PRICE CHANNEL
the pattern

Commodity or stock prices go up and down from time to time. When you draw a pair of parallel lines to approximate the trend of the prices, you are creating a price channel. When the prices pass through the channel and stays through a trend indicating resistance or support, there exists a “breakout”.

MOVING AVERAGE
the mean

When dealing with time series data, a moving average smooths out short-term fluctuations. It also highlights long-term trends. Practical applications of the moving average would be in the analyses of technical data like trade volumes, stock prices, gross domestic product (GDP), employment, and other time-series data.

Simple Moving Average

The term simply means the unweighted mean of the previous n data points.
Example: Computing for a 10-day simple moving average of price is the mean of the previous 10 day prices. If the prices are pM, pM-1 , … , pM-9 then the formula is
SMA = { pM + pM-1 + … + p_{M-9} / 10 }
When dealing with successive values, a new value is used and an old value is removed.
SMAtoday = SMAyesterday – {p(M-n) / n} + {p(M) /n}
Moving average levels may be used to show support in a rising market or resistance in a falling market. The moving average always lags behind the most recent data point. Old data points may also affect the average in a negative manner. To address this concern, weighted and exponential moving averages may be used.

If the data have periodic fluctuations, applying a simple moving average on that time period will remove that variation.

Cumulative Moving Average

If an investor wants to look at more data points, he might want to use the cumulative moving average (CMA). This is the average of all the data points up to the current time. For example, the CMA price of stock A from January 1 to March 8 is the average of all the prices of stock A from January 1 to March 8. On March 9, there is a new CMA price since the March 9 price is now going to be added in the computations.

In equation form, the CMA is the unweighted average of the sequence of i values x1, …, xi up to the current time:
CAi = {{x1 + … + xi} / i}
To update the cumulative average if a new datum xi+1 arrives, this formula is used:
CAi+1 = {{xi+1 + i CAi} / {i+1}}, where CA0 can be taken to be equal to 0.

Weighted Moving Average

The simple moving average and cumulative moving average does not take into account the weights. The weighted moving average (WMA) has weights that decrease. Given n days, the latest day has n as its weight, the second latest has n-1, and so on, until zero. The formula is:

WMAM = { n pM + (n-1) pM-1 + … + 2 pM-n+2 + pM-n+1 / n + (n-1) + … + 2 + 1}
Note: the denominator can be computed using the formula [n(n+1)/2].

Exponential Moving Average

The exponential moving average applies weights that exponentially decreases. The later data gets heavier weights as compared to the earlier data points.
1. The decrease in the weights is expressed as a constant smoothing factor α, a number between 0 and 1. This factor can be expressed as a percentage, so a value of 20% is equivalent to α = 0.2. If there is a higher α, the older observations are decreased faster. The α may also be expressed in terms of N time periods, where α = 2/(N+1). For example, N = 9 is equivalent to α = 0.2. The half-life of the weights is approximately N/2.8854 and is within 1% if N > 5.
2. The observation at a time period t is designated Yt, and the value of the EMA at any time period t is designated St.
Note: The half-life of the weights is the interval over which the weights decrease by a factor of two
The S1 is undefined. S2 is commonly set to Y1, or one may also set S2 to be the average of the first 4 or 5 observations. Smaller α values make the S2 choice relatively more important as compared to larger α values.

The Formula:
The formula for calculating the EMA at time periods t > 2 is as follows,
St = α * Yt-1 + (1-α) * St-1
This is according to Hunter (1986). The weights will obey α(1 − α)x Yt − (x + 1). An alternate approach by Roberts (1959) uses Yt instead of Yt−1:
St,alternate = α * Y_t + (1-\alpha) \times S_{t-1}
It can also be expressed as follows:
EMAtoday = EMA yesterday + α * (price today – EMAyesterday)
Expanding out EMA {yesterday} each time will result in the power series, expressed below:
EMA = α * (p1 + (1-α) p2 + (1-α)2 p3 + (1-α)3 p4 + … )
The one above is an infinite sum with decreasing terms.
In an N-day EMA, the N periods only specify the α factor. For sufficiently large N, The first N data points represent 86% of the total weight in the calculations:
α * {1 + (1-α)+(1-α)2 + … +(1-α)N} / {α * { 1 + (1-α)+(1-α)2 + … +(1-α)∞} = 1 – { 1 – (2 / N+1 ) } N+1
i.e. lim N to ∞ [ 1 - (1 - (2 / N+1) )N+1] ,… tends to 1-e-2 = 0.8647

