Crossover Trading Systems

OVERVIEW
Crossover trading systems consist of various indicators and oscillators and are unique in the technical analysis of security prices. Rather than predicting future numeric values, they signal a particular market action to execute, such as (1) initiate a long position, (2) initiate a short position, (3) liquidate a long position, (4) liquidate a short position, (5) reverse a long position equivalent to (3) and (2), or reverse a short position equivalent to (4) and (1).

MOVING AVERAGES
Moving averages (MAs) are an important instrument used to study trends and generate market entry and exit signals. An MA is the arithmetic mean of the closing prices over a given period. The longer the period studied, the weaker is the magnitude of the moving-average curve. The number of closes in the given period is called the moving-average index. Market signals are generated by calculating the residual-difference value:

Residual = close(x)−MA(x)

1 Daily Close with Five-day Moving Average.

In the chart shown in Figure 1, the curve with higher peaks and lower valleys is the daily close, whereas the smoother curve is a five-day moving average of the closes.

In the chart shown in Figure 2, called a moving-average convergence/divergence (MACD) histogram, the following signals are triggered:

1. When the residual difference rises above zero, a buy signal is generated.
2. When the residual difference falls below zero, a sell signal is generated.

A significant refinement to this residual-difference method, called moving-average convergence/divergence (MACD), involves the use of two moving averages. When the MA with the shorter MA index, called the oscillating MA index, crosses above the MA with the longer MA index, called the basis MA index, a sell signal is generated.

MACDresidual = basisMA(x) oscillatingMA(x)

2 Residual Difference.

The reliability of the MACD method depends ultimately on the MA indices chosen. These two indices can be optimized by a computer program that performs a brute-force search for the most profitable parameters on the most recent daily closes. However, as market conditions change in the underlying time series, the indices must be adjusted accordingly.

It should be noted that some traders prefer to use exponentially smoothed moving averages rather than arithmetically smoothed moving averages, although this is usually a subjective decision on the part of the investor. In addition, we note that the MACD method is credited to Gerald Appel in the early 1960s in his book, Technical Analysis: Power Tools for Active Investors (Prentice-Hall, 1961).

RELATIVE STRENGTH INDEX
The relative strength index (RSI) was introduced by J. Welles Wilder in the June 1978 issue of Commodities (now known as Futures) magazine and later in his book, New Concepts in Technical Trading (Trend Research, 1978). The index is designed to follow the momentum of price as an oscillator that ranges between 0 and 100. The index tracks recent price to itself and therefore is a measure of velocity.

3 Relative strength Index

RSI is a front-weighted momentum indicator that measures a commodity’s price relative to its past performance, and therefore, it gives a better velocity reading than other indicators. RSI is less affected by sharp rises or drops in a commodity’s price performance. Thus it filters out some of the white noise in a security’s trading activity (Figure 3). The RSI formula is as follows:

where
U
= average of up closes
D =
average of down closes

For a nine-day RSI calculation, the following steps are involved:

1. Add the closing values for the up days, and divide this total by 9.
2. Add the closing values for the down days, and divide this total by 9.
3. Divide the up-day average by the down-day average. Store this as the RS factor in the formula.
4. Add 1 to the RS factor.
5. Divide 100 by the number arrived at in step 4.
6. Subtract the number arrived at in step 5 from 100.

Repeat steps 1 through 6 for day number 10. Drop day number 1 from the calculation. Wilder originally proposed a 14-day RSI and later a 9- and a 25- day period. In modern times, this index can be optimized by a brute-force software program.

RSI values range from 1 to 100. Traditionally, buy signals are triggered at 30, and sell signals are triggered at 70. However, many analysts are now using 20 for buy signals and 80 for sell signals. RSI
lends itself to support and resistance studies such as trend-line penetration and price patterns. Overbought and oversold conditions are suppose to be an asset in interpreting the RSI, but as you can
see, overbought and oversold conditions do poorly in a strong trending environment.

The RSI shows whether a currency is overbought or oversold. Overbought indicates an upward market trend because the financial operators are buying a currency in the hope of further rate increases. Sooner or later, saturation will occur because the financial operators have already created a long position. They show restraint in making additional purchases and try to make a profit. The profits made can very quickly lead to a change in the trend or at least a consolidation.

Oversold indicates that the market is showing downward trend conditions because the operators are selling a currency in the hope of further rate falls. Over time, saturation will occur because the financial operators have created short positions. They then limit their sales and try to compensate for the short positions with profits. This can rapidly lead to a change in the trend.

STOCHASTIC OSCILLATORS
In a strictly mathematical sense, the term stochastic signifies a process involving a randomly determined sequence of observations, each of which is considered as a sample of one element from a probability distribution. In technical analysis, the term has evolved to signify an indicator that compares the current close with the highest high and the lowest low over a predetermined number of days.

