Posted by: Livy | February 12, 2009

Mathematical Indicators

There are a number of mathematical indicators that are available for use. Some might tell you that a particular one is the secret to making millions over night, but the truth is all of them have their particular strengths and weaknesses. As stated before, if there was one indicator that worked 100% of the time than trading stocks would be easy, and where’s the fun in that? Personal choice, which often comes simply from what works well for you or with your trading system, typically dictates the usage. This article will explain what these indicators show and how they are computed, but in terms you should be able to understand.

Moving Averages (MA)
A fundamental indicator, found on even the most basic of charts, is the moving average. The moving average is just that. It adds up the end of day price, or whatever your time measurement unit may be, for a certain period, then divides by that same certain period. Presto, an average. Plot that over time and you get nice pretty line. If a securities price is below the MA than it is considered bearish, above and it’s bullish. The most simple of trading techniques, is to buy when it cross above the MA line, sell when it crosses below.

There is more than one kind of moving average. Since a MA, like most indicators, reflects only historical prices the indicator could show an attractive upward moving line while the security price goes to the cellar.

  • The aforementioned is known as the standard moving average (SMA).
  • The exponential moving average (EMA) minimizes the difference between the current price and the MA line.
  • The weighted moving average (WMA) puts more emphasis on more recent prices
  • The adaptive moving average (AMA) reduces the importance of ‘out of the park’ prices that skews the data.

Many traders chart two separate MA’s and watch for a crossover.  This occurs when the short time frame MA line crosses the long time frame MA (bullish, time to buy) or vice versa (bearish, time to sell).  As you can imagine the shorter time frame MA is more volatile, but also more reactive to changes in the price so may provide a better indicator. Finally, if a stock has little change in it’s price over time the MA will be mostly useless, just like investing in a stock that doesn’t change in price.

Notice the legend in the upper left corner of the chart below. Look closely at what happens, even to a small degree, to the price of this security when the lines cross. It lags slightly, as an average based on historical data will do, but the price follows the bull and bear indicators with strong regularity. In this example I used a 5 day (one week) and 20 day (one month) SMA.

There are traders that make every decision based solely off the momentum indicator. They hope that physics will apply to the stock (sometimes it seems to) and an upward momentum indicates that the price will continue to go up. It’s basic Newton’s Law. Any line above zero is upward momentum, and any line below zero is downward momentum. Momentum is figured by taking the current price vs a historical price, usually 5 or 10 days. If there are a number of lines in a row that are the same height it doesn’t mean that the price isn’t moving, it simply means it’s moving with the same momentum from day to day. A broad rule is to sell when it drops below zero, and to buy when it rises above. In my personal opinion indicators that include momentum but also take into consideration other factors, like MACD, RSI, etc are more appropriate.

This particular example shows why multiple charting websites are necessary. Not every web page has every indicator, and you may notice this is from a different source.


Moving Average Convergence and Divergence (MACD)
This indicator, plotted below the chart, takes the MA and momentum indicators one step further and charts the convergence (the trend as the two lines get closer) and the divergence (the trend as the two lines grow apart) with a momentum ‘soundwave’ underlay. Notice how similar the soundwave shape below is to the one above. The purpose of this is to give traders a little more knowledge to help anticipate the crossovers by showing the momentum of the lines.  Mistakes can be made in ‘predicting’ if the trend will continue, the lines could crossover then abruptly pull an about-face and return the way they came, but it provides a better picture that may allow earlier entry and exits. Used with an indicator such as the RSI or Stochastic this can be a powerful weapon in your arsenal.

MACDOn-Balance Volume (OBV) and the Chaikin Oscillator
Volume is an important indicator and should be on every chart you create that is going to be used to make trading decisions. Heavy volume indicates the market agrees with the change, light volume can indicate an anomaly or give guidance that a price bar is in left field, not part of a new pattern.

The OBV is a very simple and straightforward indicator. It brings together volume and price, the two most important parts of a stock. That being said, the OBV is a great tool to check, but subject to inaccuracy. It takes all the volume and adds it to the OBV line if the price of a security is up at the end of that time frame (minute, day, week, etc) and subtracts it if the price is down. Obviously in a time frame you can’t generalize that just because a price is up all of the action was buying. Traders watch for the OBV line to change directions from the price line. When it does, there usually is a change in price trend.  If they travel in the same direction the status quo will likely continue.

A variation that is a little ‘softer’ with less sharp points in the graph is known as the Chaikin Oscillator. The only difference is that we only add volume when the price is up over the midday point, rather than the end of day, and take away volume in the same manner if below the midday point.  The OBV is right below the line chart and the Chaikin Oscillator is at the bottom.

OBV and ChaikinRelative Strength Indicator (RSI)
The RSI builds upon the simple momentum indicator. The RSI takes the average up move and compares it to the average down move, giving weight to the upward or downward momentum.  It’s put on a scale of 0-100. Anything above 80 is considered overbought, anything below 20 is considered oversold. When the RSI changes direction from the price it is likely a reversal in price will follow. After all, if the RSI changes direction it means that the momentum has. This, in theory, gives traders a more efficient and timely indication of momentum.


Stochastic Oscillator (Fast and Slow)
It’s hard to describe this one in simple English, simply because the creator of this indicator, Dr. Lane, must have enjoyed complexity. Fortunately, the computer will do the calculations. This, like the RSI, gives the trader an idea if the stock is overbought or oversold.  Essentially this indicator compares the closing price with the price movements over time. As prices rise, the close tends to be near the top at the end of the day, as the prices sink, the close tends to be near the bottom. There are two lines, the actual oscillator (%K) and the signal line (%D). They are figured out as follows:
%K = 100 X (Closing price – Low price) / (Closing price – High price)
%D is the three period moving average of %K

This is known as the Stochastic Fast. The Stochastic slow lags, since it incorporates %D for %K, but is smoother and more reliable.  The chart below shows both forms and you can see while the trends are very similar, they do differ at times. Just as the RSI, anything over 80 is overbought and anything below 20 is oversold. It should be used with another indicator for confirmation of a price change. Just being oversold doesn’t indicate when the buying will resume.
StochUltimate Oscillator
Another method of determining if a security is overbought or oversold. The ultimate oscillator combines the price over three separate periods to create a line chart. The ultimate oscillator rarely has wild swings or extreme results. The most recent time frame is to all three separate time periods, so it has the most magnitude on the chart. When the line drops below 30 the security is oversold, above 70 is overbought. This is often used with other indicators to signify when the price reversal will occur, as it provides no indication when the price will turn. While it may not cross the 70/30 thresholds, the plotted line does mirror, and sometimes predict, the price movements of a security.
UltimateAverage Directions Movement Index (ADX)
This may also be called Wilder’s DMI in some places. It shows the strength of a price movement, but should be used with an accurate an up-to-date chart since it doesn’t indicate if the price is rising or falling. Many people also use the MACD or the momentum indicator to show which way the price is trending. There are three lines on the typical ADX.  There is the ADX, the +DI and -DI.

The DI+ and DI- measure the current price range to a historical price range, typically a two week period. They move in opposite directions and when the lines cross it indicates a buy when the +DI rises above the –DI and vice versa.  However, these lines cross frequently and any profits would be lost in excessive commissions.  Enter the ADX line. As a general rule of thumb don’t make a trade unless the ADX is above 30, indicating the trend has strength behind it and should produce the best profits. Each trader needs to determine their entry and exit points based off their needs and desires. If +DI is rising with the AMX then buy, if –DI is rising with the ADX, then sell short. Imagine if you sold short in early November as the ADX indicates (notice the lines touch, but don’t actually cross until the security plummets), and taken your profits at the end of November in the chart below!!
ADXThere are a number of different indicators. Many traders swear by two or three.  The truth is the indicators are only as good as the mind interpreting the data. Practice and experience will help make better use of these tools, but you can’t rely on one particular indicator to make profits, every single time. Explore the web and the charting software/website you use and broaden your knowledge beyond these fundamental indicators. The section on Support and Resistance will also take your ability to recognize trend reversals and solidify your entry and exit points to the next level and will include MA Envelopes and Bollinger Bands that are popular overlays in charting.



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