Introduction to Technical Analysis in Investment Trading

TECHNICAL INDICATORS

INTRODUCTION ........................................................................................................................................ 2
MOVING AVERAGES ................................................................................................................................ 2
STOCHASTICS (%K, %D FAST, %D SLOW)........................................................................................ 4
RELATIVE STRENGTH INDEX (RSI) .................................................................................................... 5
MOVING AVERAGE CONVERGENCE DIVERGENCE (MACD) ...................................................... 7
BOLLINGER BANDS ................................................................................................................................ 10
COMMODITY CHANNEL INDEX (CCI) .............................................................................................. 13
DIRECTIONAL INDICATORS (ADX, +DI/-DI, DMI).......................................................................... 15
TRIPLE EXPONENTIAL AVERAGE (TRIX) ....................................................................................... 16

Any unauthorized reproduction for commercial usage is strictly prohibited.
© Prashant Ram, All rights reserved

__________________________________Technical Analysis____________________________________

Introduction
Technical Analysis is the practice of analyzing stock charts to uncover patterns in
stock prices and predict the future behavior of the stock. This document introduces
and describes in detail the calculation of some major Technical Indicators. The
Technical Indicators (TAs) module form a part of most of the major trading packages
available in the market today including Realtick, esignal, Bloomberg etc.

MOVING AVERAGES
Calculation:

SIMPLE MOVING AVERAGE (SMA)

SMA = Σ Prices / N
Where, N is the time period over which the SMA is calculated

Example:
Following is SMA calculation over 5-day period

SMA 1-Nov to 5-Nov

EXPONENTIAL MOVING AVERAGE (EMA)

EMAt = EMAt-1 + A(Pt - EMAt-1)
With EMA1 = P1
A = 2 / (period -1)

Note: EMA at time T is the EMA at time T-1, plus Alpha times the difference
between the current price and EMA T-1. Thus based on the value of Alpha, EMA
“reacts” more or lesser on the new price.

Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 2


Calculation:

Closing EMA = 22.33 – 0.5 * (22.54 – 22.33)
Dates Prices SMA EMA
1-Nov 22.33 Note: A = 2/ (period – 1) = 2 / (5-1) = 0.5

2-Nov 22.54 22.44
3-Nov 23.56 23.00
4-Nov 23.50 23.25
EMA = 22.44 – 0.5 * (23.56 – 22.44)
5-Nov 24.59 23.30 23.92
8-Nov 27.00 24.24 25.46
9-Nov 26.98 25.13 26.22
10-Nov 26.55 25.72 26.38
11-Nov 26.54 26.33 26.46
12-Nov 25.30 26.47 25.88
15-Nov 25.00 26.07 25.44
16-Nov 25.98 25.87 25.71

Usage and Description:

One of the most basic and widely used indicators in a technical analyst's tool box,
moving averages help traders verify existing trends, identify emerging trends, and
view overextended trends about to reverse. Moving averages are lines overlaid on a
chart indicating long term price trends with short term fluctuations smoothed out.

There are three basic types of moving averages:

• Simple
• Weighted
• Exponential

A simple moving average gives equal weight to each price point over the
specified period. The user defines whether the high, low, or close is used and these
price points are added together and averaged. This average price point is then
added to the existing string and a line is formed. With the addition of each new
price point the sample set drops off the oldest point. The simple moving average is
probably the most widely used moving average.

A weighted moving average gives more emphasis to the latest data. A weighted
moving average multiplies each data point by a weighting factor which differs from
day to day. These figures are added and divided by the sum of the weighting
factors. A weighted moving average allows the user to successfully smooth out a
curve while having the average more responsive to current price changes.

An exponential moving average is another way of "weighting" the more recent
data. An exponential moving average multiplies a percentage of the most recent
price by the previous period's average price. Defining the optimum moving average
for a particular currency pair involves "curve fitting". Curve fitting is the process of
selecting the right number of periods with the correct type of moving average to
produce the results the user is trying to achieve. By trial and error, technicians
work with the time periods to fit the price data.



After determining the optimum moving average for a currency, this average price
line can be used as a line of support in maintaining a long position or resistance in
maintaining a short position. Breaches of this line can also be used as a signal that a
currency is in the process of reversing course, in which case a trader will want to
pare back an existing position or come up with entry levels for a new position

Reference:
1. http://www.forex.com/forex_technical_indicators.html

STOCHASTICS (%K, %D Fast, %D Slow)
Description and Usage:

Stochastic studies, or oscillators, are another useful tool for monitoring the expected
sustainability of a trend. They provide a trader with information about the closing
price in the current trading period relative to the prior performance of the instrument
being analyzed.

Stochastics are measured and represented by two different lines, %K and %D and
are plotted on a scale ranging from 0 to 100. Indications above 80 represent strong
upward movement while level indications below 20 represent strong downward
movements.

Fast stochastics (%K) can be very choppy. One can reduce choppiness by either
increasing the number of periods or by using the further smoothed form, %D Slow.
%D Slow is a moving average of %D. To create %D Slow you must select the
number of intervals to include in the average as well as the parameters used to
create %K and %D.

Calculation:

%K = [ (Close – Low) / (High – Low) ] * 100

Where,
Close = Closing price for that period
Low = Lowest price for that period
High = Highest price for that period

From above equation you will notice that
1. Since, (Close – Low) will always be <= (High – Low), %K will always be
between 0 and 100.
i.e. When Closing Price = Low , %K = 0
When Closing price = High, %K = 100

2. Note: Since (Close – Low) is a fraction of (High – Low) , %K will increase if
the security closes at a higher price i.e. closer to the highest price. Closing



levels that are consistently near the top of the range indicate accumulation
(buying pressure) and those near the bottom of the range indicate
distribution (selling pressure).

%D (fast) = SMA (%K)
%D (slow)k = (9/10) * %D(slow)k-1 + (1/10) *%Dk

Reference:
1. http://www.stockcharts.com/education/IndicatorAnalysis/indic_stochasticOscillat
or.html

RELATIVE STRENGTH INDEX (RSI)

A high RSI (upwards of 80) indicates that the security is overbought and suggests
that a downward trend in the price is expected. Consequently a low RSI (lower than
20) is indicative that the security is oversold and the prices of the security are
expected to rise (RSI values range between 0 and 100).

Other ways RSI can be used is as follows,
Center line Cross over
The centerline for RSI is 50. Reading above 50 indicates that average gains are
higher than average losses and a reading below 50 indicates that losses are winning
the battle.

Divergence
A rising RSI over a falling stock price indicates a positive divergence which indicates
a buy signal. The underlying stock will soon reverse its direction soon after a
divergence. Similarly, a falling RSI over a rising stock price indicates a negative
divergence and indicates that prices may be expected to fall (See chart below).



Calculation:
RSI = 100 - [ 100 / (1 + RS) ]
RS = (Avg of N period UP Close) / (Avg of N Period DOWN Close)
N is typically, 14 period

Example:
Following example calculates RSI over a 14 day period,
1.
Date Close UP DOWN 22.61 – 22.44
Up close since
1-Nov 22.44 prices are closing
2-Nov 22.61 0.17 up
3-Nov 22.67 0.06
4-Nov 22.88 0.21
5-Nov 23.36 0.48
8-Nov 23.23 -0.13
9-Nov 23.05 -0.18 23.23 – 23.36
10-Nov 22.86 -0.19 Down close since
prices are closing
11-Nov 23.17 0.31
down
12-Nov 23.69 0.52
15-Nov 23.77 0.08
16-Nov 23.84 0.07
17-Nov 24.32 0.48
18-Nov 24.80 0.48
14 Days Total 2.86 0.5
2.
Avg of 14 period UP Close = 2.86 / 14 = 0.204
Avg of 14 period DOWN Close = 0.5 / 14 = 0.036

3.
RS = 0.204 / 0.036 = 5.72
1 + RS = 6.72

4.
RSI (on 19 Nov) = 100 – [ 100 / 6.72 ] = 85.12

RSI for 19th Nov is 85.12 which is indicative that the stock is possibly overbought
and the stock prices are expected to fall. Note how the large series of up days and
the very small number of down days led to this up extreme reading.

