# On the world's financial markets and stock exchanges. Part 8

## 1. Introduction

To become a modern trader who uses a computer in his trading, you need to do three steps: choose the software, the computer and the data for analysis.

If you want to work on wood or metal, you will go to a tool shop and buy a set in a drawer. You will have to learn how to use these tools correctly in order to work intelligently and efficiently. In turn, technical analysis toolkits offer electronic means of processing market data.

The toolkit draws daily and weekly charts, divides the screen into several windows and builds price and indicator charts. A good toolkit has many popular indicators: average price movement indicator, channels, MACD, MACD histogram, stochastic, relative strength index and many more. It allows you to customise all the indicators. For example, at the touch of a button it allows you to go from 5-day to 9-day stochastics.

Modern computer programmes allow you to write your own indicator and add it to the system. In addition to ready-made indicators, you can have your own favourite formula. The software allows you to compare any two markets and find similarities between them. If you trade options, the program should definitely include an option valuation model. Sophisticated programs can check the profitability of trading.

As we mentioned before, technical analysis is divided into two methods:

- Graphical - based on the analysis of price charts - plotting the change in price over a certain period of time.
- Mathematical - a computer method of analysis using indicators.

## 2. The main groups of indicators and oscillators

Indicators allow you to find trends and the moments of their changes. They allow to better understand the balance of forces between bulls and bears. Indicators are more objective than drawn charts.

The problem with indicators is that they sometimes contradict each other. Some work better in a trend, others in a quiet market. Some are better at detecting pivot points, others are better at identifying trends.

Most amateurs look for a single indicator: the silver bullet that kills all doubts in the market. Others collect many indicators and try to average their signals. Either way, a careless beginner with a computer is like a teenager with a sports car and you should expect disaster. In case you set up for serious trading, you should know which indicators work best in strictly defined conditions. Before you use an indicator, you need to know what it measures and how it works. Only then will you be able to use their signals with confidence.

The main feature of oscillators is their ability to signal a market reversal. They are very useful when working in a channel. The main signal of oscillators is divergence.

The following points should be considered when using oscillators:

- Intersection with zero line as a signal is weak and taken into account only if it doesn't contradict the main price trend;
- Critical values of oscillators indicate only that the current price movement is too fast, and, therefore, a correction can be expected soon. It also follows, however, that the oscillator can reach the over-zone long before the end of the trend (if prices changed significantly at the beginning of the trend), and stay there for a long time as the trend develops further. Therefore, an especially strong signal occurs when the oscillator makes several oscillations in the over-zone and only then leaves it;
- The divergence of the price chart and the oscillators (divergence). The price chart forms a new peak that is higher in absolute value than the previous one, but the oscillator does not confirm it. The divergence value itself does not influence the strength of the subsequent price change. The use of divergence is one of the most reliable methods of technical analysis;
- It is useful to use trend lines, support and resistance on the oscillator charts. You will often see the classic figures of technical analysis, which may be of greater importance than on the price chart;
- Overbought and oversold zones should be set individually, depending on the type of market and time frame on which the chart is plotted. Sometimes they can be 2-5% to filter out false signals;
- The shorter is the oscillator period, the more frequently signals appear and their lag is less, respectively, the higher is the proportion of false signals. With oscillators with a larger period the number of signals decreases, the lag increases, but the reliability increases.

Indicators and oscillators can be divided into 3 major groups:

- Trend-following - help to work in a trend and include Moving Averages (Moving Average), Envelopes, MACD, Bollinger Band, Parabolic, +/-DM indicators, ADX indicator;
- Flatteners (channel) help to trade out of trend and are made up of: Stochastic oscillators, Momentum oscillators, ROC, CCI, RSI, MACD histogram;
- Volume indicators analyse the dynamics of volume change, which is seen by analysing volume indicators and their interaction with the price chart.

Trend indicators work well when the market is on the move, but give dangerous signals if the market is standing still. Flat oscillators show pivot points in a stationary market, but give premature and dangerous signals when the market begins to move in a trend. Volume indicators give a better insight into the psychology of the masses. The secret of successful trading is to combine several indicators and oscillators from different groups, so that their negative qualities are mutually compensated, while the positive ones remain intact.

## 3. trend indicators and oscillators

### 3.1 Moving averages

Probably the most real money is made today by using moving averages (MA), rather than all other technical indicators put together. Because they can be used for any purpose, such as finding long-term monthly trends, setting stops for day trading, and much more. Moving averages have been the subject of more discussion in technical literature and other sources than any other technical study. One of the reasons they have become so popular is that when markets are trending, these simple little lines perform as well or even better than indicators requiring a doctorate for their calculation and interpretation.

Moving averages smooth out market fluctuations and short-term volatility, giving the trader a sense of where the market is heading. Equally important to know is what they do not do. They are trend following indicators in their purest form. They always show the direction of the trend, but they do not measure how strong or weak the trend is. Their function is to determine the direction of the trend and then smooth out or silence its volatility. Moving averages handle these important tasks simply and well.

There are so many different types and variations of moving averages, that it is meaningless to try to list them all. Most types were created in the 1970s, when moving averages were considered a very sophisticated and advanced technical analysis tool. Many talented and inventive technical analysts have spent much of their time coming up with new ways to use and improve on moving averages. The interest in them has been generously rewarded - the 1970s were the time of markets in a constant state of trend, and moving averages worked exceptionally well.

The disadvantage of moving averages is that the averages lag in relation to the rate of the value in question. Moving averages differ in the method of averaging.

There are three basic types of simple moving averages:

- Simple Moving Average - Simple Moving Average (SMA);
- Linear Weighted Moving Average (LWMA);
- Smoothed Moving Average (SMMA);
- Exponential Moving Average (EMA).

The only thing where moving averages of different types differ considerably from each other - is in different weight coefficients, which are assigned to the last data. In case of simple moving average, all prices of the time period in question are weighted equally. Exponential and Weighted Moving Averages give more weight to recent prices.

The most common method of interpreting a price moving average is to compare its movement to the movement of the price itself. When the instrument price rises above the Moving Average there is a signal to buy, when it falls below the indicator line - a signal to sell.

This trading system, which is based on the moving average, is not designed to provide entrance into the market right in its lowest point, and its exit right on the peak. It allows you to act according to the current trend: buy soon after the prices reach the bottom, and sell soon after the prices have reached their peak.

