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# Chapter 3 Lagging Indicators ## 1.) Moving Averages

Moving average is a widely used technical indicator that helps smoothen out the volatility in a stock’s price action by filtering out the noise from random price fluctuations. A moving average is a trend-follow lagging indicator as it is calculated taking past data into consideration. As the name suggests, a moving average is an average that moves as old values are dropped with the availability of new values. Moving averages can be employed to identify the current trend of a scrip.

### Types of moving averages

There are 3 types of moving averages

• Simple Moving Average (SMA)

It is obtained by computing the simple average of price data over a defined period of time. In general, we use the closing price of the security to compute the SMA as it is considered to have more significance compared to the remaining price points (namely, open/high/low price for the day). Thus, a five-day SMA is calculated by adding the closing price of five days and dividing this sum by the total number of days (in this case, five).

For e.g., the five-day SMA of ITC can be calculated as follows:

ITC

Date Close Price 5 Period SMA
Jul 3, 2017 342.5 --
Jul 4, 2017 337.25 --
Jul 5, 2017 331.05 --
Jul 6, 2017 337.10 --
Jul 7, 2017 334.30 336.44
Jul 10, 2017 333.30 334.60
Jul 11, 2017 330.40 333.23
Jul 12, 2017 328.85 332.89
5-day SMA on July 7 = 336.44 = (342.50+337.25+331.05+337.10+334.30)
5
5-day SMA on July 7 = 336.44 = (342.50+337.25+331.05+337.10+334.30)
5
5-day SMA on July 7 = 336.44 = (342.50+337.25+331.05+337.10+334.30)
5
5-day SMA on July 10 = 334.6 = (337.25+331.05+337.10+334.30+333.30)
5
5-day SMA on July 11 = 333.23 = (331.05+337.10+334.30+333.30+330.40)
5
5-day SMA on July 12 = 332.89 = (337.10+334.30+333.30+330.40+328.85)
5

To calculate the moving average of the scrip after the close of market hours on July 7, 2017, we will consider the closing price of the last five trading sessions (from July 3 to July 7) and divide it by 5.

To recalculate the five-day SMA at the close of the next trading session on July 10, 2017, exclude the closing price from July 3 and consider the one on July 10 i.e. the new data value.

As illustrated in the example, price gradually decreases from 342.5 to 328.85 over a period of eight days; in the same timeframe, the five-day SMA also decreases from 336.44 to 332.89, indicating a lag associated with the moving averages. Hence, larger the time period, larger is the lag.

• Weighted Moving Average (WMA)

Weighted moving average moves a step ahead of simple moving average. Here, we assign a weight to each value, with bigger weights assigned to the most recent data points as they are more relevant than historical data points. The sum of weights should add up to 1 (or 100%). As new data points are added, the new weights will align accordingly. In contrast, each value is assigned the same weight in SMA. Ideally, traders calculate WMA on the basis of the closing price.

WMA is calculated by multiplying the given price by its assigned weight and then dividing the sum by the total number of days. The weights assigned are subjective in nature are at the discretion of the trader. Because of its calculation methodology, WMA follows prices more closely than a corresponding SMA. This reduces lag to an extent.

ITC

Date Close Price Weights WMA
Jul 3, 2017 342.5 0.13
Jul 5, 2017 331.05 0.20
Jul 5, 2017 331.05 0.20
Jul 6, 2017 337.10 0.27
Jul 7, 2017 334.30 0.33 335.34
Jul 10, 2017 333.30 334.29
Jul 11, 2017 330.40 332.89
Jul 12, 2017 328.85 331.43
5-day WMA on July 7 = 335.34 = (342.50*0.07+337.25*0.13+331.05*0.20+337.10*0.27+334.3*0.33)
5
5-day WMA on July 10 = 334.29 = (337.25*0.07+331.05*0.13+337.10*0.20+334.3*0.27+333.3*0.33)
5
5-day WMA on July 11 = 332.89 = (331.05*0.07+337.10*0.13+334.30*0.20+333.3*0.27+330.4*0.33)
5
5-day WMA on July 12 = 331.43 = (337.1*0.07+334.30*0.13+333.30*0.20+330.4*0.27+328.85*0.33)
5
• Exponential Moving Average (EMA)

Exponential moving average widely differs from the simple and weighted moving averages methodologies as it is calculated by considering all historical data points since the inception of the stock. Ideally, to calculate 100% accurate EMA, we should use all closing prices right from the first day a stock was listed.