References:
1. http://www.streetauthority.com/terms/r/rsi.asp
2. http://www.stockcharts.com/education/IndicatorAnalysis/indic_RSI.html



MOVING AVERAGE CONVERGENCE DIVERGENCE
(MACD)
Calculation:
MACD (12,26,9)

1. MACD = EMA (12 period) – EMA (26 period)
2. Trigger Line = EMA (9 period) of MACD

Note:
The MACD is calculated and then compared with the trigger line (which is a EMA(9
period of MACD). Whenever the MACD crosses the trigger line it is indicative of
change in trend. For example if the MACD line crosses up the trigger line it indicates
that the prices are rising. Consequently a crossing down is indicative of falling prices.

Histogram = MACD – signal,

The purpose of the histogram is to help show when a crossing occurs, since when it
crosses through zero the MACD crosses the signal line. The histogram can also help
visualizing when the two lines are coming together. Both may still be rising, but
coming together, so a falling histogram suggests a crossover may be approaching.

Description and Usage

Three types of trading signals are generated,
1. MACD line crossing the signal line
2. MACD line crossing zero line
3. Divergence between price and MACD levels

1. As indicated earlier, the MACD line crossing the EMA(9) signal line is indicative of
change in trend, a crossing up suggests rising prices a crossing down suggests falling
prices.

2. The zero line is the horizontal line when MACD = 0, A MACD line crossing the
EMA(9) signal line and then also crossing the MACD=0 line confirms the trend. See
the chart below



3. When the MACD trend diverges from the price trend, it can provide a signal that a
trending market may slow or reverse. A negative, or bearish, divergence occurs
when the MACD is making new lows while prices fail to reach new lows. A positive, or
bullish, divergence occurs when the MACD is making new highs while prices fail to
reach new highs. See chart below
i.e.
Positive divergence = MACD high, Prices still showing low, BULLISH MARKET
Negative divergence = MACD low, Price may be going high or low, BEARISH MARKET

The MACD proves most effective in trending markets rather than choppy, sideways
markets.

Note: A moving average over a shorter period “reacts” quicker to changes in stock
prices. A moving average over a longer period “holds” on to the older values and
hence “reacts” slower to the changes in stock prices. Consequently any fluctuations
in prices will “move” EMA (12) more than it will move EMA (26). Thus rising stock



prices will increase the value of the MACD. Since EMA (12) will rise faster than EMA
(26).

References:
1. http://en.wikipedia.org/wiki/MACD
2. http://www.chartfilter.com/reports/c22.htm



BOLLINGER BANDS
Calculation:

Bollinger Bands = SMA +- A. (SD)
Where,
A is an integer typically set to 3 or 2
SD is standard deviation of the prices over the given SMA period
Typical time period is 20-day SMA.

Unlike stochastics, which are bounded by 0 and 100, %b can assume negative values
and values above 100 when prices are outside of the bands. At 100 we are at the
upper band, at 0 we are at the lower band. Above 100 we are above the upper bands
and below 0 we are below the lower band.

%b = (Close – Lower Band) / (High Band – Low Band)
Bandwidth = (Upper Bandwidth – Lower Band) / Middle Band

Bollinger bands differ from MAs in that they adapt (i.e. expand or contract) based on
the price movements, Since BA = MA +- 3. (SD).

