Technical Analysis Explained

Technical indicators through a mathematical approach

In the "old" days before personal computers, calculating most momentum indicators was a slow and monotonous process. As a result, few traders bothered to use these indicators. Now, with the touch of a button it is possible to calculate, plot , and manipulate even the most complicated formulas. There are two schools of thought. The first is the traditional one which argues in favour of manual calculations because the trader can get a better "feel" for the data. The second believes that this labour-intensive method is not important and that the use of the computer gives the trader a far wider range of indicators with which to do the analysis. Deciding between the two will depend a great deal on the individual. It is often best to choose the method that makes you feel more comfortable.

The simple moving average

The simple moving average is probably the widest used of all technical indicators and can be easily constructed. It calculates an average of a certain body of data. For example, if a 10-day average of closing prices is desired, the prices for the last ten days are added up and the total is divided by ten. The term moving is used because only the latest ten days' prices are used in the calculation. Therefore, the body of data moves forward with each new trading day. The most common way to calculate the moving average is to work from the total of the last ten days' closing prices. Each day the new closing is added to the total and the close 11 days back is subtracted. The new total is then divided by the number of days. The results of the calculations are plotted on the corresponding price chart as illustrated in figure(33). The moving average is a trend following system. As long as closing prices remain above the

Figure 33

calculated line, one should play the market from the long side. A position would be closed and even reversed as soon as the line is violated. If a short-term average is employed (a 5- or 10-day), the average tracks closing prices very closely and several crossings occur. This action can be either good or bad. While the shorter average generates more false signals (whipsaws - see figure 34), it has the advantage of giving trend signals earlier in the move. The trick is to find the average that is sensitive enough to generate early signals, but insensitive enough to avoid most of the random "noise".

By the way, the use of Fibonacci figures (13,21,34,55 ...) often provides good results. The 21-moving average in a daily chart and in the weekly chart the 13-week average has proven valuable in both stocks and commodities.

Figure 34

Weighted moving average

In this calculation, the closing price of the tenth day would be multiplied by ten, the ninth day by nine, the eighth day by eight, and so on. The greater weight is therefore given to the more recent closings. The total is then divided by the sum of the multipliers (55 in case of the 10-day average: 10 + 9 + 8 + ... + 1).

Exponential moving average

It is a weighted moving average. But while it assigns diminished importance to past price action, it does include in its calculation all of the price data available (whole life of a future contract). The formula for this average is complicated and requires the aid of a computer. As a general rule for all technical indicators we can say that a more sophisticated calculation does not necessarily provide better results! In this context the "4-weekly rule" seems worth mentioning.

The 4-weekly rule (or weekly price channel)

The rules applied for this indicator are very simple!

1. Cover short positions and buy long whenever the price exceeds the highs of the four preceding full calendar weeks.

2. Liquidate long positions and sell short whenever the price falls below the lows of the four preceding full calendar weeks.

The moving average convergence/divergence (MACD)

This system derives its name from the fact that the two moving averages (usually exponential) used in the calculation are continually converging with, and diverging from, each other. Crossovers of the lines send buy signals (short MA above long MA), respectively sell signals (short MA falls below long MA). Another possibility to provide trading signals is the subtraction. By its nature it creates a line oscillating around the zero level. Sell and buy signals are generated through a zero line cross-over (figure 35).

Figure 35


Momentum measures the velocity of a price move. It is a generic term. Just as the word "fruit" encompasses apples, grapes, bananas, and so forth, "momentum" embraces a host of individual indicators such as rate-of-change (ROC), relative strength indicator (RSI), stochastic and the above described MACD. In contrast to the already presented trending indicators like the moving averages, the momentum indicators, also called oscillators, are extremely useful in non-trending market environments where price fluctuates in a horizontal trading range. They provide valuable oversold and overbought information. This fact does not exclude that an oscillator, in conjunction with price charts during trending phases, can become an extremely valuable ally by alerting the trader that the trend is losing momentum before that situation becomes evident in the price action itself.


To construct a 10-day rate of change oscillator, the latest closing price is divided by the close 10 days ago. The formula is as follows:

Rate of change: 100 (V/Vx) where V is the latest close and Vx is the closing price x days ago.

In this case, the 100 line becomes the reference line (figure 36). If the latest price is higher than the price ten days ago (prices are rising), the resulting rate of change value will be above 100. If the last close is below ten days ago, the ratio would be below 100.

Figure 36

The easiest way to utilise the oscillator is to detect a crossing of the reference-line as a signal generator. Buy when the oscillator moves above the zero line and sell when it moves below. These trading signals are most effective when taken in the direction of the market trend. The second possibility to use oscillators is edge band analysis, or the identification of extremes. In other words, the outer boundaries of the oscillator band are used to warn of market extremes. Positions can be taken accordingly. But probably the most important oscillator analysis is to watch for divergences. A divergence describes a situation when the oscillator line and the price line diverge from one another and start to move in opposite directions. In an up-trend, the most common type of oscillator divergence occurs when prices continue to rise, but the oscillator fails to confirm the price move into new highs. This is often an excellent warning of a possible rally failure and is called a bearish, or negative, divergence. (compare with figure 37) In a downtrend, if the oscillator fails to confirm the new low move in prices, a positive or bullish divergence exists and warns of a near term bounce.

Relative Strength Index (RSI)

The formula for the RSI is as follows:

RSI = 100-100/(1+RS)

whereas RS = Average of x day's up closes divided by Average of x day's down closes

The analysis of this calculation is basically the same as described above. On the chart (figure 37) one can see a classic example of a multiple divergence.

Figure 37

Divergence analysis provides the oscillator's greatest value. However, the reader is cautioned against placing too much importance on divergence analysis to the point where basic trend analysis is either ignored or overlooked.

So if the trend is up, then a buying strategy is called for; buy when the market is oversold in an up-trend. Sell short when the market is overbought in a downtrend. The importance of trading in the direction of the major trend cannot be overstated.


The Stochastic indicator, invented by George Lane, rests on the assumption that prices tend to close near the upper part of the trading range during an up-trend and near the lower part during a downtrend. As the trend approaches a turning point, the price closes further away from its extreme (away from the daily high in a rising market and from the daily low in a declining one). The objective of the Stochastic formula is to identify these points since they indicate that a trend reversal is at hand.

The indicator is plotted in the form of two lines, known as "Percent D" and "Percent K". The %K is the more sensitive, but it is the %D line that carries the greater weight and gives the major signals. The formula of the %K is as follows:

%K = 100 (C-L5) / (H5 - L5)

where C is the latest close, L5 is the lowest low for the last five days, and H5 is the highest high for the same five days

The formula simply measures, on a percentage basis of 0 to 100, where the closing price is in relation to the total price range for a selected number of days. A very high reading (over 70) would put the closing price near the top of the range, while a low reading (under 30) near the bottom of the range.

The %D line is the smoothed version of %K. Its calculation uses the following formula:

%D = 100 (H3 / L3)

where H3 is the 3-day sum of (C - L5) and L3 is the 3-day sum of (H5 - L5).

The "Stochastic" takes the form of two oscillators. The %K is usually plotted as a solid line, and its slower %D counterpart is expressed as a dashed or dotted line. Like the RSI, this indicator always falls in the range of 0 to 100. A reading near 80 is generally regarded as overbought and 20 as oversold. (figure 38)

Figure 38

Figure 39

Larry Williams %R

Larry Williams %R is based on a similar concept of measuring the latest close in relation to its price range over a given number of days. Today's close is subtracted from the price high of the range for a given number of days and that difference is divided by the total range for the same period. The scale in Williams' oscillator is reversed, so that an overbought reading is above 20 and an oversold reading is under 80. Whilst interpreting, the analyst is usually looking for divergences in overbought or oversold areas, pre-indicating reversals of the prevailing trend (figure 39).

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