Moving averages may also be applied to indicators. That being said, interpretation of Moving Averages is similar to that of price moving averages: if the indicator rises above its Moving Average, it means that the upward movement of the indicator will continue, and if the indicator falls below its Moving Average, it means that its downward movement will continue.

The exponential moving average is recommended as the basic one for application.

The basic rules for the construction of an average are as follows:

- The longer the time period, on which an average is built, the lower the order of the average should be selected (for daily charts, the order of 89 or less, for weekly charts - 21 or less), short averages can be used without restrictions;
- the longer is an average, the less sensitive it is;
- An average of a very small order gives a lot of false signals;
- an average of a very high order is constantly late; an average with a higher order than usual is used in the case of a sideways trend

Insert an example from MT where you can adjust the type of moving average, select the number of days and the colour. And add a brief description of this figure.

### 3.1.1 Simple moving average

Simple Moving Average (SMA), is calculated by adding and averaging a set of numbers representing market action over a period of time. The calculation usually includes closing prices but can also be calculated from the peaks, troughs or average of all three. The oldest data point is discarded with the appearance of a new one, hence the average "slides" and follows the market. A line connecting the daily averages will smooth out recent market fluctuations.

Longer-term moving averages will smooth out any minor fluctuations, and only show longer-term trends. Short-term moving averages will show shorter-term trends to the detriment of longer-term trends. A smaller data set representing only more recent data will create a more sensitive line. A chart showing a 5-day moving average overlaps the same chart for a 50-day average, the 5-day average reflects the data much more accurately, following every small change in price. Short-term trends are easy to see, while trends made obvious by the 50-day average are much harder to identify.

Long-term and short-term moving averages each have their own uses and disadvantages. Although the 50-day moving average stays with the trend, it always stays away from real prices and changes direction much less frequently than prices. In practice, a trading system based on a moving average of this length will be slow to enter and exit the market. A slow entry misses a significant portion of the trend start and a slow exit sacrifices a large portion of the return. On the other hand, a 5-day moving average is quick to enter and exit, but is not in harmony with the underlying trend and is just as often on the wrong side of the market as it is on the right side.

Another interesting property of simple moving averages (and many other technical studies of this type) is that they are also affected by old prices, which are thrown out of the averaging as well as new ones. An unexpected turn in a moving average could mean that fresh prices have turned. It can also mean that fresh prices are behaving relatively neutrally, but significant prices have been thrown out of the other end of the data. This is not necessarily a bad thing. After all, the purpose of a moving average is to smooth the data. But one must be prepared for this effect. This phenomenon can sometimes explain what seems to be an inexplicable change in a moving average or other indicator.

For example, a 5-day moving average shows the average prices of the last 5 days, etc.

A simple, or arithmetic, moving average is calculated by summing up the closing prices of an instrument over a certain number of unit periods (for instance, 12 hours), and then dividing the sum by the number of periods. The formula for calculating a simple moving average:

SMA = SUM (CLOSE (i), N) / N

where:

SUM - amount;

CLOSE (i) - closing price of the current period;

N - number of calculation periods.

The main drawback of MA is that it reacts to one change of the rate twice: when it is received and when it is withdrawn from the calculation. MA has an inertia. The bigger n is, the smoother МА is formed, but the more its changes lag behind the price changes. Usually two or more moving averages are used, and one assesses not only what each of them shows, but also their location relative to each other.

3.1.2 Linear Weighted Moving Average

In a Weighted Moving Average - Weighted Moving Average (LWMA), the most recent data is given a higher weight, and the earlier data is given a lower weight. A Weighted Moving Average is calculated by multiplying each of the closing prices in the series in question by a certain weighting factor.

LWMA = SUM (CLOSE (i) * i, N) / SUM (i, N)

where:

SUM - sum;

CLOSE(i) - current closing price;

SUM (i, N) - sum of weights;

N - period of smoothing.

### 3.1.3 Smoothed moving average

The first value of smoothed moving average - Smoothed Moving Average (SMMA), is calculated as a simple moving average (SMA):

SUM1 = SUM (CLOSE (i), N)

SMMA1 = SUM1 / N

The second value is calculated according to the following formula:

SMMA (i) = (SUM1 - SMMA (i - 1) + CLOSE (i)) / N

Subsequent moving averages are calculated using the following formula

PREVSUM = SMMA (i-1) * N

SMMA (i) = (PREVSUM - SMMA (i - 1) + CLOSE (i)) / N

where:

SUM - sum;

SUM1 - sum of closing prices of N periods, counted from the previous bar

PREVSUM - the smoothed sum of the previous candle;

SMMA (i - 1) - smoothed moving average of the previous candlestick

SMMA (i) - smoothed moving average of the current candlestick (except the first one);

CLOSE (i) - current closing price;

N - period of smoothing.

As a result of arithmetic transformations the formula can be simplified:

SMMA (i) = (SMMA (i - 1) * (N - 1) + CLOSE (i)) / N

### 3.1.4 Exponential moving average

Like car builders who modify old models - traders modify already created indicators. Exponential Moving Average - Exponential Moving Average (EMA), gives more value to new data and reacts more clearly to current changes.

An exponentially smoothed moving average is determined by adding a certain fraction of the current closing price to the previous moving average. With exponentially smoothed moving averages, the latest closing price is given more weight. An exponential moving average will be of the following form:

EMA = (CLOSE (i) * P) + (EMA (i - 1) * (100 - P))

where:

CLOSE (i) - closing price of the current period;

EMA (i - 1) - value of the moving average of the previous period;

P - the share of using the price value.

The main advantage of EMA is that it includes all prices of the previous period, and not only the segment defined at period setting. At the same time, more weight is given to the later values.

What should be considered when choosing parameters of averaging? The main thing is to sense changes (change direction) and to filter changes, i.e. to refrain from abrupt changes.

Another interesting feature - the MA serves as support and resistance lines!

Hence the use of a combination of MAs of different orders. By comparing the position of the means of different orders, relative to each other, we assess the presence of a trend over large intervals. General rules of analysis:

- find intersection points between the average and the price chart;
- find intersection points of averages with each other;
- analyse the position of averages in relation to a price chart (whether they are above or below the chart);
- find points following the maximum or minimum of an average;
- find the points of greatest divergence between the average and the price chart;
- follow the direction of movement of an average.

### 3.1.5 Double Moving Averages

The most popular moving average systems use two moving averages. They usually consist of a longer moving average, which serves to define the trend, and a shorter moving average, which gives trade signals on the crossover with the longer-term average. The best known of these systems is Richard Donchian's 5-day/20-day system, which, by the way, is not a simple reversal system, but uses an elaborate set of filters.

The main signal of the double moving averages is a crossover. Buy when the shorter moving average crosses below the longer moving average, and sell when the opposite occurs. You can also use crossovers as trend reversal points and trade only in the direction of the marked trend, using other shorter term methods for entries and exits.

Most of the research we have seen and done has shown that a double moving average system is generally more profitable than other moving average combinations. Research also shows that all moving average systems have long periods of gains and losses, depending on the trendiness of the markets.

Interesting signals are given by a combination of 9-day and 14-day moving averages. The point of intersection of the two lines MA9 and MA14 is a signal of a change in trend. The disadvantage is the systematic lag in the signal. The advantage - it is easy to determine the trend direction, and you can also use them as support and resistance lines.

### 3.1.6 Triple moving averages

One of the most popular triple moving averages is the widely used 4-9-18 day moving average, popularised by R.K. Allen in the early 1970s. The third moving average opens up a large number of potential trading opportunities. In general, when the market has bottomed out, the main indication of a change in the trend is the crossover between the 4-day and the 18-day. The crossover between the 9-day and the 18-day is a confirmation signal. When the prices are at the peak, the crossing of the 4-day and the 9-day will be the preliminary signal of a possible change in the trend. The earnings at this point will help overcome the characteristic feature of moving average systems, which is the return of earnings. The trend reversal will only end when the 4-day and the 9-day cross the 18-day.

We like triple moving average systems because they provide the advantage of a neutral zone as opposed to the continuous reversal trade generated by single or double moving average methods. For example, in the 4-9-18 system, when 4 crosses 9, we exit our position and do not enter a new position until 9 crosses 18. We also like triple systems because the crossing of 4 and 9 is a quick earnings mechanism, which solves some of the problems associated with returning too much income we mentioned earlier. We believe that in a good trading system, exits should always be faster than entries. Entries should be slow and selective, perhaps requiring an extraordinary event to enter the trade. Exits should be slow enough to allow profits to flow in, but fast enough to eventually lock in the bulk of the potential profit.

The triple MA is also used in Williams' world famous trading strategy "Alligator" with parameters 13 - 8 - 5.

### 3.1.7. Four moving averages

The use of four moving averages is not as strange or complicated as it seems. When used properly, the four moving average approach circumvents some of the problems inherent in moving averages without losing any of its virtues. The method uses four moving averages in sets of two. The two longest moving averages are used strictly as trend identifiers and are most easily applied when set as oscillators. The two shorter moving averages are more sensitive and are used for timing entries and exits (usually based on crossovers), trading exclusively in the direction signalled by the longer-term oscillator.

Trading against the trend is eliminated by definition. If there is an uptrend as determined by the long term oscillator, only long trades will be accepted based on the short term crossover signal. Conversely, only short trades will be accepted when there is a downtrend. There will be neutral periods during trend corrections and sideways market movements, when the short-term and long-term moving averages fail to confirm the direction. Jerks will not be completely eliminated, but their number will be significantly reduced.

### 3.1.8 Finding a filter

Instead of blindly following all crossovers, many traders use different filters to determine the suitability of the primary signal. Filters fall into two categories: price filters and time filters.

Filtering signals by price usually means delaying entry into a trade until the price satisfies some additional criterion. This can be determined by measuring the magnitude of the breakout behind the moving average or by measuring the distance that one moving average has from the other after crossing. The trader, in this case, is looking for confirmation that the moving average crossing was not a random price event, but is in fact a trend change. A new trade will not begin until the price has surpassed the moving average by some minimum value. Another variation on this filter would be to wait for prices to rise by some percentage relative to the moving average. The next possibility (which we find generally accepted) is to wait for a given period after the crossing until the market has reached a new peak or trough in the last p days, which is a channel break. One of our favourite filters or confirmation methods is very simple: wait for the close in the direction of the new trend.

Time filters use waiting for a certain number of time periods after a cross before entering a trade in the new direction. Many traders who use moving averages have noticed that most twitches occur very close to the beginning of a trend, and a slight delay in entering will help avoid most of them. The waiting period is usually one to five days. If price stays on the new side of the moving average for the minimum time period, we conclude that the signal was correct. Obviously, the longer the waiting period, the less twitching there will be, but at the same time it can lead to such a late entry that the bulk of the movement is missed.

### 3.1.8. Conclusions on the use of moving averages

Moving averages are the simplest and most elegant trend-following studies available. Up to a certain limit, they can be very effective, but their limitations can be significant. Most markets spend more time in sideways movement than in trending movement. A non-trending (flat, channel) market can bring down a most carefully chosen moving average system. Here are some of our thoughts and conclusions on how to help your moving average system survive.

Try to limit your trading to trending markets. Diversification helps, but don't trade all markets in the same way. At any given time, typically less than 50 per cent of all markets can be defined as trending. Most of the time the actual number of them is significantly less. Find a way to objectively determine whether a market is trending or not and only then apply moving averages. We recommend Weilder's DMI / ADX as a reliable study that measures whether the market is trending or not. The simple explanation is that when the ADX is rising, the market is trending, and when it is falling, the market is losing direction. The channel breakout filter we mentioned earlier can also be effective.

Long-term moving averages generally react too slowly to be useful for exits. Use an alternative exit strategy. We think the most common mistake with moving averages is to use the same set of moving averages for entries and exits. If you use slow averages, you will be slow to exit and lose most of your income. If you use a faster moving average, you will have better exits, but you will find that you get jerks on the entries.

### 3.2 MACD

The Moving Average Convergence-Divergence Trading Method (MACD for short) was developed in 1979 by Gerald Appel as a timing tool for the stock market.

The MACD is best used as a trend-following study. The MACD trading method works particularly well in quiet long-term markets, where you can stay with the main trend while ignoring weaker price movements. One of the best uses of the MACD would be to use it on weekly or monthly charts as an indicator of long-term market direction. Usually using the MACD in a flat market is not successful. Look for divergences when the markets are not in a trend.

The MACD is a combination of three exponentially smoothed moving averages, which are represented by two lines. The first line represents the difference between the 12-period exponential moving average and the 26-period exponential moving average. The second line (called the signal line) is the approximate exponential equivalent of the 9-period moving average of the first line. Exponential values of 0.15, 0.075 and 0.20 are used. The MACD is usually displayed as an oscillator line or as a histogram.