Example:



Usage:
Bollinger Bands can be combined with price action and other indicators to generate
signals and foreshadow significant moves. A double bottom buy signal is given when
prices penetrate the lower band and remain above the lower band after a subsequent
low forms. In the chart below the stock penetrated the lower band in late September
(red arrow) and then held above on the subsequent test in October. The October
breakout above the middle band (green circle) provided the bullish confirmation.



References:
1. http://www.bollingerbands.com/services/bb/?page=7
2. http://www.stockcharts.com/education/IndicatorAnalysis/indic_Bbands.html



Commodity Channel Index (CCI)
The CCI determines if the security is overbought or oversold securities. CCI typically
oscillates above and below a zero line, within the range of +100 and -100. Values
above +100 imply an overbought condition and indicate that the price of the stock
will fall. Values below -100 imply an oversold condition and indicate possible future
rise in stock prices.

The assumption behind the indicator is that commodities (or stocks or bonds) move
in cycles, with highs and lows coming at periodic intervals. Lambert recommended
using 1/3 of a complete cycle (low to low or high to high) as a time frame for the
CCI. If the cycle runs 60 days (a low about every 60 days), then a 20-day CCI would
be recommended.

Calculation:
For the purpose of this example, a 20-day CCI is used.
There are four steps in the calculation of CCI.

1. Calculation of typical price, TP = (H+L+C) / 3
Where, H- high price, L- low price , C- closing price

NOTE: in some cases we may simply use the closing price
Eg. CCI (20, Close), TP = Closing price

2. Calculate the 20-period SMA of the TP

3. Calculate the Mean Deviation. First, calculate the absolute value of the
difference between the last period's SMATP and the typical price for each of
the past 20 periods. Add all of these absolute values together and divide by
20 to find the Mean Deviation

4. CCI = (TP – SMATP) / ( (0.015) * Mean Deviation )

Example:
The following example uses a 5-day period to calculate CCI



References:
1. http://en.wikipedia.org/wiki/Commodity_Channel_Index
2. http://www.stockcharts.com/education/IndicatorAnalysis/indic_CCI.html



Directional Indicators (ADX, +DI/-DI, DMI)
The ADX indicator ranges from 0 to 100, although values above 60 are rare.
Typically values crossing over 40 and below 20 indicate a corresponding strong trend
and weak trend respectively. Note that the ADX DOES NOT indicate bullish or bearish
signal but merely reinforces the strength of the current trend. So if the stock is in a
downward trend, an ADX value is above 40, it indicates that the downward trend is
strong and expected to continue. ON the other hand an ADX of 15 on a downward
trend indicates that the trend is weakening and a turn in trend may be expected.
Similarly on an upward trend an ADX of 40 indicates that the trend is strong.

In the most basic form +DI/-DI can be used to generate buy/sell signals as follows.
When +DI crosses –DI upwards it indicates a buy signal, when +DI crosses – DI
downward it indicates a sell signal.

References:
1. http://www.stockcharts.com/education/IndicatorAnalysis/indic_ADX.html



Triple Exponential Average (TRIX)
The TRIX is a leading indicator which can be used in conjunction with a signal line to
indicate a buy/sell signal or can be used based on the price divergence. When it is
used in conjunction with a signal line, when the TRIX crosses up the signal line it is
indicative of a buy signal, conversely when it crosses down the signal line it is
indicative of a sell signal. Typically TRIX(15,9) is taken where 9-EMA is the signal
line.

Calculation:
For a 15 day period
1. Calculate the 15-day EMA of the closing price
2. Calculate the 15-day EMA of the prices in step 1
3. Calculate the 15-day EMA of the prices in step 2
4. Calculate the 1-day percentage change of the prices in step 3

NOTE:
EMAt = EMAt-1 + A (Pt – EMAt-1)
Where,
EMA0 = P0
A = 2 / (period -1) = 1 / (15 – 1) = 0.14

References:
1. http://www.stockcharts.com/education/IndicatorAnalysis/indic_trix.htm


Introduction to Technical Analysis in Investment Trading

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