The formula above gives a starting value for a particular day. After which, the successive days formula shown first could be applied. How far back to go for an initial value depends on the data. If one assumes that prices don’t vary too much, then he can just consider the weighting. The weight omitted by stopping after k terms is found as follows:
α * [ (1-α)k + (1-α)k+1 + (1-α)^k+2 + ... ],
which is
α * (1-α)k * (1 + (1-α) + (1-α)2 + … ]
i.e. a fraction
(1 – α)k
out of the total weight.
As an example, to have 99.9% of the weight,
k = log (0.001) / log (1-α)
terms must be used. Since log,(1-α) approaches -2 / N+1 as N increases, this can then be simplified to approximate
k = 3.45(N+1)
for this example (99.9% weight).

Modified Moving Average:
This is also called running moving average (RMA), or smoothed moving average.
MMAtoday = (N – 1) * MMA yesterday + price / N
This is therefore an EMA, with α = 1 / N.

It is Simply an Average

A pivot point is calculated as an average of significant prices, namely the High, Low, and Close from the performance of a market in the previous trading period. If the market in the following period trades above the pivot point it is usually evaluated as a bullish feeling. On the other hand, trading below the pivot point is viewed as bearish. It is a price level of significance in analysis of a financial market. Traders use this as a predictive indicator of market movement.

In a market, a pivot point, its associated support and resistance levels, are often turning points for the direction of price movement. If the market is trending up, the pivot point and the resistance levels may represent a ceiling level in price above which the uptrend is no longer sustainable. A reversal may also occur when this happens. A pivot point and the support levels may represent a low price level of stability or a resistance to further decline in a declining market.

The custom is to calculate additional levels of support and resistance, below and above the pivot point, respectively, by subtracting or adding price differentials calculated from previous trading ranges of the market.

How to Compute For the Pivot Point
There are many methods for calculating the pivot point (P) of a market. Most commonly, it is the arithmetic average of the high (H), low (L), and closing (C) prices of the market in the prior trading period:
P = (H + L + C) / 3.

Sometimes, the average also includes the previous period or the current period’s opening price (O):
P = (O + H + L + C) / 4.
In other situations, the traders like to highlight the closing price, P = (H + L + C + C) / 4, or the present period’s opening price, P = (H + L + O + O) / 4.

Price Support and Resistance Levels: Key Trading Tools
In any market, price support and resistance levels are key trading tools. Depending on whether the price level is approached in an up-trending or a down-trending market, their roles may be interchangeable. It is calculated from the range of price movement in the previous trading period, added to the pivot point for resistances and subtracted from it for support levels.

By recognizing the upper and the lower halves of the prior trading range, the first and the most significant level of support (S1) and resistance (R1) is obtained. It is defined by the trading above the pivot point (H − P), and below it (P − L). The first resistance on the up-side of the market is given by the lower width of prior trading added to the pivot point price and the first support on the down-side is the width of the upper part of the prior trading range below the pivot point.
• R1 = P + (P − L) = 2P – L
• S1 = P − (H − P) = 2P − H

This level may be calculated by subtracting the previous low (L) and high (H) price, respectively, from twice the pivot point value.

