Sometimes, it’s hard to see where the market is headed. It drives higher, only to fall back. Price might careen wildly sideways, ultimately ending several points higher or lower. Amid such madness, while markets churn and spike, retreat and recover, it’s difficult to determine the bias behind the moves. Is it bullish or bearish? And to what degree? The goal is to smooth out the surges and corrections, to eliminate the noise. The answer, for many traders, is a moving average of price.

A moving average is probably the most popular technical indicator used by traders. In its simplest rendition, it is the mathematical mean of a series of price points. The “moving” part of the name refers to how the newest market price replaces the oldest price as new prices occur. The selection of prices used to calculate the average shifts forward with time.

The moving average is usually plotted on the same chart with price. While price is generally displayed as an open-high-low-close chart, the moving average will be a line. Some traders display the last point of the average in the middle of the time frame used in calculating the average, recognizing the condition that the average represents all points in the range equally, but most find it more relevant to an active trading approach to align the last point of the moving average with the most recent price point (see “Smoothed moves”).

The number of prices used to calculate the moving average is called the average’s length. The length is the most important attribute of a moving average because it will have the biggest effect on how sensitive the moving average is to price changes. Longer moving averages are less responsive to price changes. Shorter moving averages are more responsive to price changes. The benefit of a longer average is it will be less affected by short-term market noise. The benefit of a shorter average is it will reflect a trend change much sooner — which, of course, is only a benefit if the trend change persists.

The lengths used for moving averages vary as much as individual trading styles. It’s not uncommon for commodity traders to employ lengths anywhere between five and 50 periods. Stock traders tend to prefer longer length averages, with the 50- and 200-day averages popular.

Another choice that needs to be made with each average is which price to use in the calculation, such as the open, the high, the low, the close or some other price, such as the mid-point of the day. The most popular input price is, by far, the close.

AVERAGE CALCULATIONS

Although all methods have the same goal of smoothing price data, there are different ways to calculate a moving average.

The most common is the simple moving average (SMA). A SMA is determined by adding up the values in the series and dividing the sum by the number of values in the series. When a new price occurs, it is added to the series and the oldest price is dropped. The SMA treats all prices the same. That is, the oldest price in the calculation is just as relevant to the moving average value as the most-recent price.

Some traders believe that more recent prices are more important than older prices. For them, a weighted moving average (WMA) makes more sense. A WMA can stress some values over others, typically giving more recent prices greater weight in the calculation. The formula for a five-period WMA, where N = weight and P = price is:

(P 1N1 + P 2N2 + P 3N3 + P 4N4 + P 5N5) / (N1 + N2 + N3 + N4 + N5) = WMA

Another moving average that gives more weight to recent prices is an exponential moving average (EMA). Technically, all past prices in the series play some role in the current EMA value. The “length,” or sensitivity, of the average can be set to closely resemble shorter- or longer-term SMAs, but the EMA will always, in some small way, reflect all past price action.

The EMA accomplishes this feat by using the EMA value for the most recent period as well as the current period’s relevant price in its calculation. All past price activity is accounted for because the last period’s exponential moving average was affected by the one before it, which was affected by the one before it, and so on.

The sensitively of the EMA is determined by a smoothing constant. To calculate the smoothing constant, where Z is the number of SMA periods intended to replicate, use this formula:

2 / (Z + 1) = smoothing constant

Next, insert the smoothing constant into the formula for calculating the EMA. It is, where P = price, A = smoothing constant, and EMAt - 1 = the last period’s exponential moving average:

EMAt - 1 + (A * (P - EMAt - 1) = EMA

In “Dueling averages”, both the SMA and the EMA based on an input length of 10 experience similar shifts in direction, but the EMA is much less sensitive to small price changes. This may allow the EMA to use a shorter theoretical length input before it becomes too erratic.

TRADING WITH AVERAGES

The most common interpretation of a moving average is that a break through the moving average line by price marks the beginning of a trend. If price breaks above the moving average, that’s a buy signal. If price breaks below the moving average, that’s a sell signal. Unfortunately, trading isn’t always that simple. Clearly, there are periods that experience many moving-average breaks in succession. This is a matter of course during sideways markets. Trading on these short-term breaks will generally result in a series of small losses that slowly, but consistently, drag down your account equity.

One obvious solution to this problem is to use longer-term moving averages. However, this also has the unwanted effect of delaying signals, as price takes longer to reach, and break, the longer-term moving average.

Another concept marries two moving averages of different lengths on the same screen. Traders will then trade based on the crossovers of these moving averages (see “Marking the trend”). That is, when the shorter-term averages breaks from below the longer-term average to above it, a long position may be considered. When the shorter-term average breaks below the longer-term average, a short position is looked at. As for the lengths of the long and short averages – and, for that matter, whether to use the open, high, low or close – that’s subjective and depends on the trader’s time horizon and risk tolerance.

MODIFICATIONS

Another common modification is to shift a moving average forward (generally half the number of periods used). This moves the average further from actual price activity and also protects against false crossovers at the expense of sensitivity. Another modification is to use two averages, one each of the high and low, perhaps offset from price action by yet some other factor. This would create an envelope or channel that price may, perhaps, trade within.

Moving averages are some of the most popular technical indicators for good reason. One, moving averages are simple and familiar; most understand averages and what they purport to accomplish long before they consider trading. Two, moving averages are flexible; without making the indicator much more complicated, if at all, moving averages can be adjusted to reflect highs, lows, longer periods or shorter ones.

As such, moving averages often find themselves at the center of far more complex technical tools. This makes them one of the most important tools to study and practice as you build a more imposing technical arsenal.