The stochastic oscillator was developed by George C. Lane in the late 1950s. It is used most commonly to identify overbought and oversold conditions, as well as divergence between the oscillator and the price. The original stochastic plot consisted of two lines. The curve with higher peaks and lower valleys is referred to as %K, and the other (more smoothed) line is called %D (Figure 4). The stochastic oscillator compares where a security’s price closed relative to its price range over a given time period. The basic formula is as follows:

%K = 100(C − L)/(H − L)

4 Stochastic Oscillators.

where
C
= current close
H
= highest high over given period of time
L =
lowest low over same period of time

The full stochastic oscillator has four variables:

1. %K periods. This is the number of time periods used in the stochastic calculation.
2. %K slowing periods. This value controls the internal smoothing of %K. A value of 1 is considered a fast stochastic; a value of 3 is considered a slow stochastic.
3. %D periods. This is the number of time periods used when calculating a moving average of %K. The moving average is called %D and usually is displayed as a dotted line on top of %K.
4. %D method. The smoothing method (i.e., exponential, simple, time series, triangular, variable, or weighted) that is used to calculate %D.

To calculate a 10-day %K, first find the security’s highest high and lowest low over the last 10 days. As an example, let’s assume that during the last 10 days the highest high was 46, and the lowest low was 38, a range of 8 points. If today’s closing price was 41, %K would be calculated as:

100 * (4138)/(4638)
37.5%

The 37.5 percent in this example shows that today’s close was at the level of 37.5 percent relative to the security’s trading range over the last 10 days. If today’s close was 42, the stochastic oscillator would be 50 percent. This would mean that the security closed today at 50 percent, or the midpoint, of its 10-day trading range. This example used a %K slowing period of one day (no slowing). If you use a value greater than one, you average the highest high and the lowest low over the number of %K slowing periods before performing the division.

A moving average of %K then is calculated using the number of time periods specified in the %D periods. This moving average is called %D.

The stochastic oscillator always ranges between 0 and 100 percent. A reading of 0 percent shows that the security’s close was the lowest price that the security has traded during the preceding x time periods. A reading of 100 percent shows that the security’s close was the highest price that the security has traded during the preceding x time periods.

Popular interpretations of the stochastic oscillator include:

• Buy when the oscillator (either %K or %D) falls below a specific level (e.g., 20) and then rises above that level. Sell when the oscillator rises above a specific level (e.g., 80) and then falls below that level.
• Buy when the %K line rises above the %D line, and sell when the %K line falls below the %D line.

Look for divergences, for example, where prices are making a series of new highs and the stochastic oscillator is failing to surpass its previous highs. Ways to use the stochastic oscillator as a confirming signal generator include:

• A buy is indicated when the %K or %D falls below a specified level (typically 30) and then rises above that level. A sell is indicated when the line rises above a specified level (typically 70) and then goes below that level.
• A buy is indicated when the %K line rises above the %D line. A sell is indicated when the %K line falls below the %D line.

When prices are making new highs and the stochastic does not exceed its previous highs, a divergence occurs, often indicating a change in the current trend.

The buy/sell signals are triggered when the %K line crosses the %D line after the %D line has changed direction. At the bottom, the buy signal is generated. At the top, the sell signal is generated.

BOLLINGER BANDS
This indicator was developed by John Bollinger and is explained in detail in his book, Bollinger on Bollinger Bands (McGraw-Hill, 2001). The technique involves overlaying three bands (lines) on top of an OHLC bar chart or a candlestick chart of the underlying security.

5 Bollinger Bands.

The center line is a simple arithmetic moving average of the daily closes using a trader-selected moving-average index. The upper and lowers bands are the running standard deviation above and below the central moving average. Since the standard deviation is a measure of volatility, the bands are self-adjusting: widening during volatile markets and contracting during calmer periods. Bollinger recommended 10 days for short-term trading, 20 days for intermediate-term trading, and 50 days for longer term trading. These values typically apply to stocks and bonds; thus shorter time periods will be preferred by commodity and currency traders (Figure 5).

Bollinger Bands require two trader-selected input variables: the number of days in the moving-average index and the number of standard deviations to plot above and below the moving average. Over 95 percent of all the daily closes will fall with three standard deviations of the mean of the time series. Typical values for the second parameter range from 1.5 to 2.5 standard deviations.

As with moving-average envelopes, the basic interpretation of Bollinger Bands is that prices tend to stay within the upper and lower bands. The distinctive characteristic of Bollinger Bands is that the spacing between the bands varies based on the volatility of the prices. During periods of extreme price changes (i.e., high volatility), the bands widen to become more forgiving. During periods of stagnant pricing (i.e., low volatility), the bands narrow to contain prices.

Bollinger notes the following characteristics of Bollinger Bands:

• Sharp price changes tend to occur after the bands tighten as volatility lessens.
• When prices move outside the bands, a continuation of the current trend is implied.
• Bottoms and tops made outside the bands followed by bottoms and tops made inside the bands call for reversals in the trend.
• A move that originates at one band tends to go all the way to the other band. This observation is useful when projecting price targets.

Bollinger Bands generally do not trigger buy and sell signals alone. They should be used with another indicator, usually the RSI. This is so because when the price touches one of the bands, it could indicate one of two things: a continuation of the trend or a reaction the other way. Thus Bollinger Bands used by themselves do not provide all of what technicians need to know, which is when to buy and sell. MACD can be used in conjunction with Bollinger Bands and the RSI.

OTHER CROSSOVER SYSTEMS
The techniques and methods just listed in no way represent all the crossover trading systems available to technical analysts. Numerous range and momentum oscillators also have been devised as crossover triggers, as well as several volume oscillators.