The second set of resistance (R2) and support (S2) levels are above and below the first set. It is determined from the full width of the prior trading range (H − L), added to and subtracted from the pivot point, respectively:
• R2 = P + (H − L)
• S2 = P − (H − L)

A third set is calculated again, as common practice. This represents another higher resistance level (R3) and a yet lower support level (S3). Here, the method of the second set is continued by doubling the range added and subtracted from the pivot point:
• R3 = P + 2(H − L)
• S3 = P − 2(H − L)

Furthermore, this concept is sometimes extended to a fourth set. The tripled value of the trading range is used in the calculation.

For quality, the second and higher support and resistance levels are always located symmetrically around the pivot point. Unless the pivot point happens to divide the prior trading range exactly in half, this is not the case for the first levels.

The Pivot Point can be Used as a Trading Tool
Depending on the overall market condition, the pivot point itself represents a level of highest resistance or support. If the market is direction-less, meaning it is undecided, prices will often fluctuate greatly around this level. The fluctuation will not stop until a price breakout develops. The pivot point is a leading indicator that provides advanced signaling of potentially new market highs or lows within a given time frame.

We can use the support and resistance levels calculated from the pivot point and the previous market as exit points of trades. It is however rarely used as entry signals. As an example, if the market is trending upwards and breaks through the pivot point, the first resistance level is usually a good target to close a position. This is because the chance of resistance and reversal increases by much.

This is a technical analysis tool invented by John Bollinger in the 1980s. This evolved from the concept of trading bands. Bollinger Bands are typically used to measure the highness or lowness of the price relative to the trades previously made.

Composition of Bollinger Bands:
1. a middle band being an N-period simple moving average (MA)
2. an upper band at K times an N-period standard deviation above the middle band (MA+K*sigma)
3. a lower band at K times an N-period standard deviation below the middle band (MA-K*sigma)

Typical values for N and K are 20 and 2, respectively. The default choice for the average is a simple moving average, but other types of averages can be employed as needed. A common second choice is exponential moving averages. Usually the same period is used for both the middle band and the calculation of standard deviation.

Purpose
Bollinger Bands are there to provide a relative definition of high and low. Prices are high at the upper band and low at the lower band. This definition can help in pattern recognition and is also useful in comparing price action to the action of indicators to arrive at systematic trading decisions.

Indicators derived from Bollinger Bands
There are two indicators derived from Bollinger Bands, %b and BandWidth:
%b, pronounced ‘percent b’, is derived from the formula for Stochastics and tells you where you are in relation to the bands. %b equals 1 at the upper band and 0 at the lower band. Writing upperBB for the upper Bollinger Band, lowerBB for the lower Bollinger Band, and last for the last (price) value:
%b = (last – lowerBB) / (upperBB – lowerBB)
BandWidth tells you how wide the Bollinger Bands are on a normalized basis. Writing the same symbols as before, and middleBB for the moving average, or middle Bollinger Band:
BandWidth = (upperBB – lowerBB) / middleBB
Using the default parameters of a 20-period look back and plus/minus two standard deviations, BandWidth is equal to four times the 20-period coefficient of variation.
Uses for %b include system building and pattern recognition. Uses for BandWidth include identification of opportunities arising from relative extremes in volatility and trend identification.

Interpretation
The use of Bollinger Bands varies much among traders. Some buy when price touches the lower Bollinger Band and some exit when price touches the moving average in the center of the bands. Others buy when price goes above the upper Bollinger Band or sell when price falls below. The use of Bollinger Bands is not confined to stock traders; options traders, most notably implied volatility traders, often sell options when Bollinger Bands are historically far apart or buy options when the Bollinger Bands are historically close together. In both instances, they are expecting volatility to go back towards the average historical volatility level for the stock.

When the bands lie close together this indicates a period of low volatility in stock price. On the other hand, if they are far apart this indicates a period of high volatility in price. The price of a stock is predictably found to go up and down between the bands, as though in a channel, if the bands have only a slight slope and lie approximately parallel for an extended time.