Calculating the EMA involves a three-step process:

Step 1: Since it would not be practical to calculate historical data right from the inception of the stock, we use the SMA value as the initial EMA value. So, a simple moving average is used as the previous period's EMA in the first calculation.

Step 2: To calculate the weighting multiplier, we divide 2 by the sum of total periods and add it to 1.

Step 3: We subtract the EMA of the previous day from the current closing price and multiply this number with the multiplier. We then add this product with its previous period EMA to find out the final EMA value.

Therefore, the current EMA value will change depending on how much past data we use in our calculation. The more data points we use, the more accurate our EMA will be. The goal is to maximize accuracy while minimizing calculation time.

Initial EMA value = 5-day SMA
Weighting Multiplier= (2 / (Time periods + 1)) = (2 / (5 + 1)) = 0.3333 (33.33%)
EMA= {Close – EMA of previous day} x multiplier + EMA of the previous day

A five-day EMA applies a 33.33% weighting to the most recent prices, while a 10-day EMA has a weighting multiplier of 18.18%. The shorter the time period, larger the weighting multiplier will be. We notice that as the time period doubles, the weighting multiplier drops 50%.

Date Close Price Five-day SMA Weighting factor Five-day EMA
Jul 3, 2017 342.5 -- -- --
Jul 4, 2017 337.25 -- -- --
Jul 5, 2017 331.05 -- -- --
Jul 6, 2017 337.10 -- -- --
Jul 7, 2017 334.30 336.44 -- 336.44
Jul 10, 2017 333.30 334.60 0.3333 335.39
Jul 11, 2017 330.40 333.23 0.3333 333.73
Jul 12, 2017 328.85 332.79 0.3333 332.10

5-day EMA on July 7 = 5-day SMA= 336.44

5-day EMA on July 10 = 335.39 = (333.30-336.44) x 0.33 + 336.44

5-day EMA on July 11 = 333.73 = (330.40-335.39) x 0.33 + 335.39

5-day EMA on 12 = 332.10 = (328.85 -333.72) x 0.33 + 333.72

### Comparison of the three moving averages

Different values are generated when we compare the computation methodology of the three different moving averages. The most common moving average among traders is EMA.

Moving Averages SMA WMA EMA
• Smoothened average
• Less prone to whipsaws
• Best average to consider for support & resistance
• Reduction in price lag, so can be implemented for short-term trading
• Reduction in price lag, hence, can be used for short-term trading
• No omission in price data points
• Has maximum price lag
• Assigns same weight to all price data
• Omission of previous data points leads to all price data not being considered
• Omission of previous data points leads to all price data not being considered
• Chance of whipsaws
• Chance of whipsaws

Moving average value comparison: The following table represents the comparison between the values of the three different moving averages over the same period of time

Date Close Price Five-day SMA Five-day WMA Five-day EMA
Jul 3, 2017 342.5 -- -- --
Jul 4, 2017 337.25 -- -- --
Jul 5, 2017 331.05 -- -- --
Jul 6, 2017 337.10 -- -- --
Jul 7, 2017 334.30 336.44 335.34 336.44
Jul 10, 2017 333.30 334.60 334.29 335.39
Jul 11, 2017 330.40 333.23 332.89 333.73
Jul 12, 2017 328.85 332.89 331.43 332.10

### Graphical comparison on the three moving averages As seen in the above graph, where blue, green, and pink are the five-day EMA, WMA, and SMA, respectively, when there is a sharp correction in the price, EMA and WMA react the most as they assign a higher weight to the most recent prices compared to the SMA.

## Applications of Moving Averages

### Trend Identification

Traders use moving averages to identify the trend of a stock. A rising 200-day moving average reflects that the long-term trend is up and the stock can be traded with a positive bias. Similarly, a falling 200-day moving average reflects a long-term downtrend and hence, we can consider shorting the stock or refrain from investing in it. (Blue: 10-day EMA; green: 89-day EMA; pink: 200-day EMA)

From the above graph, we can clearly see that L&T Finance is in a long-term uptrend as the short- and medium-term averages are trading above its long-term 200-day moving average, which is also showing an upward momentum. A price dip towards its medium-term average can be considered as a buying opportunity.

### Buy/sell signals based on crossover

A buy signal is generated when a bullish crossover occurs, i.e. the short-term moving average crosses the long-term moving average, popularly referred to as a golden cross. For e.g., when the 89-day EMA crosses above the 200-day EMA, a bullish trade can be initiated.

