Moving Average Formula

Moving Averages (MA) are one of the most popular technical analysis tools. It is an indicator that shows the average value of a security's price over a period of time. It is used to eliminate short-term fluctuations in time series and to highlight long-term trends and cycles.

Moving averages may be : - 1. Simple
2. Weighted
3. Exponential

The two most popular types of moving averages are the Simple Moving Average (SMA) and the Exponential Moving Average (EMA).

Simple Averages -------
The most basic is the Simple Moving Averages which takes the Prices from the previous user defined number of periods, sums them up and divides the summation by the number of Periods.

Weighted Averages --------
In order to reduce the lag of the Simple Average, more weight can be assigned to Recent Data and less to Older Data. A weighted 10 day Moving Average assigns a weight of 1 to first Day, 2 to the Second Day and so forth until the most Current Day which is assigned a weight of 10. The 10 weighted values are added together and the sum is divided by the sum of the weights which in this case is 55.

Formula:- ( P1x1 + P2x2 + P3x3 + ……… P9x9 + P10x10) / 55,
Where P10 = Yesterday’s, i.e., the most current Day’s Price
And P1 is the first Day’s, 10 Days back.

Exponential Average -------

A weighted average is an arithmetic weighting whereas an Exponential Average is geometric weighting. As such, it gives much more weightage Current Data than the weighted average. So, it reacts faster to Price changes than the other averages. In today’s computerized environment putting or plotting Exponential Weighted Average gives us no pain.

Formula:- Exponential Moving Average = P today x K + EMA yesterday x ( 1 – K)
When, K = 2 ( N + 1 ), N is number of days in the EMA (e.g., in 13 EMA, n=13)
P today = Price today and EMA testrday = EMA of yesterday.
For computation of EMA value, you can start with the Simple Moving average at the beginning.

To compute 13 days EMA:-

1) You may compute the Simple Moving Average at first for the 13 days,
P1 + P2 + P3 + P4 + P5 + ………… P13 / 13
2) On the 14th day, Multiply Closing Price by K,
3) Multiply previous days M.A. ( as calculated in step 1) by ( 1 – K )
4) Add the two ( 2+ 3 ). The result will be the 13 EMA for the 14th day.
5) Now, the process will be continued and extended with the EMA as obtained.
6) Here, K will be = 2/13+1 = 2 /14 = 1/7
7) 1 – K will be = 1 - 1/7 = 6/7

Drawbacks of Moving Average~~~~~~~~
These are lagging indicators. They summarize Previous Data and plot it on Current Prices so an analyst using only Moving Averages will probably not be able to call Tops and Bottoms in the market. The change in Trend will be seen only after it has happened. So, these are Trend following indicators. They cannot tell us the Trend in advance.

Moving Averages are very useful in trending market. But if no Trend is present in the market, i.e. in sidewise phases, they fail and cannot provide the Analyst any good signal.