Most software allows users to change the values when calculating the MACD. Some systems require exponential values while others use the available number of periods for the three moving averages. It is advised not to try to change the initial MACD values to fit the data curve. However, it is important to note that Appel recommends two different sets of values, one for the buying side of the market and one for the selling side. Both use a 9-period (0.20) signal line, but the combination of 0.15, 0.075 is only recommended for the selling side. The values for the buying side are 8-period (0.22) and 17-period (0.11).

Using a buy formula and a sell formula can require a completely different way of thinking from casual MACD users. It is always good to stick to the original, but you should be aware of the developer's way of thinking when you use any technical study. If the default settings for the sales side of your software are set to the most common values, or if the software does not allow you to change these values, you may find that you are not using the MACD the way its developer intended. Ideally, your computer monitor should be set up to display a price chart and two additional charts, one to show the buying side MACD and one for the selling side formula. You will find that the buying formula is slightly faster and slightly prone to twitching. The selling formula is slower. The intention seems to have been to buy quickly and try to hold the position in order to let the profits flow. We think it would be possible to apply the buy-side construction to both formulas, provided there is an understanding of their original purpose. For non-equity markets, you can stick with the standard sell-side formula until you need a faster and less reliable signal.

The basic MACD signal is a crossover. Buy signals are generated when the faster line crosses the slower line from below, while sell signals are generated in the opposite case. We would like to warn you right away: in most markets, trading mechanically at every MACD cross will result in frequent jerking and significant losses. You will quickly find that narrow trading ranges are devastating for the indicator, giving many false signals and collecting losses. Fortunately, there are additional MACD interpretations to help traders avoid the jerks and other drawbacks.

The MACD method can be used to identify the points at which the market becomes overbought or oversold, and is thus susceptible to a reversal. By looking at the faster of the two MACD lines, Appel, for example, established overbought/oversold areas for the S&P index at +/-2.50 on the MACD scale. For the NYSE index, he recommends +/-1.20. When another line has reached these critical areas, any crossover generates a buy or sell signal. Crossovers that occur before the extremum level is reached can be ignored, and thus most twitching will be removed. With a little research, similar levels can be detected for any market that is in a wide trading range with large price movements. Remember, the MACD is best used as a long-term trend following tool rather than a short-term trading timer. Signals occurring in the middle area of the MACD chart should only be accepted if another validated indicator confirms that the trade will be in the direction of the trend.

One very curious way to use the MACD is to mark a jump before crossing by drawing a trend line on the MACD itself and then trading on a breakout of the trend line instead of waiting for a crossover. A MACD trendline breakout can precede an important change in the market and serves as an early warning signal of a market turn. MACD crossings which are preceded or followed by a breakout of the trend line have much more technical significance than MACD crossings by themselves. Aggressive traders might consider entering the market immediately after a trendline breakout in anticipation of a MACD crossover, while more cautious traders might wait for an actual crossover to confirm. Remember, if you trade relying solely on trendline breakouts without waiting for a crossover, the trade will have little justification in case a crossover does not occur in the near future. You could get into an unfortunate situation using the MACD system and will be forced to look for some other method to exit the market.

### 3.3 Envelopes

Envelopes can be as simple or as sophisticated as you want them to be. The simplest is a simple moving average with bars on each side, calculated as a percentage of the value of the moving average on a given interval. For example, a 10-day moving average with the bars removed by 5 per cent from the average. The area inside the two bands theoretically acts as a buffer zone which will contain prices within itself, mainly when the market is inside the trading range. The beginning of a trend will be indicated when prices break through the band. When a correction or end of trend occurs, prices will move back inside the bands in the direction of the moving average.

Envelope curve calculation:

Upper curve = SMA (CLOSE, N) * [1 + K / 1000]

Lower curve = SMA (CLOSE, N) * [1 - K / 1000]

Where:

UPPER BAND - upper line of the indicator;

LOWER BAND - bottom line of the indicator;

SMA - simple moving average;

CLOSE - closing price;

N - period of averaging;

K / 1000 - value of deviation from the average (in tenths of a percent).

In envelopes, the moving average can be smoothed exponentially or in some other way. The percentage of prices contained within the bars may vary depending on what position is being considered, long or short, biasing the study towards higher volatility in the direction of the trend. For instance, in an uptrend market the bar could be placed 5 per cent above the moving average and 10 per cent below. Another possibility is to use moving averages of peaks and troughs as bands on either side of the closing moving average. Bands were conceived to contain within themselves and identify price movements within a trading range. Any breakout outside the bands should signal.

There are almost as many trading rules for envelopes as there are rules for their construction. The rules are (or should be) based on the idea that an envelope contains a significant amount of market price movement and that a move outside one of the bands is a deviation from price behaviour and should be responded to.

Traditional trading rules for envelopes are:

1. Enter the market in the direction of the breakout at the moment the band is crossed. This signals the possible start of a trend.

2. Exit and change positions when the opposite bar is crossed.

We recommend using crossovers based only on closes outside the band boundaries to avoid some twitching. Prices will often jump out of the boundaries during the day and close inside the bands.

Another option:

1. Enter the market in the direction of the breakout at the moment the band is crossed.

2. Exit the market when the moving average between the bands is reached, but do not change positions.

Both sets of rules guarantee that the main trend will not be missed. The first set of rules is basic and gives a regular reversal system.

Each trader chooses their own, most preferred set of trading rules. The advantage of the second set is that the bands are also used for entry, but the moving average is used for exit. If prices are inside the bands after a trade is stopped, the market is in neutral zone and there will be no new trades until a new breakout. Another reason why some traders prefer the second set of rules is that the theoretical risk on each trade is reduced to the distance between the band and the moving average instead of the full distance between the bands.

Like moving averages, envelopes work well in trending markets and not so well in frequently changing markets, and the "best" envelope changes over time. Frequent optimisation to find the right values is useless. It is recommended to trade in the trend direction when the price jumps out of the envelope, and to use counter-trend techniques when it is inside.

A logical and effective technique, which is rarely discussed, involves using the bars as overbought/oversold indicators so that the trade is inside the bars and not outside. This technique has been used very successfully when markets have been in a sideways trend. The trading rules are relatively obvious and simple. Buy as soon as the price touches the lower band. If the trade goes against you, as indicated by a close outside the lower band, exit quickly and take a small loss. If the trade starts moving in your direction, as it often will, stay in a profitable position and reverse the trade on the upper band, applying the same rules, only in reverse. This method seems effective because it combines the tactic of taking small losses and large gains, with a trading strategy of buying on troughs and selling on peaks. The real challenge is making sure you are in a sideways trend.

How do you know if the market is in a limited trading range or in a trend? An objective method is to use the ADX. If the ADX is falling, trading inside the envelope can be very advantageous. If the ADX is rising, the market is trending and you are better off using the envelope method following the trend.

### 3.4 Bollinger Bands

Bollinger Lines (Bollinger Band - BB) takes its name from its creator - John Bollinger, market analyst at CNBC/Financial News Network, and is constructed as a band around the average, but the width of the band is proportional to the standard deviation from the moving average over the analysed time period.

A decision based on BB analysis is made when the price either rises above the upper BB resistance line or falls below the lower BB support line. If the price fluctuates between these two lines, there is no reliable signal to buy or sell on the basis of the BB analysis. The decision to open a position is made only when the price chart crosses the BB line to return to its normal position.

Sometimes a BB crossing means a "false-break", i.e., when prices just tried a new level and immediately went back. In this case you have an opportunity to work against the trend, but carefully assess whether the breakout was indeed a fake one. A good confirmation in such cases is the volume indicator, which should decrease sharply in case of a false breakout.

Additional signals of BB lines. Convergence of BBs is observed when the market calms down and no significant fluctuations can be seen on it. There is a consolidation to the continuation of the current trend or the appearance of a new trend. The divergence of the BB is observed when the current trend becomes stronger or a new trend starts. Divergence with increased volumes is a good confirmation of a trend. The average is a good support level in a bull market and a good resistance level in a bear market.

The indicator contains 3 lines: the central one is the MA moving average. The other two are the upper and lower limit of the range with a shift of s standard deviation from itself.

Moving average SD is a measure of price stability, i.e. with 0.68 probability the price will deviate from the mean by 1, with 0.95 probability by 2 and with 0.99 probability not more than 3.

To calculate the moving average, we take a period of 30 to 48 hours and 21 days.

The parameter s -2.5

Formula: MA= (1/n) E{P(i)}

P(i) - closing price

i - vary from 1 to n

SD = 1/n √ E[p(i) - MA²]

BBU = MA + s x SD

BBL = MA + s x SD

If the parameters are chosen correctly, the channel will correspond to the equilibrium state of the market, and all price exits must be accompanied by a return to the equilibrium state. About 5% of prices should be outside the lines, 95% should be inside the lines.

### 3.5. Parabolic System

Parabolic price/time systems (Parabolic) are trend-following technical studies which try to overcome two problems common to most trend-following trading systems: return lag due to delayed signals to exit and failure to include time as a factor in calculating stopping points. The parabolic formula solves the problem of price lag by narrowing stops at an increasing rate when a new peak or trough is reached. The parabolic formula also incorporates a time factor into the calculation, allowing stops to remain at a distance for a short period and then approaching them inexorably regardless of price action. The result of this time function is that prices must continue to move in the direction of the trend, otherwise trading will be halted.

We believe the Parabolic system is an excellent technical tool when used only for exits. We do not recommend it for entries or as a reversal system as its developer intended.

The parabolic formula was first described by Welles Wilder in 1978 in his book "New Concepts in Technical Trading Systems". Wilder was searching for a system which could capture the most of earnings in the trend market without relying on any external methods of income retention. Parabolic calculations result in a series of trailing stops which, if triggered, signal a trend reversal. Stops are recalculated daily (or for each time period you use) and get closer as the trend progresses. If the trend fails to continue, the sliding stop will reverse and a new time period will begin.

A parabolic system is a reversal system which is always in the market looking for a trend. The parabolic system is not considered one of the best trend following technical studies that can work on its own. However, in combination with other indicators it can be extremely effective. The Parabolic System is most valuable when used as a method of placing stops.

In order to use it most effectively, it will be helpful to explain the nature of the different elements that make up the Parabolic System. As we said, the Parabolic System was conceived by Wilder as a negotiable system.

Wilder called the point at which the system reverses, "Stop And Reverse" (SAR). As you can see in the figure, a series of SAR points form a line similar to a trend line, but taking the shape of a parabola, so that the stop points remain close to the market.

To calculate the first SAR you must choose some sort of starting point. Wilder recommended going back a few weeks on the chart and finding a significant peak or trough there to start the calculation. Most computer studies start on the left side of the screen. If the first few days are trending upwards, then the formula will assume an uptrend. If the first few days are downward, the formula will assume a downtrend. For practical use, it does not matter which direction the Parabolic system starts, because it will end up on the trend side. We recommend that software users with variable window widths make sure that the Parabolic window contains at least 100 data points. Without these minimum data points, the first SAR points may determine incorrect trends.

When the first entry point and the first SAR are set, the formula for subsequent SARs is as follows: SAR (tomorrow) = SAR (today) + AF*(EP - SAR (today)).

AF is the acceleration factor and EP is the extreme point (peak or trough) of the previous trade (EP - extreme point). Note that the price of the previous extremum and the acceleration factor are used together to keep SAR points close to the trend.

The price of the previous extremum EP is quite clear. AF, however, is what makes the Parabolic system unique. AF is a weighted factor. Wilder used an initial AF value of 0.02. AF then increases by 0.02 each time price creates a new extremum, leading to accelerating points on the chart. AF does not increase until a new ER is produced, and it never rises above the value of 0.20. Thus, the range of variation of the acceleration factor is from 0.02 to 0.20 in increments of 0.02. These are the default values for most software packages, but can sometimes be set by the user.

A change in AF values will manifest itself in approaching or receding SAR stops, thus making the system more or less sensitive to market movements. If AF increases, stops get closer and the system becomes more sensitive. If AF decreases, the stops are removed and the system is made slower. The following charts allow us to compare AF values starting at 0.01, in 0.01 steps, and AF values starting at 0.03, in 0.03 steps.

It is almost always possible to find a set of initial values and step values for a Parabolic system that will show a return when tested on historical data. We recommend to use standard default values. Try to avoid fitting the indicator to the data curve.

Wilder made the following important observation in his book: "I have tried many different accelerating factors and found that a series increase of 0.02 works best, however, if you want to customize your system to change the breakpoints possibly used by other traders, use a range of incremental increases between 0.018 and 0.021. Any incremental increase in that range will work well."

Wilder seems to have been worried about too many stops at one market point, and this worry is justified. Some acceleration modifications may not serve the purpose of optimization, but to make your stops different from those used by the crowd. Remember, the Parabolic System is a widely known and popular study, perhaps much more popular than Wilder envisaged when he suggested individualising the formula.