On the other hand, a bearish death cross occurs when the short-term moving average crosses below the long-term moving average. The generated signals tend to occur with a lag as we make use of two lagging indicators. The best trading opportunities are obtained in a trending market as compared to a sideways market, wherein whipsaws or false signals are generated.

Price 89-day EMA Action/View Technical term
Trading above 200-EMA Crosses above 200-EMA Bullish Golden cross
Trading below 200-EMA Crosses below 200-EMA Bearish Death cross In the above graph, we see how moving averages can be used to generate trading signals. Moving averages can also be used to generate signals with simple price crossovers. A bullish signal is generated when prices move above the moving average and a bearish signal is generated when prices move below it. The advantage of price signals is that it reduces time lag and allows traders to react quicker. As in the Fortis case represented above, traders could have initiated a short position or could have closed their long positions when the stock closed below its 200-day EMA. Consequently, a huge surge in trading volumes, with the MACD-Histogram moving into the negative territory, indicated a change in momentum. This hinted traders to take a bearish view, thus resulting in an 18% fall in the stock.

### Support & Resistance Levels

Moving averages also tend to act as support and resistance levels. A stock in a long-term uptrend could find support near its medium-term EMA during a pullback. Similarly, a stock in a long-term downtrend could face resistance near its medium-term EMA during any bounce backs.

In fact, some moving averages may offer support or resistance simply because they are widely used by many traders. For e.g., a trader may not short a stock if it is trading near its 200-day EMA out of fear that other traders may be using it as a buy zone. In the above example of JSW Steel, we see how the stock has taken support along its medium-term 89-day EMA on multiple occasions and has acted as a good support level to purchase the stock.

### Moving Averages in sync with the Candlestick Pattern Moving averages can also be traded in tandem with candlestick patterns. In the above chart of Bata India, the bullish candlestick pattern can be traded with added confidence as it coincides with the support of the 200-day EMA.

### Moving Average in sync with Price Pattern In the above chart of United Spirits, a buy signal is generated when the bullish crossover coincides with a cup and handle breakout on the daily chart, affirming a bullish bias in the stock.

### Construction of Indicators

Moving averages are used to construct technical indicators such as Bollinger Band and MACD, which are widely used by market technicians.

## Key Moving Averages Used by Technical Analysts

Moving averages are used based on the trading horizon.

For e.g.,

5-day MA Short-term
13-day MA Short-term
50-day MA Medium-term
89-day MA Medium-term
200-day MA Long-term

### Observations on Moving Averages

• It is used in a trending market to indicate a clear trend direction by eliminating the noise
• In case of a sideways market, the moving average would lead to whipsaws, hence, using other indicators like RSI and stochastic would be more helpful
• Signals generated by moving averages tend to have a lag
• Provides best results when combined with other technical indicators and price patterns

## 2.) Bollinger Bands®

Bollinger Bands® are one of the most widely indicators used in technical analysis. They are volatility bands that are placed above and below a moving average and automatically expand or contract with a change in volatility. The dynamic nature of Bollinger Bands allows them to be used on different securities without having to change the setting. Famous technical trader John Bollinger developed this tool and registered it as his trademark.

### Computing Bollinger Bands

There are three lines that compose Bollinger Bands: a simple moving average (middle band) and an upper and a lower band.

Middle band = 20-day SMA of the closing price

Upper band = 20-day SMA + (20-day standard deviation of price * 2)

Lower band = 20-day SMA - (20-day standard deviation of price * 2)

The default setting of the middle band, i.e. the simple moving average is usually set at 20 days. A simple moving average is used because the standard deviation formula also uses a simple moving average. The upper and lower bands are usually set two standard deviations above and below the middle band, respectively.

## Interpretation

### Overbought and oversold levels

Traders use Bollinger Bands to determine overbought and oversold levels. A trader will try to sell when the price, backed by a bearish signal on the price chart, reaches the top of the band, and will execute a buy when the price, backed by a bullish signal on the price chart, reaches the bottom of the band. According to Bollinger, the bands should contain 88-89% of price action, which suggests that the price would move within the band for a majority of the time.

The interpretation is that the stock price should hover around the average price. However, if the current stock price is around its upper band, it is considered expensive in respect to the average. Here, one should look at shorting opportunities if there is a confirming signal on the price chart with an expectation that the price will scale back to its average.

Likewise, if the current market price is around the lower band, it is considered cheap in respect to the average prices. Here, one can look at buying opportunities with an expectation that the price will scale back to its average. In the above example of Pidilite Industries, we observe instances where a trader can initiate trades based on oversold and overbought levels on the Bollinger Band conceding with bullish and bearish candlestick patterns on the price chart.

