Moving averages

Moving averages are popular technical indicators to capture trends (bullish / bearish / sideways). More specifically, the MACD (Moving Average Convergence Divergence) is a well known metric.

\[MACD = EMA_{ST} - EMA_{LT}\]

where:

• $EMA_{ST}$ is the short-term exponential moving average of the price –> moves fast

• $EMA_{LT}$ is the long-term exponential moving average of the price –> moves slow

As a reminder:

\[\bar x_t = \left\{ \begin{array}{ll} x_0 \text{ if } t=0 \\ \alpha x_t + (1-\alpha)\bar x_{t-1} \text{ otherwise} \end{array} \right.\]

See Time Series to have more details.

Advantages of the MACD over a simple moving average:

• It oscillates around 0, hence it can easily be combined with other indicators to find signals.

• It shows the difference between moving averages of 2 different delays, hence, intuitively, we can better spot timing changes (e.g. a strong reversal). In other words, it responds quicker to price changes.

In the below graph, the MACD (red) is also represented by the gray areas.

MACD crossover

The MACD crossover is a strategy that consists in using the MACD to detect buy and sell orders.

In addition to the MACD, the strategy involves another curve: the signal line.

\[Signal~line = EMA_{9}(MACD)\]

The signal line is thus a lagged version of the MACD. When the MACD crosses the signal and end above it, it is a good indication to buy.

Note: it is highly recommended to combine this indicator with a long term moving average (e.g. $EMA_{200}$).