While analyzing share price movements, moving average is one way to track market direction. It is mainly a follower of the market and tells us about a particular direction of the market. It is a rolling average where each observation is generated by the sum of all the closing prices over a particular time period divided by the number of days. To get the next observation, the first price needs to be dropped and the last observation needs to be added. For example for 100 days share price of a company, the 10 day moving average would be defined as

MA 1 = (P1 + P2 +………+ P10)/10

MA2 = (P2 + P3 + ………+ P11)/10

and so on, where P is price. Clearly the first MA will be posted on the 11^{th} day.

Moving averages (MA) smooth the data to form a trend following indicator. Result is a smooth line which provides information on the direction of the market and cleans out the noise. It is also a laggard as it tells us what has happened but, this ‘time lag’ can be reduced with shorter moving average like 10 day, 15 day, but it cannot be completely removed. They also form the base for many other technical indicators such as BollingerBands, MACD etc.

The two most popular types of moving averages are the **Simple Moving Average (SMA)** and the **Exponential Moving Average (EMA)**. SMA is nothing but just average of the prices of certain time period as shown above. SMA has a disadvantage as it gives equal importance to each day and no extra importance is given to recent prices. Hence to overcome this problem, EMA has been defined. It gives much greater importance to recent prices and lower importance to past prices. The weights that are used for different day’s prices fall exponentially.

For ease of understanding, we reproduce below a calculation from www.pandacash.com

Initially, for the EMA, an exponent needs to be calculated. To start, take the number of days’ EMA that you want to calculate and add one to the number of days that you’re considering (for example for a 200 day moving average, add one to get 201 as part of the calculation). We’ll call this Days+1.

Then, to get the Exponent, simply take the number 2 and divide it by Days+1. For example the Exponent for a 200 day moving average would be (2÷201) which equals 0.01

Once we’ve got the exponent, all we need now are two more bits of information to enable us to perform the full calculation. The first is yesterday’s Exponential Moving Average. We’ll assume we already know this as we would have calculated it “yesterday”. However, if you aren’t already aware of yesterday’s EMA, you can start by calculating the SMA for yesterday, and using this in place of the EMA for the first calculation (ie “today’s” calculation) of the EMA. Then tomorrow you can use the EMA you calculated today, and so on.

The second piece of information we need is today’s closing price. Let’s assume that we want to calculate today’s 200 day Exponential Moving Average for a share or stock which has a previous day’s EMA of Rs.120 and a current day’s closing price of Rs.136. The full calculation is as follows:

Today’s Exponential Moving Average = (current day’s closing price x Exponent) + (previous day’s EMA x (1-Exponent))

OR

Previous day’s EMA + (current day’s closing price – previous day’s EMA)*Exponent

So, using our example figures above, today’s 200 day EMA would be

(136 x 0.01) + (120 x (1- 0.01) which equals an EMA for today of Rs.120.16.

Examples of SMAs are given in Figure 1 for Tata Steel. Examples of EMAs are given in Figure 2 for the same company. Figure 3 gives the difference between the two MAs when plotted together.

Interaction between two moving averages provides very interesting insight into future movement of prices. That is, although MAs are based on past data, when we take 2 MAs side by side, it gives an estimate of future movement of prices. A larger period MA moves slowly as compared to a smaller period MA. The reason being that it carries with it greater baggage. The fastest moving MA is the daily data itself. Thus it can be said that a smaller period MA like a 10 day moving average (DMA) pulls the 100 DMA, the latter pulling the 200 DMA. Thus if a 10 DMA intersects the 100 DMA from above, it can be said that prices are set to fall. On the other hand, if the 10 DMA intersects the 100 DMA from below, we can say prices are set to rise. Thus, a shorter period DMA intersecting a longer period DMA from above is a bearish signal, whereas a shorter period DMA intersecting a longer period DMA from below is a bullish signal. This is clearly demonstrated in Figure 4.

Figure 1

200 DSMA (blue), 100 DSMA ( green), 10 DSMA (red)

Figure 2

200 DEMA (blue), 100 DEMA (green), 10 DEMA (red).

In ellipse 1 and 3, the 10 DMA has intersected the 100 DMA from above and hence subsequently the prices of ICICI Bank fell. Whereas in ellipse 2, the 10 DMA intersected the 100 DMA from below and prices of ICICI Bank increased. We can thus use this rule to estimate the future movement in prices. Note, however, an interesting phase given in AAA. Here the 10 DMA is falling, but the 100 DMA is rising. This is because the longer period DMA moves slower compared to the shorter period DMA. For the 100 DMA to fall, the 10 DMA has to fall for quite some time. That is why the points of intersection of the two carry meaning.

Figure 3

200 DSMA (blue) , 200 DEMA (red)

Figure 4