that the trend loses momentum.

When the indicator’s values are approximately equal to 0:

– there is no trend, the market moves without a clearly established direction.

When the indicator’s values are under 0:

– a falling line means that the falling trend becomes stronger;

– a horizontal line means a stable trend;

– a rising line means a weakening trend.

### Tactics of using indicators when taking up a position

The indicator can be used for trends identification, overestimated/underestimated levels and divergence. The parameter, which is about to be used for construction of the indicator, depends on the time range, used by the trader and the optimum value for a definite market.

The trend identification occurs as following the indicator direction (the rising line means a rising trend), the speed of the increase of the indicator’s values (slope of the indicator – a steep line means very strong “uptrend”), and an indicator break at 0 line (a change of the indicator).

The momentum can be used for identification of overestimated/underestimated levels as following the indicator’s behavior at the historic changing of the course of a given instrument for a definite period of time and then showing what values of the indicator could be considered as signalizing overestimated/underestimated levels.

One of the disadvantages of the momentum indicator is that the values could be distorted as a result of the great course movement, which has happened exactly before the n – period, i.e. great increase or decrease of the course before the n- period could lead to jerky movements in the indicator’s values, even when the running course shows insignificant change.