# MACD - Moving Average Convergence Divergence

Updated: 2024-03-12

The Moving Average Convergence Divergence (MACD) is a versatile trading indicator used in various forms of trading, including high-frequency trading (HFT).

MACD is a trend-following momentum indicator that shows the relationship between two moving averages of a security’s price.

## Calculating

### Formula

The MACD is calculated by subtracting the 26-period Exponential Moving Average (EMA) from the 12-period EMA. A 9-day EMA of the MACD, called the “signal line”, is then plotted on top of the MACD, functioning as a trigger for buy and sell signals.

Here’s the formula for the MACD:

MACD = 12-Period EMA − 26-Period EMA


To calculate the signal line, you take the 9-period EMA of the MACD.

Signal Line = 9-Period EMA of MACD


Example:

Since MACD requires 26 periods to start, we’ll calculate from the 26th minute:

MinuteOpenHighLowCloseEMA12EMA26EMA9 (Signal)MACD
1$10.0$11.0$9.5$10.0----
2$10.1$12.1$10.0$12.0----
3$12.2$15.2$12.0$15.0----
4$15.1$15.1$13.9$14.0----
5$14.1$16.1$14.0$16.0----
6$16.1$16.1$14.9$15.0----
7$15.1$17.1$15.0$17.0----
8$17.1$17.1$15.9$16.0----
9$16.1$18.1$16.0$18.0--Starts here-
10$18.1$18.1$16.9$17.0---
11$17.1$19.1$17.0$19.0---
12$19.1$19.1$17.9$18.0Starts here--
13$18.1$20.1$18.0$20.0--
14$20.1$21.1$20.0$21.0--
15$21.1$21.1$19.9$20.0--
16$20.1$22.1$20.0$21.0--
17$21.1$23.1$21.0$22.0--
18$22.1$24.1$22.0$23.0--
19$23.1$25.1$23.0$24.0--
20$24.1$26.1$24.0$25.0--
21$25.1$27.1$25.0$26.0--
22$26.1$28.1$26.0$27.0--
23$27.1$29.1$27.0$28.0--
24$28.1$30.1$28.0$29.0--
25$29.1$31.1$29.0$30.0--
26$30.1$32.1$30.0$31.0Starts hereStarts here
27$31.1$33.1$31.0$32.0
28$32.1$34.1$32.0$33.0
29$33.1$35.1$33.0$34.0
30$34.1$36.1$34.0$35.0

In python it can be calculated in the following way:

import pandas as pd

# Assuming 'df' is your DataFrame and 'Close' is the column with closing prices
df['MACD'] = df['EMA12'] - df['EMA26']


## Pros and Cons

Pros:

• Trend Identification: MACD can identify the start of a trend, providing good entry points.
• Signal Line Crossovers: The MACD’s signal line can provide clear buy and sell signals.

Cons:

• False Signals: Like any indicator, MACD can produce false signals, particularly in volatile markets.
• Lag: MACD can sometimes lag behind the market because it’s a trend-following indicator.
• It may not work well in ranging (non-trending) markets, where price movements can be random.

## Example of signals

True Positive:

A true positive in MACD is a situation where the MACD line crosses above the signal line and the price goes up, indicating a strong bullish signal, or the MACD line crosses below the signal line and the price goes down, indicating a strong bearish signal.

These signals can help traders decide when to enter or exit trades.

False Positive:

A false positive in MACD is typically a situation where the MACD line crosses above the signal line (potential buy signal), but the price does not go up, or the MACD line crosses below the signal line (potential sell signal), but the price does not go down. It’s important to confirm MACD signals with other indicators or patterns to avoid false positives.