Quantitative Analysis · Data Science · Machine Learning

# Moving Average Convergence Divergence – MACD

## What is the MACD?

The Moving Average Convergence Divergence (MACD) is a technical indicator that is used to identify trend changes in the price of a financial instrument, such as a stock, commodity, or currency pair. It is based on the difference between two exponential moving averages (EMAs) of the price, which are lagging indicators that smooth out price action and help to identify trends.

The MACD is calculated by subtracting the 26-day EMA from the 12-day EMA. The resulting line is then plotted on a chart along with a signal line, which is a 9-day EMA of the MACD line. The MACD line is plotted in relation to the zero line, which represents the point where the two EMAs are equal.

Traders often use the MACD to identify potential buy and sell signals. When the MACD line crosses above the signal line, it is typically interpreted as a buy signal, indicating that the trend may be shifting to the upside. Conversely, when the MACD line crosses below the signal line, it is often interpreted as a sell signal, indicating that the trend may be shifting to the downside.

In addition to its use as a trend indicator, the MACD can also be used to identify momentum and overbought or oversold conditions in the market. However, it is important to note that the MACD is a lagging indicator and may not provide timely signals in all market conditions. As with any technical indicator, it is important to use the MACD in conjunction with other analysis tools and techniques to make informed trading decisions.

The formula for the MACD is as follows:

### MACD = 12-day EMA – 26-day EMA

To calculate the MACD, you will need to first calculate the 12-day and 26-day EMAs of the security’s price. The formula for calculating an exponential moving average is:

### EMA = (Price * K) + (Previous EMA * (1 – K))

Where “Price” is the current price of the security, “K” is a smoothing factor, and “Previous EMA” is the previous period’s exponential moving average. The smoothing factor is calculated as follows:

### K = 2 / (N + 1)

Where “N” is the number of periods used to calculate the moving average (in this case, 12 or 26).

Once you have calculated the 12-day and 26-day EMAs, you can then subtract the 26-day EMA from the 12-day EMA to get the MACD.

It’s important to note that the MACD is typically displayed with a histogram, which shows the difference between the MACD line and a signal line (usually a 9-day EMA of the MACD line). The MACD histogram can help to visualize the momentum of the security’s price movement, as it reflects the distance between the MACD line and the signal line.

## How can the MACD be used in an algorithmic trading strategy?

The MACD can be used as a component of an algorithmic trading strategy in a number of ways. Some common techniques include:

1. Crossover: One way to use the MACD in an algorithmic trading strategy is to look for a crossover between the MACD line and the signal line. A buy signal is generated when the MACD line crosses above the signal line, while a sell signal is generated when the MACD line crosses below the signal line.
2. Divergence: Another way to use the MACD in an algorithmic trading strategy is to look for divergences between the MACD line and the security’s price. A bullish divergence occurs when the MACD line is making higher lows while the security’s price is making lower lows, indicating that the security may be about to experience upward momentum. A bearish divergence occurs when the MACD line is making lower highs while the security’s price is making higher highs, indicating that the security may be about to experience downward momentum.
3. Trend confirmation: The MACD can also be used to confirm trends in the security’s price. If the MACD is consistently above zero and rising, it can be taken as a sign that the security is in an uptrend. Conversely, if the MACD is consistently below zero and falling, it can be taken as a sign that the security is in a downtrend.

It’s important to note that the MACD should be used in conjunction with other technical analysis tools and fundamental analysis in order to provide a well-rounded view of a security’s market conditions.