**Moving Average (MA)**

A moving average , as the name suggests means, is an average. It is an indicator which is frequently used in technical analysis and shows the average value of a security’s price over a certain period. As the security’s price changes, its average price also moves up or down. Moving averages thus simply measure the average price over a specific time frame. MAs are trend following indicators and are generally used for measuring momentum – and for identification and / or confirmation of a trend. A moving average also helps define possible areas of support and resistance. It is a trend following or lagging indicator as it is based on past prices. Finally, it is also a barometer of crowd behavior and defines the direction of crowd movement and current trend.

The longer the time period for the moving average, the greater the lag. Thus, a 200-day moving average will lag much more degree than a 20-day moving average because it contains prices from the past 200 days. 50-day and 200-day moving averages for stocks are widely used by investors and traders and are considered as important trading signals.

A rising moving average indicates that the security is in an upward trend, while a decreasing moving average indicates that it is in a downward trend. Likewise, upside momentum is confirmed with a bullish crossover, which occurs when a short-term moving average crosses above a long-term moving average. On the other hand, downside momentum is confirmed with a bearish crossover, which occurs when a short-term moving average crosses below a long-term moving average. Moving averages come in various forms but their underlying purpose remains the same, to help technical traders track the trends of financial assets by smoothing out the day to day price fluctuations, or noise.

The two most popular types of moving averages are :

- Simple Moving Average (SMA),
- Exponential Moving Average (EMA).

**Simple Moving Average (SMA)**

SMA = (A_{1}+A_{2}+…..+A_{n})/n

where:

A=Average in period n

n=Number of time periods

**Exponential Moving Average (EMA)**

The exponential moving average is a type of moving average that gives more weight to the current value in an attempt to make it more liable to new data. To calculate the EMA, you must first calculate the simple moving average (SMA) at a particular time. Next, you need to calculate the multiplier for the weight of the EMA (referred to as the “performance”), which generally follows the standard: [2 / (time-selected time + 1)]. Thus, for a 20-day moving average, the product would be [2 / (20 + 1)] = 0.0952. You then use the relationships associated with the previous EMA to arrive at the current value. The EMA thus gives more weight to the previous rates, while the SMA gives the same weight to each price.

EMA_{t} = [V_{t}×(s/1+d)]+EMA_{y}×[1−(s/1+d)]

where:

EMA_{t} = EMA today

V_{t }= Value today

EMA_{y }= EMA yesterday

s = Smoothing

d = Number of days