# Moving averages – the fast and the slow

While searching for promising forex strategies on the web, for sure you have encountered trading systems that rely on the crossover of a faster and a slower moving average. In this post I explain how one moving average can actually be faster or slower than another.

## Moving averages

Moving averages are among the most widely used indicators in foreign exchange trading. A moving average MA(x) is a single value, the average or mean, that is computed from a given number x of historical prices. This version of a moving averages is also often called a simple moving average or SMA because it is based on the simple arithmetic mean of prices.

MA(1) is actually no average at all, it is just the current price. MA(2) is the average of the current and the second-but-last price, MA(3) the average of the last three prices, MA(4)… you get it. By recalculating each time a new price gets available (every hour, every minute, every tick – depending on the timeframe you choose) the moving average actually gets moving.

## The influence of x

The x in MA(x) gives the amount of historical prices to include into the calculation. The larger x is, the more values are averaged and the smoother a plot of the moving average will be. But a larger x also means that older prices are included in the calculation of the average. This makes the moving average lag behind the current price. The larger x the larger the lag, the slower the moving average. The smaller x the smaller the lag, the faster the moving average.

## How can moving averages be fast or slow?

Consider the following illustrating example, where the prices (y-axis) moves from one level to another one over time (x-axis). The original price is plotted by the blue line. It first is constant 1.20, then increases gradually to 1.30. The other curves show different moving averages. Notice that you need as many values as the x in MA(x) to actually start the calculation, this is why the curves start at different points in time. The MA(1) (original price in blue graph) is always up to date, it is actually as fast as it can get. MA(5) only reaches the new higher level some time after the real price did, MA(10) is even slower, etc. Thus, the farther we have to look into the past for the calculation of the moving average, the slower it adapts to changes in the level of price. While MA(1) is the fastest of the graphed moving averages, MA(20) is the slowest. A fast moving average is more sensitive to changes in price than a slow one.

## Some real data

The graph below contains the hourly opening prices of EUR/USD for roughly the first half of October 2014. The blue line again represents the original prices. Two moving averages are additionally drawn, one faster than the other. MA(20) can be first calculated after 20 hours. It already lags behind the original prices, especially visible in the sheer drop after about a third of the graph. MA(40) starts after 40 hours. As the slower of the the two moving averages it lags even further behind. The slow or fast property is more often used in conjunction with the stochastics indicator. Read for example Casey Murphy’s article What is the difference between fast and slow stochastics in technical analysis? on Investopedia.

The graphs in this post have been created with the great R software environment for statistical computing and graphics. R is free! Check it out on http://www.r-project.org.