Although the Parabolic system solves one of the major problems of most trend-following indicators by placing the setups closer to the market, it still fails when the market becomes volatile, i.e. non-trendy. What is needed is a filter that will reduce entries into unstable markets and an entry timer that will allow the parabolic system to do what it does best - set stops in trending markets.

Wilder understood the limitations of the Parabolic system and suggested to use it together with a directional movement index (DMI) or commodity selection index (CSI), but he didn't give any specific prescriptions or rules.

## 4. Flat indicators and oscillators

Momentum, ROC, CCI, RSI, Stochastic, MACD-histograms;

### 4.1. RSI

The Relative Strength Index (RSI) is probably the most popular of all the flattened oscillators. The index gives reliable overbought and oversold signals in most market conditions. RSI also produces excellent long-term divergence patterns, which can be used to identify major peaks and troughs. RSI can be used both as a mechanism of income and as a tool for fine-tuning market entries derived from signals from other methods.

The RSI formula was invented by J. Welles Wilder Jr. and was explained in full in his 1978 book "New Concepts in Technical Trading Systems". RSI calculates the ratio of upper closes to the lower closes on a specified time frame and shows the result as an oscillator with a scale from 0 to 100. The formula is as follows: RSI = 100 - (100 /1 + RS), where RS = average upper closing within the last n days divided by the average lower closing within the last n days. A value near 0 indicates an oversold market, while a value near 100 indicates an overbought market. Wilder recommended the use of a 14-day time period, which he understood as half a cycle in most markets.

When using 14 days as the default value, market peaks and troughs can be expected to occur some time after RSI rises above 70 or falls below 30. We do not recommend buying or selling exactly at these values because when there is a trend, RSI often "sticks" to one end of the range for days or even weeks, giving false evidence of a peak or trough.

Wilder and others have advocated the use of some standard charting techniques with RSI, arguing that certain index figures predict similar underlying data patterns. What follows are a few examples of RSI signals that we find useful based on our own research and experience.

### 4.1.1. Failure Swings

The first of these formations is the false swings, which are easier to observe on the study of the RSI proper rather than on the underlying chart. A false swing consists of a spike formed by the RSI rising above 70, followed by a new spike with a lower peak than the first. A real sell signal is made when the lower point between the RSI spikes is crossed. A buy signal would be an inverse pattern with two spikes pointing downwards and then crossing the high point between them upwards.

A false swing can be a powerful signal. Remember, the best signals occur when the first spike goes well over 30 down or well over 70 up. You cannot afford to ignore such events. They usually mark significant intermediate changes in market direction. Beware of false swings, which have so many small deviations that they take a long time to detect. Our experience suggests that the best false swings occur rather quickly and are easy to spot.

### 4.1.2. RSI divergence patterns

Weekly Charts.

The most significant and powerful RSI signals come in the form of divergences between the index structure and the underlying chart structure. We have found these divergences to be particularly useful in detecting major long-term peaks and troughs on the weekly charts.

Daily charts.

We recommend using the 10-day and 14-day RSI to detect daily divergence patterns. Note that the divergence is confirmed by the inability of the RSI to reach a new trough, showing that the market is technically strong. Make sure that your entry into buying comes after the day of the rise marking the bottom of the second spike and not at an earlier time.

While it is difficult to formulate a rule of thumb, you will find that divergences which have peaks separated by just a few days or more than 10 weeks do not usually give good signals.

### 4.1.3. Filter of occurrences

One of the most common problems faced by trend following systems is entering the market after a strong reversal. The entry is never exactly on a market turn, but occurs after a significant price movement in a new direction. Often a short-term trend reversal movement makes the market either overbought or oversold, making it vulnerable to a short-term correction. Almost everyone has encountered this problem after receiving a trend following signal caused by a powerful change in direction. So when to enter the market?

The solution to this common problem. If the RSI value is above 75 (if you are buying) or below 25 (if you are selling), then delay your entry. Only enter when the RSI returns back to a level between 75 and 25. There will necessarily be minor market corrections, and your entry will not come at overbought or oversold levels.

### 4.1.4. Re-entry with RSI

Let's assume that your trade has been stopped and the trend is still going on. What you need in such a situation is a precise way of timing the re-entry, so that your initial loss is minimal.

Use a short-term (e.g. 3-day) RSI and wait for it to reverse, and only enter in the direction of the trend. To illustrate, let's assume your indicators say the market is moving downwards and you need a re-entry point. Next, let's assume that the RSI has been falling and is now below 50. Try to wait for the RSI to return above 50, then when it turns down, sell immediately. Expecting a slight upward movement of the very sensitive short-term RSI has the effect of easing any intermediate-term overbought or oversold conditions, allowing you to re-enter during a minor trend correction.

### 4.1.5. Income fixing with RSI

One of the most valuable applications of RSI is using it to lock in income. It is always nice to sit back and let the returns flow, but using relatively slow studies will inevitably result in the loss of some income before the exit signal is generated. You need an exit method that recognises quickly when the market is at a peak, combined with a stop-tracking method that allows income to flow while the market continues to move.

Try using the short-term RSI to lock in earnings, the 10- or 14-day RSI is usually not sensitive enough. A profit-taking signal finishes when the RSI reaches 75 or higher (25 or lower if you are short), and then returns 10 points or more. For example, the RSI rose to 87 and then went back down to 65. At this point, the market slows down and steps must be taken to protect your gains. Set stops at either the nearest trough in the last n days or at a predetermined value, whichever is closer.

We have found that the n-day trough is very useful as a tracking point. Quite often the market will move backwards without triggering your stop and you can keep tracking it for quite some time.

### 4.2. Stochastic Oscillators

Stochastic oscillators (Stochastics) are designed for use in flat markets. A stochastic oscillator is one of the best tools in this area. If you care about staying on the trend side, it can also be used in trend markets.

Stochastic oscillators were popularized by George Lane, who has been using them in his investment education courses since the early 50s. He perfected the use of stochastic oscillators over the years of his trading career and was able to find innovative ways to make them work well in almost any situation.

The basic formula for a stochastic oscillator is as follows:

%K = (Ct - Ln ) / (Hn - Ln) x 100%,

Where

Hn - the highest price of the last n periods;

Ln - lowest price for last n periods;

Ct - current price;

%K = today's close minus the trough of the last n days, divided by the peak of the last n days, minus the trough of the last n days;

%D is a slow stochastic, three-period moving average of %K.

The %K and %D produce what is known as a fast stochastic oscillator, which is rarely used due to its excessive sensitivity.

