Mathematical Trading Methods (Indicators)

The mathematical trading methods provide a more objective view of price activity. In addition, these methods tend to provide signals prior to their occurrence on the currency charts. The tools of the mathematical methods are moving averages and oscillators.

Moving Averages

A moving average is an average of a predetermined number of prices over a number of days, divided by the number of entries. The higher the number of days in the average, the smoother the line is. A moving average makes it easier to visualize currency activity without daily statistical noise. It is a common tool in technical analysis and is used either by itself or as an oscillator.

As one can see from Figure 5.35., a moving average has a smoother line than the underlying currency. The daily closing price is commonly included in the moving averages. The average may also be based on the midrange level or on a daily average of the high, low, and closing prices.

Figure 5.35. Examples of three simple moving averages—5-day (white), 20-day (red) and 60-day (green)

It is important to observe that the moving average is a follower rather than a leader. Its signals occur after the new movement has started, not before.

There are three types of moving averages:

As described, the simple moving average or arithmetic mean is the average of a predetermined number of prices over a number of days, divided by the number of entries.

Traders have the option of using a linearly weighted moving average (See Figure 5.36.). This type of average assigns more weight to the more recent closings. This is achieved by multiplying the last day's price by one, and each closer day by an increasing consecutive number. In our previous example, the fourth day's price is multiplied by 1, the third by 2, the second by 3, and the last one by 4; then the fourth day's price is deducted. The new sum is divided by 9, which is the sum of its multipliers

Figure 5.36. Example of a 20-day simple moving average (red) as compared to a 20-day weighted moving average (white)

The most sophisticated moving average available is the exponentially smoothed moving average. (See Figure 5.37.) In addition to assigning different weights to the previous prices, the exponentially smoothed moving average also takes into account the previous price information of the underlying currency.

Figure 5.37. Example of a 20-day simple moving average (red) as compared to a 20-day exponential moving average (white)

Trading Signals of Moving Averages

Single moving averages are frequently used as price and time filters. As a price filter, a short-term moving average has to be cleared by the currency closing price, the entire daily range, or a certain percentage (chosen at the discretion of the trader).

The envelope model (See Figure 5.38.) serves as a price filter. It consists of a short-term (perhaps 5-day) closing price based moving average to which a small percentage (2 percent is suggested for foreign currencies.) are added and substracted. The two winding parallel lines above and below the moving average will create a band bordering most price fluctuations. When the upper band is penetrated, a selling signal occurs. When the lower band is penetrated, a buying signal occurs. Because the signals generated by the envelope model are very short-term and they occur many times against the ongoing direction of the market, speed of execution is paramount. The high-low band is set up the same way, except that the moving average is based on the high and low prices. As a time filter, a short number of days may be used to avoid any false signals.

Figure 5.38. An envelope model define the edges of the band. A close above the upper band sends a buying signal and one below the lower band gives a selling signal

Usually traders choose a number of averages to use with a currency. A suggested number is three, as more signals may be available. It may be helpful to use intervals that better encompass short-term, medium-term, and long-term periods, to arrive at a more complex set of signals. Some of the more popular periods are 4, 9, and 18 days; 5, 20, and 60 days; and 7, 21, and 90 days. Unless you focus on a specific combination of moving averages (for instance, 4, 9, and 18 days), the exact number of days for each of the averages is less important, as long as they are spaced far enough apart from each other to avoid insignificant signals.

A buying signal on a two-moving average combination occurs when the shorter term of two consecutive averages intersects the longer one upward. A selling signal occurs when the reverse happens, and the longer of two consecutive averages intersects the shorter one downward. (See Figure 5.39.)

Oscillators