Together with other indicators, many traders often use Bollinger Bands to see if there is confirmation. It is common practice to use a non-oscillator indicator like chart patterns or a trendline, with an oscillator like Bollinger Bands; through these indicators the recommendation of the Bollinger Bands is confirmed and the trader will have greater evidence that what the Bands forecast is true.

Bollinger Bands and Statistics
Security prices usually have no known statistical distribution bet ir normal or not. They are characterized to have fat tails versus the Normal. The sample size typically used, which is 20, is too small to be reliable for conclusions to be derived from statistical techniques such as the Central Limit Theorem. For this reason, these techniques usually require the sample to be independent and identically distributed. This is not the case for a time series like security prices.

Because of these reasons, it is wrong to assume that the percentage of the data outside the Bollinger Bands will always be limited to a certain amount. Therefore, instead of finding about 95% of the data inside the bands, as would be the expectation with the default parameters and a normal distribution, one should find less. How much less is a function of the volatility of the security.

Here’s a quick overview of our current educational sections.

Candlestick Charts

Candlesticks are usually composed of the body (black or white), and an upper and a lower shadow (wick). The wick illustrates the highest and lowest traded prices of a security during the time interval represented. The body illustrates the opening and closing trades. If the security closed higher than it opened, the body is white or unfilled, with the opening price at the bottom of the body and the closing price at the top. If the security closed lower than it opened, the body is black, with the opening price at the top and the closing price at the bottom. A candlestick need not have either a body or a wick.

• Bearish Candlesticks
  • 1. High Reliability
  • 2. Medium Reliability
  • 3. Low Reliability
• Bullish Candlesticks
  • 1. High Reliability
  • 2. Medium Reliability
  • 3. Low Reliability

Chart Overlays

These are usually used to help stock traders smooth out a stock chart, or to quick see when a stock might be going lower or higher than usual.

Read more about chart overlays…

Technical Indicators

Chart Technicals are commonly used by stock trader to forecast the future movement of a stock.  They make no guarantees of futures price patterns.  However, they do help investors anticipate what is likely to occur.  Many technicals, for example, show when a stock seems to have become oversold or overbought, allowing an investor to help plan their trades.

Read more about technical indicators…

Chart Patterns

Another way to help predict price patterns in a stock is to use specific chart patterns.  Certain pattern types can help an investor recognize an upcoming bullish move or caution them of a possible upcoming bearish pullback.

Read more about chart patterns…

ON-BALANCE VOLUME
price-volume relationship

Based on a cumulative volume, the on-balance volume relates price and volume in the stock market, and it has the formula:

OBV = OBVprev
+ volume … if close > closeprev then { + volume}
+ 0 … if close = closeprev then { + 0}
- volume … if close < closeprev then { – volume}

If the closing price is higher on a particular day, the total volume is assigned a positive value. The reverse is applied if the closing price is lower (a negative value is assigned). So prices and OBV are directly related. If prices are going up, OBV should also be going up.

Woods and Vignolia originally called this technique cumulative volume. In 1946, Joseph Granville termed it on-balance volume. It can be applied to stocks based on their daily upward or downward close. OBV is generally used to check price moves. The general assumption is volume is higher on days where the price move is in the dominant direction. For example, there is more volume on up days than during down days.

MONEY FLOW
price times volume

Money flow approximates the dollar value of a certain day’s trading. The formula is price multiplied by volume. Generally, a value of 80 is counted as overbought while a value of 20 is considered as oversold. Differences in the MFI (money flow indicator) and price action are significant. If the price makes a new rally high but the MFI high is lower than the previous high, then it is counted as a weak advance. And this situation is likely to reverse.

Furthermore, money flow refers to dollar volume, the total value of shares traded. It should be differentiated from money “flowing into” the stock. An up day represents the enthusiasm of the buyers while the down day represents the enthusiasm of the sellers. An excessive proportion to a certain direction will likely result in a price reversal.

MFI and RSI (relative strength index) have a similarity. Both look at up days against total up plus down days, but what is accumulated on those days, is dollar volume for the MFI, as opposed to price change amounts for the RSI.