The fast %K and %D, again smoothed by the three-day moving average, produce a slow stochastic oscillator, which is used more often.

In what follows we will look at the slow, smoothed version of the stochastic oscillator.

The stochastic oscillator formula expresses the relationship between today's close and the range between the peak and trough of the past n days. For example, if today's close is 30 and the range over the last 10 days is 20 to 50, then the fast %K = 30 - 20 / 50 - 20 = 0.33 represents a relatively small value. If today's close is 40, which is closer to the top of the range, the fast %K will be O.66. %K and %D cannot be less than 0 or greater than 100. As days accumulate, %K and %D will be represented as lines oscillating between 0 and 100. Values close to 0 are theoretically indicative of an oversold market. Values close to 100 theoretically indicate an overbought market.

The basic stochastic oscillator signals are crossings of the lines %K and %D combined with the level of %K and %D, which indicate an overbought or oversold market. Oversold conditions are normally indicated by %D values below 30 and overbought conditions above 70. Values of 80 and 20 are also often used. There are also traders who are indifferent to %K and watch when %D reaches overbought or oversold levels.

The arrows in the figure mark the entry points into the market for buying or selling.

Usually the recommended time period for a slow stochastic oscillator is 18, but George Lane applies a wide range of values, finding what he understands to be the dominant cycle of the market being traded and then using half of this number as the period for the stochastic oscillator. Experience and testing suggests that a range between 9 and 12 is the best compromise between the speed of signals (crossing %K and %D) and the suitability or logical completion of the signal they produce, with a minimum of false signals. Like all other technical studies, stochastic oscillators respond faster to market action when using shorter time periods, and slower on longer periods. We will discuss some technical techniques used by other technical analysts to speed up signals. We believe that these techniques are not necessary. If you need faster signals, simply shorten the time period. Keep in mind that faster is not always better. You should look for a safer signals and not the fast ones.

Stochastic oscillators work best on broad price ranges or on soft trends with a slight upward or downward bias. The worst market for the normal use of stochastic oscillators is a market which is in a steady trend and subject to only minor corrections. In such a market, the stochastic oscillators will produce many flagging entry points which will be quickly extinguished by the trend. If you continue to use standard trading techniques with stochastic oscillators, you will end up with a serious losing streak. Remember: the trader who coined the adage "the trend is your friend" was not using stochastic oscillators.

How to identify and quantify a market which is in a "strong" trend? There are many ways, however, if the course of a "strong" trend is not obvious, try to measure the trend with the ADX. You can trade with the stochastic oscillator on a trend if you ignore the usual 70/30 or 80/20 overbought and oversold levels, and enter the market on the signal of the end of trend resistance given by the stochastic oscillator crossing at any level. However, there are better ways to follow the trend, and we believe that stochastic oscillators get their main value as trough and peak indicators.

### 4.3. Momentum

Many traders use Momentum more than any other tool, except perhaps for moving averages. Momentum is not always used by them as the main tool, but traders keep a close eye on it and use it along with other technical studies to make more timely trading decisions. Among the many reasons for its popularity are its simplicity, versatility, and the fact that it is considered a rare "leading indicator. Aside from simply reacting to the direction of prices, torque can change direction before prices do. Very few technical studies can arm a trader with such a valuable leading indicator.

Because of the versatility we have discussed, momentum is difficult to classify as a trend following or flagging indicator. It can be used to show the trend direction and can also give very good overbought/oversold cautions, making it a useful flotation trading tool. This seemingly simple indicator actually contains much more information than what is immediately apparent. The wealth of information hidden in the calculations opens up many options for using the momentum. A full understanding of what we are calculating should help you exploit the full potential of torque.

The torque indicator provides us with an accurate measure of market speed and to some extent the limit to which the trend is still full. The calculation is simple: subtract the closing price n days ago from today's closing price. The result will be a positive or negative number fluctuating around the zero point or line. The formula is as follows:

M = Pt - Pt-n

where

M - moment;

Pt - today's closing price;

Pt-n - closing price in n periods (usually n days) before Pt.

The value of n is the only part of the formula that can be changed by the trader, and most commonly the value of 10 is used here.

Some software packages allow the user to select open, peak, trough, close and some other price values for periods. We see no reason to use anything other than a close in the calculation. The result of the calculation is a technical study that oscillates around the zero line (which makes it an oscillator). If the market is moving up, the momentum will cross the zero line from the bottom to the top and, in general, it will maintain an upward slope. If the market moves down, the momentum oscillator will cross the zero line from top to bottom and, in general, will maintain a downward slope. All of this looks simple enough, but the momentum oscillator has other and more complex properties. For example, the farther apart in price Pt and Pt-n are, the greater the distance between the momentum values. When the market is moving quickly in an upward direction (we will assume that the market is bullish), the momentum oscillator behaves in the same way. But when the market is approaching its peak and closing prices become closer together, momentum slows down considerably and the momentum line becomes horizontal or slopes down, even though prices may continue to rise. When the market peaks and negative Pt - Pt-n values appear, the momentum line will begin to dive behind the zero line. Momentum clearly signals that the market speed is slowing down. The momentum formula measures not only the speed of movement, but also the rate at which that movement slows down. It describes both the speed of the market and the rate of change in that speed when the market is approaching a peak or passing its peak. As the market deviates further, negative momentum values become dominant and its line will approach and cross the zero line from time to time, signalling a change in trend direction from bullish to bearish.

What makes momentum react in this way? In order for the momentum value to increase and its direction to be upward, recent price values must outperform older ones. If recent price values are the same as older prices, the momentum line will be flat, even though the market is still moving up. If recent prices are less than the old prices, even if prices are still rising, the rate of change will further slow down and momentum will fall. The flattening and subsequent deflection of the momentum line down ahead of time shows us something that a normal price chart might not show. Momentum gives us an early warning that the market is slowing and that the rate of price increase is now slowing.

### 4.3.1. Momentum signal - trend following

When Momentum is used as a trend-following indicator, its most important signals come at points where the zero line is crossed. When the line is crossed from bottom to top, momentum is bullish. When the line is crossed from top to bottom, it is bearish. We would not recommend entering into a position against the direction of the momentum.

