The advance block is a three-candle bearish reversal pattern appearing on candlestick charts.

Advance block is the name given to a candlestick trading pattern. The advance block candlestick pattern has the following four characteristics:
1.  The price action has displayed an upward trend or a significant bounce within a downtrend.
2.  Three white candles appear that have progressively shorter real bodies.
3.  The open of the second and third candles lie within the real body of the previous candles respectively.
4.  The upper shadows of the three candles gradually become taller—especially the shadow of the last candle.
This pattern is considered to forecast a price reversal in the next several periods immediately following the pattern. The pattern is a three-candle bearish setup that is considered to be a reversal pattern—a suggestion that price action is about to change from what had been an upward trend to a downward trend in relatively short time frames. The bearish reversal is confirmed when the first subsequent price bar trades through the midpoint of the first candle’s real body.
The advance block pattern was relatively rare in the years before algorithmic trading but has since grown more common, reflecting a greater frequency of intraday counter swings. This chart pattern best forecasts a reversal pattern during temporary upward moves and pullbacks within larger-scale downtrends and when candles have long real bodies.

Advance Block

An autoregressive integrated moving average (ARIMA) is a statistical analysis model that leverages time series data to forecast future trends. 

An autoregressive integrated moving average, or ARIMA, is a statistical analysis model that uses time series data to either better understand the data set or to predict future trends.
A statistical model is autoregressive if it predicts future values based on past values. An ARIMA model can be understood by outlining each of its components as follows:
_Autoregression (AR)_: refers to a model that shows a changing variable that regresses on its own lagged, or prior, values.
_Integrated (I):_ represents the differencing of raw observations to allow for the time series to become stationary (i.e., data values are replaced by the difference between the data values and the previous values).
_Moving average (MA)_:  incorporates the dependency between an observation and a residual error from a moving average model applied to lagged observations. An autoregressive integrated moving average, or ARIMA, is a statistical analysis model that uses time series data to either better understand the data set or to predict future trends.
A statistical model is autoregressive if it predicts future values based on past values. For ARIMA models, a standard notation would be ARIMA with p, d, and q, where integer values substitute for the parameters to indicate the type of ARIMA model used. Autoregressive integrated moving average (ARIMA) models predict future values based on past values.

Autoregressive Integrated Moving Average (ARIMA)

A statistical model is autoregressive if it predicts future values based on past values (i.e., predicting future stock prices based on past performance).

A statistical model is autoregressive if it predicts future values based on past values. Multiple regression models forecast a variable using a linear combination of predictors, whereas autoregressive models use a combination of past values of the variable. For example, an investor using an autoregressive model to forecast stock prices would need to assume that new buyers and sellers of that stock are influenced by recent market transactions when deciding how much to offer or accept for the security. Autoregressive models operate under the premise that past values have an effect on current values, which makes the statistical technique popular for analyzing nature, economics, and other processes that vary over time. However, since autoregressive models base their predictions only on past information, they implicitly assume that the fundamental forces that influenced the past prices will not change over time.

Autoregressive Defined

A bell curve describes the shape of data conforming to a normal distribution.

Table of Contents
What Is a Bell Curve?
Understanding a Bell Curve
Non-Normal Distributions
Limitations of a Bell Curve The width of a bell curve is determined by the standard deviation—68% of the data points are within one standard deviation of the mean, 95% of the data are within two standard deviations, and 99.7% of the data points are within three standard deviations of the mean. The highest point on the curve, or the top of the bell, represents the most probable event in a series of data (its mean, mode, and median in this case), while all other possible occurrences are symmetrically distributed around the mean, creating a downward-sloping curve on each side of the peak. In addition to teachers who use a bell curve when comparing test scores, the bell curve is often also used in the world of statistics where it can be widely applied. A bell curve is a symmetric curve centered around the mean, or average, of all the data points being measured.

Bell Curve

The Box-Jenkins Model is a mathematical model designed to forecast data from a specified time series.

The Box-Jenkins Model is a mathematical model designed to forecast data ranges based on inputs from a specified time series. Overall, initial analysis of the data prepares it for forecasting by determining the parameters (p, d, and q), which are then applied to develop a forecast.
A one-time shock will affect subsequent values of a Box-Jenkins model infinitely into the future. Box-Jenkins Models are used for forecasting a variety of anticipated data points or data ranges, including business data and future security prices. The Box-Jenkins Model is a mathematical model designed to forecast data ranges based on inputs from a specified time series. The Box-Jenkins Model is a forecasting methodology using regression studies on time series data.

Box-Jenkins Model

Buying the dips is a phrase that refers to purchasing an asset following a decline in price.

"Buy the dips" means purchasing an asset after it has dropped in price. If an investor is already long and buys on the dips, they are said to be averaging down, an investing strategy that involves purchasing additional shares after the price has dropped further, resulting in a lower net average price. While there may be unrecognized intrinsic value, buying additional shares simply to lower an average cost of ownership may not be a good reason to increase the percentage of the investor's portfolio exposed to the price action of that one stock. Buying the dips refers to going long an asset or security after its price has experienced a short-term decline, in repeated fashion. When an investor buys an asset after a drop, they are buying at a lower price, hoping to profit if the market rebounds.

Buy The Dips

Counterattack lines are two-candle reversal patterns that appear on candlestick charts. There are both bullish and bearish versions.

The counterattack lines pattern is a two-candle reversal pattern that appears on candlestick charts. For a bullish reversal during a downtrend, the first candle is a long black (down) candle, and the second candle gaps down but then closes higher, near the close of the first candle. For a bearish reversal during an uptrend, the first candle is a long white (up) candle, and the second candle gaps higher but then closes lower, near the close of the first candle. The second candle gaps higher on the open, is black with a real body that's similar in size to the first candle, with a close that's near the first candle's close. 3.  The second candle gaps down on the open, is white with a real body that's similar in size to the first candle, and closes near the first candle's close.

Counterattack Lines  and Example

A cup and handle is a bullish technical price pattern that appears in the shape of a handled cup on a price chart.

How to Make Money in Stocks: A Winning System in Good Times and Bad, Fourth Edition

Wynn Resorts, Limited Reports Third Quarter Results

A cup and handle price pattern on a security's price chart is a technical indicator that resembles a cup with a handle, where the cup is in the shape of a "u" and the handle has a slight downward drift. Stop loss orders may be placed either below the handle or below the cup depending on the trader’s risk tolerance and market volatility.
Now let's consider a real-world historical example using Wynn Resorts, Limited (WYNN), which went public on the Nasdaq exchange near $13 in October 2002 and rose to $154 five years later.﻿﻿﻿﻿﻿ ﻿﻿﻿﻿﻿ The subsequent decline ended within two points of the initial public offering (IPO) price, far exceeding O'Neil's requirement for a shallow cup high in the prior trend. A cup and handle is a technical indicator where the price movement of a security resembles a “cup” followed by a downward trending price pattern. For example, if the distance between the bottom of the cup and handle breakout level is 20 points, a profit target is placed 20 points above the pattern's handle. Alternatively, wait for the price to close above the upper trend line of the handle, subsequently place a limit order slightly below the pattern’s breakout level, attempting to get an execution if the price retraces.

Cup and Handle

Data smoothing is done by using an algorithm to remove noise from a data set. This allows important patterns to stand out. 

Helps identify real trends by eliminating noise from the data
Allows for seasonal adjustments of economic data
Easily achieved through several techniques including moving averages
Removing data always comes with less information to analyze, increasing the risk of errors in analysis
Smoothing may emphasize analysts' biases and ignore outliers that may be meaningful While data smoothing can help predict certain trends, it will inherently lead to less information in the sample that may lead to certain data points being ignored. Random walk smoothing assumes that future data points will equal the last available data point, plus a random variable. A simple moving average (SMA) places equal weight on both recent prices and historical ones, while an exponential moving average (EMA) puts more weight on recent price data.

Data Smoothing

The derivative oscillator is similar to a MACD histogram, except the calculation is based on the difference between an SMA and a double-smoothed RSI.

Table of Contents
What Is the Derivative Oscillator? The derivative oscillator is a technical indicator that applies a moving average convergence-divergence (MACD​) histogram to a double-smoothed relative strength index (RSI) to create a more advanced version of the RSI indicator. This technical indicator is a more advanced version of the relative strength index (RSI) that applies moving average convergence-divergence (MACD) principles to a double-smoothed RSI (DS RSI) indicator. It is in this way that the derivative oscillator uses MACD principles, since the derivative oscillator is also derived from subtracting the SMA from the double-smoothed RSI. The derivative oscillator can produce a large number of trade signals, especially during choppy trading conditions when the indicator is most susceptible to giving false or losing signals.

Derivative Oscillator

A double bottom pattern is a technical analysis charting pattern that describes a change in trend and a momentum reversal from prior leading price action.

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A double bottom pattern is a technical analysis charting pattern that describes a change in trend and a momentum reversal from prior leading price action. Once the closing price is in the second rebound and is approaching the high of the first rebound of the pattern, and a noticeable expansion in volume is presently coupled with fundamentals that indicate market conditions that are conducive to a reversal, a long position should be taken at the price level of the high of the first rebound, with a stop loss at the second low in the pattern. Although the pattern may appear on intraday price charts, it is very difficult to ascertain the validity of the double bottom pattern when intraday data price charts are used. A double bottom pattern is a technical analysis charting pattern that describes a change in trend and a momentum reversal from prior leading price action. At least a three-month duration is considered appropriate for the lows of the double bottom pattern, in order for the pattern to yield a greater probability of success.

Double Bottom

The Dow theory states that the market is trending upward if one of its averages advances and is accompanied by a similar advance in the other average.

The Dow theory is a financial theory that says the market is in an upward trend if one of its averages (i.e. industrials or transportation) advances above a previous important high and is accompanied or followed by a similar advance in the other average. Remember, a follower of Dow theory trades with the overall direction of the market, so it is vital that they identify the points at which this direction shifts.
One of the main techniques used to identify trend reversals in Dow theory is peak-and-trough analysis. 1:36
The Dow theory is an approach to trading developed by Charles H. Dow who, with Edward Jones and Charles Bergstresser, founded Dow Jones & Company, Inc. and developed the Dow Jones Industrial Average in 1896. Dow used the two indices that he and his partners invented, the Dow Jones Industrial Average (DJIA) and the Dow Jones Transportation Average (DJTA), on the assumption that if business conditions were, in fact, healthy, as a rise in the DJIA might suggest, the railroads would be profiting from moving the freight this business activity required. The Dow theory is a financial theory that says the market is in an upward trend if one of its averages (i.e. industrials or transportation) advances above a previous important high and is accompanied or followed by a similar advance in the other average.

Dow Theory

A dragonfly doji is a candlestick pattern that signals a possible price reversal. The candle is composed of a long lower shadow and an open, high, and close price that equal each other.

A Dragonfly Doji is a type of candlestick pattern that can signal a potential reversal in price to the downside or upside, depending on past price action. Following a price decline, the dragonfly doji shows that the sellers were present early in the period, but by the end of the session the buyers had pushed the price back to the open. The price wasn't dropping aggressively coming into the dragonfly, but the price still dropped and then was pushed back higher, confirming the price was likely to continue higher. Following the dragonfly, the price proceeds higher on the following candle, confirming the price is moving back to the upside. The long lower shadow suggests that there was aggressive selling during the period of the candle, but since the price closed near the open it shows that buyers were able to absorb the selling and push the price back up.

Dragonfly Doji Candlestick

The Elliott Wave theory is a technical analysis toolkit used to predict price movements by observing and identifying repeating patterns of waves.

The Elliott Wave theory is a theory in technical analysis used to describe price movements in the financial market. It has three unbreakable rules that define its formation:
Wave two cannot retrace more than 100% of the first wave
The third wave can never be the shortest of waves one, three, and five
Wave four can't go beyond the third wave at any time
If one of these rules is violated, the structure is not an impulse wave. As with the motive wave, each sub-wave of the diagonal never fully retraces the previous sub-wave, and sub-wave three of the diagonal may not be the shortest wave. They possess three rules: the second wave cannot retrace more than 100% of the first wave; the third wave cannot be shorter than wave one, three, and five; wave four cannot surpass the third wave ever. Elliott Wave International’s artificial intelligence system, EWAVES, applies all Elliott wave rules and guidelines to data to generate automated Elliott wave analysis.

Elliott Wave Theory

The exhausted selling model is used to estimate when a period of declining prices for a security has ended and higher prices may be forthcoming.

Table of Contents
Exhausted Selling Model Although different investors might use modified versions of the exhausted selling model, most versions involve the following guidelines:
First, the security in question must have recently declined based on unusually high trading volume.
Second, there must be recent evidence of buying pressure (following the decline), such as a bullish engulfing pattern or any type of bullish chart pattern within the price or in a technical indicator.
Third, the stock tests a support area, such as an important moving average (MA) or a price where the security bounced off on prior declines, signaling a base of demand from buyers.
If all of these factors are in place, the exhausted selling model would predict that the stock has reached its low point in price and that a positive reversal will soon take place. The exhausted selling model relies on price and technical information, such as recent trading volume, support, and candlestick or chart patterns.
The exhausted selling model is well-suited for periods following unusually intense selling, otherwise known as panic selling. The exhausted selling model is similar to techniques used by value investors, who look for bargain opportunities by monitoring companies with low price-to-book (P/B ratios), low price-to-earnings (P/E) ratios, and similar metrics. Because it is principally based on price chart information, the exhausted selling model is generally used by traders who follow a technical analysis approach to trading.

Exhausted Selling Model

Footprint charts are a type of candlestick chart that provides additional information, such as trade volume and order flow, in addition to price.

Footprint charts are a type of candlestick chart that provides additional information, such as trade volume and order flow, in addition to price. Common footprint charts include footprint profile, bid/ask footprint, delta footprint, and volume footprint. Some of the most common footprint charts used by traders include the following:
**Footprint profile**: Shows traders the volume at each price through a vertical histogram, in addition to the regular footprint bars. **Volume footprint**: Unlike the volume histogram on traditional charts, the volume footprint segments volume not only by time, but also by price. These charts may also be grouped with other multi-variable charts used by advanced traders, such as level 2 quote charts or depth of market (DOM) charts.

Footprint Charts

The Gartley pattern is a harmonic chart pattern, based on Fibonacci numbers and ratios, that helps traders identify reaction highs and lows.

Fibonacci Ratios With Pattern Recognition

The Gartley pattern is a harmonic chart pattern, based on Fibonacci numbers and ratios, that helps traders identify reaction highs and lows. These Fibonacci levels do not need to be exact, but the closer they are, the more reliable the pattern.
The bearish version of the Gartley pattern is simply the inverse of the bullish pattern and predicts a bearish downtrend with several price targets when the pattern reaches completion by the fourth point. At point 4, the pattern is complete and buy signals are generated with an upside target that matches point 3, point 1, and a 161.8% increase from point 1 as the final price target. The Gartley pattern above shows an uptrend from point 0 to point 1 with a price reversal at point 1. The Gartley pattern is a harmonic chart pattern, based on Fibonacci numbers and ratios, that helps traders identify reaction highs and lows.

Gartley Pattern

Ladder bottom/top are reversal patterns composed of five candlesticks that may also act as continuation patterns.

Ladder bottom/top are two types of candlestick patterns used to indicate a reversal in the price direction of an asset. Therefore, traders may wish to trade breakouts from the pattern—price moves above or below the pattern high or low, respectively—in either direction.
The bottoming pattern tended to show the best performance when the price was in an overall downtrend, and breakouts higher or lower tended to work out about equally.
The ladder bottom is a bullish reversal pattern with the following characteristics:
The market is in a downtrend. A long could be taken following the green candle in a bottoming pattern, with a stop loss below the pattern low or below the green candle, for example. As with the bottoming pattern, a breakout from the ladder top pattern tends to produce a decent-sized move in the days following the pattern, but the breakout could occur in either direction. In theory, the ladder bottom indicates a price reversal to the upside following a downtrend, while the ladder top indicates a price reversal to the downside following an uptrend.

Ladder Bottom/Top

The line of best fit is an output of regression analysis that represents the relationship between two or more variables in a data set.

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. A regression with two independent variables such as the example discussed above will produce a formula with this basic structure:
y= c + b1(x1) + b2(x2)
In this equation, y is the dependent variable, c is a constant, b1 is the first regression coefficient and x1 is the first independent variable. Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. In a simple regression with one independent variable, that coefficient is the slope of the line of best fit. To perform a regression analysis, a statistician collects a set of data points, each including a complete set of dependent and independent variables.

Line Of Best Fit

The matching low is a two-candle bullish reversal pattern that appears on candlestick charts. In reality, it acts more often as a continuation pattern.

Bulkowski on the Matching Low Candle Pattern

A matching low is a two-candle bullish reversal pattern that appears on candlestick charts. With three stars in the south, the first candle is a long down candle, the second candle is also a down candle, but fails to make a lower low, and the third candle is smaller, has no lower shadow, and is within the range of the second candle. Quite often it acts as a continuation pattern—about 61% of the time, according to the _Encylopedia of Candlestick Charts_ by Thomas Bulkowski.﻿﻿ Therefore, the price may move down following the pattern, and a trader could also enter a short position in this case, with a stop loss above the first or second candle high.
Suppose the market is engaged in an active downtrend, building bearish energy while bull confidence slumps. The matching low pattern is a two-candle bullish reversal pattern with the following characteristics: The theory behind the pattern is that the failure of the second candle to close below the first candle's close generates a support level for a bullish reversal.

Matching Low  and Example

Mean reversion is a financial theory positing that asset prices and historical returns eventually revert to their long-term mean or average level.

Mean reversion, or reversion to the mean, is a theory used in finance that suggests that asset price volatility and historical returns eventually will revert to the long-run mean or average level of the entire dataset. Mean reversion, or reversion to the mean, is a theory used in finance that suggests that asset price volatility and historical returns eventually will revert to the long-run mean or average level of the entire dataset. Mean reversion, in finance, suggests that various phenomena of interest such as asset prices and volatility of returns eventually revert to their long-term average levels. This mean level can appear in several contexts such as economic growth, the volatility of a stock, a stock's price-to-earnings ratio (P/E ratio), or the average return of an industry. The theory of mean reversion is focused on the reversion of only relatively extreme changes, as normal growth or other fluctuations are an expected part of the paradigm.

Mean Reversion

The modified hikkake pattern is a rare variant of the basic hikkake that is used to signal reversals. It contains more candles/price bars than the basic hikkake.

Table of Contents
Modified Hikkake Pattern
Understanding the Concept The pattern consists of two price bars in which the first price bar—an inside price bar—has a lower high and higher low than the previous price bar.
From here, two versions of the hikkake pattern can develop, a bullish and bearish version. Therefore, the modified version consists of a context bar, an inside bar, a fake move, followed by a move above (bullish) or below (bearish) the inside bar high or low, respectively. If the next price bar after the inside bar has a higher high and higher low, this sets up a potentially bearish pattern. If the next price bar after the inside bar has a lower high and lower low, this sets up a potentially bullish pattern.

Modified Hikkake Pattern

The on neck candlestick pattern theoretically signals the continuation of a downtrend, although it can also result in a short-term reversal to the upside.

The on neck pattern occurs when a long real bodied down candle is followed by a smaller real bodied up candle that gaps down on the open but then closes near the prior candle's close. The on neck pattern occurs during a downtrend, or a pullback within an uptrend, when a bearish candle with a long real body is followed by a smaller bullish candle that fails to close above the bearish candle's close. In theory, the pattern is a continuation pattern to the downside, but in reality, it acts as a continuation pattern and a reversal pattern with nearly the same frequency. The on neck pattern occurs when a long real bodied down candle is followed by a smaller real bodied up candle that gaps down on the open but then closes near the prior candle's close. The pattern is created by a long real bodied down candle, followed by a smaller real bodied up candle with the same close as the prior candle.

On Neck Pattern  and Example

Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa.

Table of Contents
What Is Negative Correlation?
Understanding Negative Correlation
The Importance of Negative Correlation For example, if variables X and Y have a correlation coefficient of -0.1, they have a weak negative correlation, but if they have a correlation coefficient of -0.9, they would be regarded as having a strong negative correlation. By the same token, two variables with a perfect positive correlation would have a correlation coefficient of +1, while a correlation coefficient of zero implies that the two variables are uncorrelated and move independently of each other. In statistics, a perfect negative correlation is represented by the value -1.0, while a 0 indicates no correlation, and +1.0 indicates a perfect positive correlation. As the energy sector, for obvious reasons, has a positive correlation with crude oil prices, investing part of one's portfolio in airline stocks would provide a hedge against a decline in oil prices.

Negative Correlation

The Norton High/Low Indicator leverages the Demand Index and Stochastics to identify potential price reversals several periods in advance.

The Norton High/Low Indicator leverages the Demand Index and stochastics​ to identify potential price reversals. The Demand Index is a complex oscillator that combines price and volume to provide traders with a leading indicator, while stochastics are commonly used as a momentum indicator to assess the strength of a trend. The Norton High/Low Indicator generates a high line (NHP) and a low line (NLP) that traders observe for movements above and below critical levels as well as crossovers that could indicate a change in the prevailing trend. The Norton High/Low Indicator leverages the Demand Index and stochastics to identify potential price reversals. The Norton High/Low Indicator leverages the Demand Index and stochastics​ to identify potential price reversals.

Norton High/Low Indicator  and Uses

Polynomial trending occurs in large data sets containing many fluctuations and describes a curved or broken pattern from a straight linear trend.

Polynomial trending describes a pattern in data that is curved or breaks from a straight linear trend. variablen\=the nature of the polynomial (e.g. squared, cubed, etc.)​
Big data and statistical analytics are becoming more commonplace and easy to use; many statistical packages now regularly include polynomial trend lines as part of their analysis. Data that is polynomial in nature is described generally by:
y \= a \+ x n where: a \= the intercept x \= the explanatory variable n \= the nature of the polynomial (e.g. squared, cubed, etc.) \\begin{aligned} & Graphs with curved trend lines are generally used to show a polynomial trend. For example, polynomial trending would be apparent on the graph that shows the relationship between the profit of a new product and the number of years the product has been available.

Polynomial Trending

The random walk index compares a security's price movements to a random sampling to determine if it's engaged in a statistically significant trend.

The random walk index (RWI) is a technical indicator that compares a security's price movements to random movements in an effort to determine if it's in a statistically significant trend. A trader buys when the long-term RWI High is above 1.0, which indicates a long-term strong uptrend, but the short-term RWI Low is also above 1.0, showing that in the short term the price has dropped, providing a favorable entry into the long-term uptrend.
Short positions may be entered when the long-term RWI Low is greater than 1.0 and the short-term RWI High peaks above one as well. Because the indicator measures both uptrend and downtrend strength, the indicator has two lines and requires separate calculations for both.
The calculation for high periods, or RWI High, is:
RWI High \= High − Low n ATR × n where: n \= number of days in the period ATR \= average true range \\begin{aligned} &\\text{RWI High} = \\frac { \\text{High} - \\text{Low}\_n}{ \\text{ATR} \\times \\sqrt{n} } \\\\ &\\textbf{where:} \\\\ &n = \\text{number of days in the period} \\\\ &\\text{ATR} = \\text{average true range} \\\\ \\end{aligned} ​RWI High\=ATR×n​High−Lown​​where:n\=number of days in the periodATR\=average true range​ RWI Low is calculated as follows:
RWI Low \= High n − Low ATR × n \\begin{aligned} &\\text{RWI Low} = \\frac { \\text{High}\_n - \\text{Low} }{ \\text{ATR} \\times \\sqrt{n} } \\\\ \\end{aligned} ​RWI Low\=ATR×n​Highn​−Low​​
The method is similar to the approach above, except now we will use today's low and the high from the prior period to create the first calculation. Often times, traders and market timers will enter long positions when a long-term RWI High is greater than 1.0 and the short-term RWI Low is also above 1.0.

Random Walk Index  and Uses

Risk-adjusted return on capital (RAROC) is a modification to the standard return on an investment that accounts for the element of risk.

Risk-adjusted return on capital (RAROC) is a modified return on investment (ROI) figure that takes elements of risk into account. It does this by accounting for any expected losses and income generated by capital, with the assumption that riskier projects should be accompanied by higher expected returns
RAROC is most often used by banks and other financial sector companies.
R A R O C \= r − e − e l \+ i f c c where: RAROC \= Risk-adjusted return on capital r \= Revenue e \= Expenses e l \= Expected loss which equals average loss e l \= expected over a specified period of time i f c \= Income from capital which equals i f c \= (capital charges) × (the risk-free rate) \\begin{aligned}&RAROC=\\frac{r-e-el+ifc}{c}\\\\&\\textbf{where:}\\\\&\\text{RAROC}=\\text{Risk-adjusted return on capital}\\\\&r=\\text{Revenue}\\\\&e=\\text{Expenses}\\\\&el=\\text{Expected loss which equals average loss}\\\\&\\phantom{el=}\\text{expected over a specified period of time}\\\\&ifc=\\text{Income from capital which equals}\\\\&\\phantom{ifc=}\\text{(capital charges)}\\times{\\text{(the risk-free rate)}}\\\\&c=\\text{Capital}\\end{aligned} ​RAROC\=cr−e−el+ifc​where:RAROC\=Risk-adjusted return on capitalr\=Revenuee\=Expensesel\=Expected loss which equals average lossel\=expected over a specified period of timeifc\=Income from capital which equalsifc\=(capital charges)×(the risk-free rate)​
Risk-adjusted return on capital is a useful tool in assessing potential acquisitions. Not to be confused with RAROC, the return on risk-adjusted capital (RORAC) is used in financial analysis to calculate a rate of return, where projects and investments with higher levels of risk are evaluated based on the amount of capital at risk. Other methods include return on risk-adjusted capital (RORAC) and risk-adjusted return on risk-adjusted capital (RARORAC). Risk-adjusted return on capital (RAROC) is a risk-adjusted measure of the return on investment.

Risk-Adjusted Return On Capital (RAROC)

The rate of change (ROC) is the speed at which a variable changes over a specific period of time.

The rate of change (ROC) is the speed at which a variable changes over a specific period of time. The price rate of change can be derived by taking the price of a security at time B minus the price of the same security at time A and dividing that result by the price at time A.
Price ROC \= B − A A × 1 0 0 where: B \= price at current time A \= price at previous time \\begin{aligned} &\\text{Price ROC} = \\frac{B - A}{A} \\times 100 \\\\ &\\textbf{where:}\\\\ &B=\\text{price at current time}\\\\ &A=\\text{price at previous time}\\\\ \\end{aligned} ​Price ROC\=AB−A​×100where:B\=price at current timeA\=price at previous time​
This is important because many traders pay close attention to the speed at which one price changes relative to another. R O C \= ( current value previous value − 1 ) ∗ 1 0 0 ROC = (\\frac{\\text{current value}}{\\text{previous value}} - 1)\*100 ROC\=(previous valuecurrent value​−1)∗100
Rate of change is an extremely important financial concept because it allows investors to spot security momentum and other trends. ROC is often used when speaking about momentum, and it can generally be expressed as a ratio between a change in one variable relative to a corresponding change in another; graphically, the rate of change is represented by the slope of a line. For example, option traders study the relationship between the rate of change in the price of an option relative to a small change in the price of the underlying asset, known as an options delta.

Rate of Change (ROC)

Rescaled range analysis is used to calculate the Hurst exponent, which is a measure of the strength of time series trends and mean reversion.

Rescaled range analysis is a statistical technique used to analyze trends in a time series. The rescaled range is calculated by dividing the range (maximum value minus minimum value) of the cumulative mean adjusted data points (sum of each data point minus the mean of the data series) by the standard deviation of the values over the same portion of the time series. Rescaled range analysis looks at a data series and determines the persistence or mean-reverting tendencies within that data. