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- 1. 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
- 2. __________________________________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
- 3. __________________________________Technical Analysis____________________________________ 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. Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 3
- 4. __________________________________Technical Analysis____________________________________ 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 Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 4
- 5. __________________________________Technical Analysis____________________________________ 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) Description and Usage: 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). Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 5
- 6. __________________________________Technical Analysis____________________________________ 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 Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 6
- 7. __________________________________Technical Analysis____________________________________ 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 Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 7
- 8. __________________________________Technical Analysis____________________________________ 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 Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 8
- 9. __________________________________Technical Analysis____________________________________ 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 Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 9
- 10. __________________________________Technical Analysis____________________________________ 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: Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 10
- 11. __________________________________Technical Analysis____________________________________ 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. Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 11
- 12. __________________________________Technical Analysis____________________________________ References: 1. http://www.bollingerbands.com/services/bb/?page=7 2. http://www.stockcharts.com/education/IndicatorAnalysis/indic_Bbands.html Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 12
- 13. __________________________________Technical Analysis____________________________________ Commodity Channel Index (CCI) Description and Usage: 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 Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 13
- 14. __________________________________Technical Analysis____________________________________ References: 1. http://en.wikipedia.org/wiki/Commodity_Channel_Index 2. http://www.stockcharts.com/education/IndicatorAnalysis/indic_CCI.html Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 14
- 15. __________________________________Technical Analysis____________________________________ Directional Indicators (ADX, +DI/-DI, DMI) Description and Usage: 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 Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 15
- 16. __________________________________Technical Analysis____________________________________ Triple Exponential Average (TRIX) Description and Usage: 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 Copyright © 2006 Prashant Ram, All rights reserved_______________________________________ 16

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