The number of times the Momentum line crosses the zero line depends on the time period used for calculating the momentum. Like other indicators, shorter time values will cause torque to be faster and respond better by crossing the zero line. Longer values will generally slow torque signals, reducing the frequency of crossovers. The smoothing effect of longer periods is obviously not the result of averaging more data, since the formula does not involve averaging closing prices. The simple logic is that if there is a trend, it will take more time to return to the price set 40 days ago than to return to the price of 10 days ago. We know traders who successfully use a wide range of time periods from 10 to 40 days. Many cycle traders seek to link the period of Momentum with the length of the cycle in the market.

Because lengthening the period of momentum will make the oscillator less responsive, and shortening it can lead to twitching, some traders find it useful to use relatively short and sensitive momentum values, and then set the bounds above and below the zero line. They then use crossing the boundaries instead of crossing the zero line as signals for new trades. When momentum fluctuates within the boundaries, it is not a signal for a new trade. This results in the market being forced to "confirm" its movement before entering a position, all of which eliminates a lot of the twitching caused by frequent zero line crossings.

Keep in mind that the most significant gains can be made when both momentum and prices are accelerating. As we have described, the slope of the momentum line will decrease when the rate of price increase slows down. An obvious and effective application of momentum would be to not enter a new trade until the momentum line slopes in the direction of the trend. When momentum moves back towards the zero line, the trend is by definition weakening or disappearing, so trading in this area can be futile.

### 4.3.2. The Momentum Signal - Going against the trend

Because momentum measures acceleration or deceleration of the market, it becomes quite useful as an overbought/oversold indicator. When the market reaches a peak, momentum flattens out and begins to fall often well before the actual market peak. A similar divergence in direction will occur at market troughs. Assuming no significant change in market volatility, the line drawn on the long term chart connecting the momentum peaks, parallel to the zero line, and the line connecting the momentum troughs, also parallel to the zero line, will represent overbought/oversold areas.

The main trading strategy here would be to sell immediately on a breakout of the upper zone, with a protective stop above recent peaks, and to buy immediately on a breakout of the lower zone, with a stop below recent troughs. Profits can be taken when the opposite zone is reached.

This flotation strategy will be productive if recent market action occurs in some price range, but if the market makes a significant breakout, it will obviously fail. We have seen formulas which attempt to deal with this problem by normalizing the momentum so that it always fluctuates between -1 and +1 or -100 and +100. This can be done by dividing the momentum values by some invariable value. We do not see much value in such an approach. Normalisation of the oscillator values will not prevent the market from a breakout, if conditions for such a breakout arise. The normalised momentum will act in much the same way as the RSI or some similar indicators in a trend market. Values will cluster at the top or bottom of the scale and give continuous buy or sell signals. The standard non-normalised momentum will continue to rise or fall to a theoretically infinite level, confirming the continuation of the trend and advising the trader not to use flattish strategies.

### 4.3.3. Long-term trading using momentum

One of the most productive ways to use momentum is to identify a long-term trend, and once the trend is determined, trades should only be made in that direction. This rule should greatly increase profitability by eliminating unprofitable trades that go against the trend. Momentum not only tells you the direction of the trend, but also gives you an idea of its strength. This valuable information will keep you out of trouble.

Our research shows that in most markets, 25-period Momentum, based on weekly charts, is a surprisingly reliable indicator of a long-term trend. Trend trading is particularly advantageous when the momentum line moves quickly away from the zero line. However, be very careful about following the trend when momentum peaks and when the momentum line veers back towards the zero line.

A logical combination of technical studies in this case would use long-term momentum to find the trend, medium-term moving averages to enter the trade when momentum is strong, and shorter-term flux indicators such as stochastic oscillator or RSI to take profits when momentum weakens.

Colby and Meyers, in their book The Encyclopedia of Technical Market Indicators, in one of several tests of momentum, optimized the rate of change on about 20 years of NYSE data (Rate of change is an indicator essentially identical to momentum.) Their trading rules were simple: buy when the indicator crosses the zero line from bottom to top, and sell when it crosses it from top to bottom. Holding a position after the first cross, passing the peak, and closing only after the opposite cross may be of academic interest, but it seems to us to ignore the basic properties of momentum (or ROC). Trading with momentum as a pivot method ignores the fact that slowing momentum is a signal to exit the market, or at least to switch to a different trading method than would be used if the market were still moving up. Unsurprisingly, the overall returns have been disappointing and the losses quite severe.

One very simple momentum test was also conducted by Bruce Babcock and described in his book The Dow Jones - Irwin Guide to Trading Systems. He tested 10-day and 28-day momentum using a simple pivot method of crossing without stopping. The results were breakeven, which is encouraging given that neither momentum nor any other oscillator should be used to trade in this way.

### 4.3.4. Trading using momentum divergence

We have always observed that the divergence between the technical study and the market often produces effective trading signals. Divergence between an oscillator such as Momentum and the market can occur when the market and Momentum create a high peak, then both retreat, and then the market creates a new peak which is not supported by the new peak of the Momentum oscillator. The theory is essentially that the divergence indicates weak support for the market and that it will not be able to continue climbing once a new peak is created. Price and momentum divergences are quite varied, a 10-period momentum based on daily charts will reveal many divergences and many significant trading opportunities, especially if the longer 25-week momentum is in its decline phase. Our standard cautionary tale regarding divergence trading says to wait until the divergence is fully confirmed before entering the market. A premature entry can very likely leave you on the wrong side of a trending market.

### 4.3.5. Using the momentum of other indicators

Many of the technical studies we have mentioned in this book measure market strength in one way or another. This is usually expressed by the slope of the line obtained by calculating the study. For example, a moving average that is in a strong trend is usually indicative of a strong market trend. The steeper the slope, the stronger the trend. Determining the exact degree of strength can be very subjective if we only look at technical research, but if we consider the momentum or rate of change of an indicator, we can objectively calculate the strength of a trend. This opens up new possibilities for us. We can filter out weakly trending markets and concentrate our efforts on markets with unusually strong trends. Or, if the market is not trending, we can buy on downtrends and sell on uptrends.

We believe that momentum has many worthwhile applications and can be rated as one of the most useful technical studies available to the trader. An imaginative and inventive technical analyst should find many interesting applications for this indicator, which is ahead of the prices, rather than following them.

### 4.4. ROC

Here, we will very briefly consider the Rate Of Change (ROC), because most of today's software packages provide this indicator in addition to timing, but despite that they are essentially identical. Rate Of Change has the following formula:

ROC= 100 (Pt / Pt-n)

A level of 100 is equivalent to the zero line of the torque graph. The only possible difference or advantage that can be discerned here is that when you use ROC instead of momentum, you do not have to deal with negative numbers. The trading rules and practical applications are the same for both indicators.