The **Moving Average Convergence Divergence (MACD)** charting study is one of the most popular tools used in technical analysis.

The MACD is an oscillating **measurement** **of momentum** of the price movement by a given security.

## There are 3 parts of the MACD indicator

**The MACD study appears as two lines and a histogram.**

** MACD Line**: each point in time on the line is calculated by taking the 12-period Exponential Moving Average (EMA) and subtracting the 26-period Exponential Moving Average (EMA). This line gives us an idea about relative price momentum changes with respect to time (IE. time being 12-period and 26-period EMA values)

**MACD Signal Line**: values of this line are calculated by taking the MACD Line that we just made, and finding the 9-period EMA value of it. This line gives us a more stable,

__averaged view of the relationship between the 12 and 26 period EMA__s.

**MACD Histogram**: values are calculated by taking the MACD Line value and subtracting the MACD Signal Line value. The result is a value which shows us the degree of abnormal recent price movement relative to time.

If you know anything about calculus, you could think of this as a second-degree derivative of the relative price movement. The Signal Line could be thought of as the first derivative. Though, neither are actually derivates. These are only the differences in price averages relative to time.

## Visualizing the MACD Line:

As we can see in the image above, I applied two studies to the pricing chart: a 12-Period Exponential Moving Average, and a 26-Period Exponential Moving Average.

Underneath the price chart is a MACD chart. For any point in time, the MACD Line is calculated by subtracting the 12 and 26 period EMAs. The result is either a positive number (where the 12-period EMA is higher than the 26), a negative number (where the 26-period EMA is higher than the 12), or 0 (where the 12 and 26 period EMA are equal at that point in time.

## Visualizing the MACD Signal Line:

We already saw how the MACD Line is calculated, simply find the difference between the 12 and 26 period EMA from the price chart. Now we are concerned with the MACD Signal Line.

The Signal Line is pretty straight forward. It’s calculated by taking all of the MACD Line values and applying a 9-Period Exponential Moving Average to it.

With the **MACD Signal Line**, you now have an **average difference** of the 12 and 26 period EMA for any point in time. Because we are using exponential moving averages, recent price values have more influence on the EMA value than older values. This is illustrated in the image above. The MACD Line was more responsive to the price drop on 7/15 which made it drop below the Signal Line.

## Visualizing the MACD Histogram:

At any given point in time, the value of the histogram is the difference of the MACD Line and the MACD Signal Line.

To understand the meaning of the histogram you have to understand each component:

The MACD Line value represents the difference of the 12 and 26 period EMA, at a specified point in time.

The MACD Signal Line shows the [exponential] moving average value of MACD Line .

So the histogram shows you how much the current diffence of the 12 and 26 EMAs are, from the average difference they usually have. In simplier terms: how much the MACD differs from the usual value of MACD.

## Entry/Exit Signals from MACD Analysis

- 1. Signal Line Crossovers
- 2. Zero Line Crossover
- 3. Divergences/Convergences

## (1.) The Signal Line Crossover

When the MACD Line crosses the MACD Signal Line it represents a recent, relative, change in momentum.

Because the MACD Signal Line is a 9-Day EMA of the MACD Line it is less responsive to recent changes in price movement than the MACD Line. For example, when the MACD Line becomes a higher value than the Signal Line, it shows that the prices are higher in the short term now, than they usually are.

This can be seen as a buy signal because price is increasing at a faster rate than normal.

Conversely, when the MACD Line becomes a lower value than that of the Signal Line, the area following that intersection/crossover shows us that the price is __increasing at a slower rate __in the short term compared to the long term, __than it does on average__. This is seen as a possible sell signal.

## (2. ) The Zero-Line Crossover

With Zero-Line Crossovers we are only concerned with the MACD Line.

Remember, the MACD Line is computed by taking the 12-period EMA and subtracting the 26-period EMA from it.

The Zero-Line Crossover occurs when when the EMA value of the 12 period falls below or increases above the EMA value of the 26 period moving average.

When we see the MACD line cross the Zero-Line, from negative to positive, we know that the exponential moving average measured over 12-periods (at any given point in time) is now higher than the exponential moving average measured over 26-periods. Because the 26-period EMA is less responsive to recent price changes, when the 12-period EMA crosses over the value of the 26 that means the price is experiencing recent positive price changes.

Conversly, the opposite is also true.

## Divergences/convergences

A MACD Divergence occurs when the price and MACD values are not acting in accordance. This happens in two different ways and are typically described as Bearish Divergences or Bullish Divergences.

The image above represents a Bearish Divergence. This means that prices are hitting higher highs, while MACD is hitting lower highs. This means that although the price is increasing, it is doing so with less upward price momentum than it previously was. This is seen as Bearish because as the momentum slows, the 12-period EMA approaches becoming equal to the 26-period EMA and then lower than it–meaning that the recent upward momentum is halting.

Bullish Divergences can be identified when prices are hitting lower lowers, while the MACD is hitting higher lows. This implies that while price movement is headed downward, it is doing-so with less downward momentum than it previously was. Ideally, the 12-period EMA value will approach the 26-period EMA and surpass it, meaning that price movement is headed higher in the short-term, relative to time.