The Exponential Moving Average

Apurva Sheth
Last time I spoke to you about the dilemma that a trader goes through when it comes to choosing a time frame which keeps you with the trend and gives him quicker signals of a reversal as well. A longer moving average will be more reliable in terms of signaling a trend change but it will also be slow. While a shorter moving average will be more sensitive to price action but it may also give false signals. Ultimately, I would say that there isn't any magic formula to choose a time frame. It is more of a trial and error than anything else.

Before speaking about the dilemma of choosing the time frame I also spoke about the 2 basic type of moving averages simple moving average (SMA) and the exponential moving average (EMA). I explained SMA with a detailed example in that earlier article. Quite a good number of our readers wrote to me that they were enthusiastic about learning the EMA as well along with a detailed example. So I thought of talking about the same in today's newsletter.

Calculating the Exponential Moving Average

On the face of it, one may feel that calculating an exponential moving average is a difficult task but I assure you that if you follow these simple steps then it will look like a piece of cake.

Step 1: Calculate the simple moving average

Calculating an exponential moving average (EMA) starts from calculating a simple moving average for the same period. You already know that a simple moving average is a calculated by totaling the closing prices of a select period and dividing the sum by the number of observations.

Step 2: Calculate the weighting multiplier

A weighting multiplier is nothing but the percentage weightage that the most recent price will get. There is a pretty straightforward formula to calculate this.

Multiplier: (2 / (Time period chosen for EMA + 1))

For example if you want to calculate the weighting multiplier for a 10 Day EMA then you just have to do this. Multiplier = 2/ (10+1) = 0.1818

Step 3: Calculate the exponential moving average

The last and final step is to calculate the EMA. You will have to again feed all the data into this formula to arrive at the EMA value on a daily basis.

EMA: (Today's Close - Previous Day's EMA) x multiplier + Previous Day's EMA

Now let's have a look at the table below and apply these formulas to arrive at the EMA.

In the table below we begin by calculating the 10 Day SMA after we have 10 days of closing data. We get a value of 20.15 as SMA on 13th April. We use the same value as EMA for 13th April.

To calculate the EMA for next day we have to calculate the weighting multiplier which will remain constant across the series at 0.1818.

Now we have all the value to arrive at the EMA for 15th April. So let's plug these values in the formula.

EMA for 15th April: (21.15 - 20.15) * 0.1818 + 20.15 = 20.33

I hope that was simple enough to understand. Now you can use the same logic and build an EMA for the stock of your choice.

Calculation of Simple Moving Average
Date Price 10-day SMA Weighting
Multiplier
2/(10 + 1)
10-day EMA
27-Mar 17.55      
30-Mar 19.35      
31-Mar 19.00      
1-Apr 19.25      
6-Apr 20.05      
7-Apr 20.10      
8-Apr 20.85      
9-Apr 21.40      
10-Apr 21.30      
13-Apr 21.60 20.15   20.15
15-Apr 21.15 20.51 0.1818 20.33
16-Apr 20.55 20.63 0.1818 20.37
17-Apr 20.45 20.77 0.1818 20.38
20-Apr 19.65 20.81 0.1818 20.25
21-Apr 19.35 20.74 0.1818 20.09
22-Apr 18.95 20.63 0.1818 19.88
23-Apr 18.90 20.33 0.1818 19.70
24-Apr 18.30 20.02 0.1818 19.45
27-Apr 18.35 19.73 0.1818 19.25
28-Apr 18.00 19.37 0.1818 19.02
29-Apr 17.95 19.05 0.1818 18.83
30-Apr 17.80 18.77 0.1818 18.64
4-May 18.20 18.55 0.1818 18.56
5-May 18.25 18.41 0.1818 18.50
6-May 17.85 18.26 0.1818 18.38
7-May 17.70 18.13 0.1818 18.26
8-May 17.85 18.03 0.1818 18.19
11-May 18.00 18.00 0.1818 18.15
12-May 18.01 17.97 0.1818 18.14
Source: Profithunter

I am sure that most of you would have understood the concept and method of calculation, but if you still find it difficult to grasp then you need not worry. You do not have to manually calculate the EMA. Almost every technical charting software provides the EMA. So you just have to plug it into your charts with a click of a button or two. The real essence lies in the analysis.

I have illustrated the daily candlestick chart of the same data that I have shown above in this picture attached below. The red line is the 10 EMA while the green line is the 10 SMA.

Although one may find it difficult to observe it in raw data but you can see in the chart below that the red line or the 10 EMA is placed much closer to the price action than the green line or the 10 SMA.

Comparison between EMA & SMA
Source: Spider Software India

Having said this I would again like to reiterate that neither a specific type of moving average nor a specific time frame will work always. You will have to try what works for the time being and discard what doesn't. It's as simple as that.

Which moving average do you prefer simple or exponential? Share your views in the Club or share your comments here.

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8 Responses to "The Exponential Moving Average"
KK
14 May, 2015
EMA and SMA are simple to understand. However, if one takes shorter period than latest price movement will have material impact on moving averages. For example if SMA 50 is 100, and current price is 120, next day SMA 50 will change on higher side (though marginally) by including last day's higher price and excluding 1st day's price which we may be higher or lower. Impact is more shorter the period. For long term direction perspective I prefer SMA 200 which practically is one year data. For short term trading my preference is EMA 30.Like 
sakeer
14 May, 2015
What is error in calculating following way: (1st day price+2nd day price)/2, (result+3rd day price)/2, ( previous result+4th day price)/2 and so on..Like 
sakeer
14 May, 2015
Simple to understand EMA. But weighting multiplier here is same for all the days . why? . Like 
DrHA!
14 May, 2015
The concept of EMA has been explained in a lucid manner and looks we the investors should prefer EMA to SMA. Am i correct? Equitymaster.com should look into the possibility of making provision for EMAs also in their charts.Like 
msruthi
13 May, 2015
I use EMA ,not SMA, I prefer 50 day and 200 day EMA, for short time of 2 to 3 months is this trend comparison good or should I switch over to 10 and 50 day EMA, pl comment.Like 
Balakrishnan R
13 May, 2015
The calculation procedure of EMA has been very nicely explained in a simple and understandable way. I would which is the best software is available with SMA, EMA and other indicators and oscillators. Any software is available screening facility.Like 
Balakrishnan R
13 May, 2015
The calculation procedure of EMA has been very nicely explained in a simple and understandable way. I would which is the best software is available with SMA, EMA and other indicators and oscillators. Any software is available screening facility.Like 
John Murnaghan
13 May, 2015
As the EMA is nearer the price action and readily available on most software packages, it seems a no brainer to ask which one prefers; if I had to do the calculations then I'd opt for the SMA which is relatively simple to calculate. HAs there been any studies done on the difference between them for various time spans?Like 
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