An important point to keep in mind is that the upper and lower Bollinger Bands together form an envelope, which expands whenever the price drifts in a particular direction, indicating a strong momentum. The Bollinger Band signal fails when there is an envelope expansion. This leads us to an important conclusion, Bollinger Bands work well in a sideways markets, and fail in a trending market.

## 3.) Standard Deviation

Standard deviation is a statistical measure to gauge the amount of variability or dispersion around an average. It measures the difference between the actual value and the average value. If a security trades in a narrow price range, the standard deviation will give a lesser value, which indicates low volatility. Conversely, if the security witnesses wild price swings, either up or down, then standard deviation gives a higher value, which indicates high volatility.

### Computing Standard Deviation

• Calculate the average (mean) price for the number of periods selected
• Determine each period's deviation (close less average price)
• Square each period's deviation
• Sum the squared deviations
• Divide the sum by the number of observations
• The standard deviation is then equal to the square root of that number

### Interpretation

Standard deviation is mainly used as a confirmatory indicator. It tends to surge as price gets volatile. As the price action declines, the standard deviation moves lower. A price move backed by a surge in standard deviation indicates above-average strength and weakness.

Market bottoms that are accompanied by decreased volatility over longer periods of time indicate a lack of interest in the security among traders, while market bottoms accompanied by a surge in volatility over a short duration indicate panic sell-offs.

### Standard Deviation Values

Standard deviation values depend on the price of the security in question. Securities with a higher price tend to have a higher standard deviation value compared to stocks with low price. Hence, a stock like Eicher Motors or Page Industries (current market price at ~Rs30,000) will always have a higher value compared to a stock like Ashok Leyland (CMP ~Rs144). However, the absolute value is not of much importance; what traders look for is the trend in the standard deviation with respect to the price action.

Standard deviation values are also affected if a security experiences a large price change over a short period of time. A stock that has surged from 15 to 60 is most likely to have a higher standard deviation at 60 than at 15. Likewise, a security that moves from 10 to 50 will most likely have a higher standard deviation at 50 than at 10. Aban Offshore’s chart above depicts a decline in price and a gradual decline in volatility, indicating a lack of buying interest in the stock. Alkem’s chart above, depicts a panic sell-off; the decline in price is accompanied by a surge in the standard deviation, indicating that traders are expecting the correction in the stock to accentuate and, hence, want to exit at any cost. On the contrary, the above chart of Bata India shows a surge in prices backed by a surge in standard deviation, thus indicating strength in the stock. This is usually witnessed when there is a huge buying interest in the stock.

## 4.) MACD-Histogram

The MACD-Histogram (Moving Average Convergence Divergence-Histogram) is an oscillator that fluctuates above and below the zero line. The MACD-Histogram is used to anticipate signal line crossovers in MACD, which turns moving averages into momentum indicators by subtracting a longer moving average from a shorter one. Since MACD-Histogram makes use of moving averages and as moving averages inherently lag behind price, there can be a delay in signal line crossovers, which could affect the reward-to-risk ratio of a trade. Bullish or bearish divergences in the MACD-Histogram can alert chartists to an imminent signal line crossover in the MACD.

### How to compute

MACD = (12-day EMA - 26-day EMA)

Signal Line = 9-day-EMA of MACD

Thus, MACD-Histogram = MACD - Signal Line

The default MACD indicator is the 12-day-EMA minus the 26-day-EMA, while a 9-day-EMA is plotted alongside the chart to act as the signal line to identify turns in the indicator. The histogram is positive when MACD is above its 9-day-EMA and negative when it is below it.

### Interpretation

The MACD-Histogram is designed to identify convergence, divergence and crossovers. It displays the extent of separation between the MACD and its signal line. The histogram is positive when MACD is above its signal line. Positive values increase as MACD diverges further from its signal line and decrease as it converges with its signal line. The MACD-Histogram crosses the zero line as MACD crosses below its signal line. The indicator is negative when MACD is below its signal line. Negative values increase as MACD diverges further from its signal line. Conversely, negative values decrease as MACD converges on its signal line.

### Signal Line Crossover

With this method, a buy signal occurs when the MACD line crosses above the signal line forming a confirmatory bullish candlestick pattern on the price chart. A sell (short) signal occurs when the MACD line crosses below the signal line along with a bearish candlestick on the price chart. In the above example of Shiram Transport Finance, we witnessed a sell signal on January 18, 2018, when the MACD-Histogram crossed below the center line with a confirmatory bearish signal on the price chart. On the other hand, a bullish signal was generated on February 23, 2018, when the MACD-Histogram witnessed a positive crossover over the center line.

There are no built-in targets with this indicator, so trades are generally held until a crossover in the opposite direction occurs. New trades can then be initiated in the direction of the new crossover.

The downfall of this strategy is that it can result in whipsaw trades, when the MACD and signal lines cross back and forth in a short amount time; hence, the indicator, just like moving averages, should be made use of in trending markets. Another way to avoid whipsaws is to only take trades in the direction of a long-term trend. If the trend is up, only take buy signals, and exit when the MACD line crosses back below the signal line.

### Divergence

The MACD-Histogram anticipates signal line crossovers in MACD by forming bullish and bearish divergences. Bearish divergence is when the price is making new highs, but the MACD is not. It shows that momentum has slowed, and that a reversal could be witnessed soon.

Bullish divergence is when the price is making new lows, but the MACD is not. It shows that selling pressure has slowed, and that a reversal could be around the corner.

It is risky to base trades solely on divergence, wait for the confirmation signal on the price chart. A stock can continue to rise (fall) for a long time even while bearish (bullish) divergence is occurring. In the above example of Bosch, notice that the price tries to make a new low late in March 2018, but the MACD is already making higher highs. This indicates that a reversal is around the corner, and it is exactly what is witnessed in the following days, with the stock witnessing a breakout on the price chart and a bullish signal line crossover on the MACD-Histogram.

## 5.) Force Index

The force index is a technical indicator that combines the price and volume to determine the strength behind a move or help identify possible turning points. Put simply, it helps gauge the strength behind price movements by looking at a combination of three key pieces of market data, i.e.

• Direction of price change
• Magnitude of price change

### Computing Force Index

Force index = {Close (current period) - Close (prior period)} * Volume

Calculation of the one-day force index is straightforward. We simply subtract the prior close from the current close and multiply the difference by current period’s volume. The force index for more than one day is computed by taking the EMA of the one-day force index. For example, a 20-day force index is the EMA of a one-day force index value for the last 20 days.

Force index is positive when the current close is above the prior close, and negative when the current close is below the prior close. For the force index to produce a large value, the price change and volume have to be significant.

In order to smoothen the one-day force index and produce less whipsaws, a trader can consider using the indicator with a 10-day- or 14-day-EMA to reduce the positive-negative crossovers.

### Interpretation

Force index produces either a positive or negative value based on the price movement. A positive price change signals that buyers were stronger than sellers, while a negative price change signals the opposite. Meanwhile, the extent of the price move along with the volume shows the commitment of the trader, i.e. a big advance on heavy volume show the bullishness of the buyer, and likewise, a big decline on heavy volume displays the bearishness of the seller.

### Trend Identification

The force index can also be used to determine the medium or long-term trend of a stock as well as reinforce the trend. The trend in question, short, medium, or long-term, depends on the parameters of the force index. While the default force index parameter is 13, chartists can use a higher number to further smoothen the chart or a lower number for less smoothening. In the above example of Avenue Supermarts, the stock witnessed a breakout on the price chart on April 5, 2018. At the same time, the 10-day-EMA force index traded in a higher top-higher bottom chart structure and gave an additional confirmation signal to the trader to place a bullish trade. Likewise, the stock witnessed a continuation in the uptrend and rallied from 1,400 to 1,490 levels in the next three trading sessions.

### Divergence

Bullish and bearish divergences can alert traders about a potential change in trend. Divergences are classic signals associated with oscillators. A bullish divergence forms when the indicator moves higher as the security moves lower. Contrariwise, a bearish divergence forms when the indicator moves lower as the security moves higher. Here, even though the security is moving higher, the indicator shows underlying weakness by moving lower.

Confirmation is an important part of bullish and bearish divergences. A bullish divergence can be confirmed with the force index moving into positive territory and with a resistance breakout on the price chart. A bearish divergence can be confirmed with the force index moving into the negative territory and a support break on the price chart. Chartists can also use candlesticks, moving average crosses, pattern breaks, and other forms of technical analysis for confirmation. In the above chart, a bullish divergence can be witnessed as Nifty forms a lower top-lower bottom structure while the force index manages to form a higher bottom structure. Nifty finally witnesses a breakout and gives a close above the declining trend line, thus, confirming the bullish divergence.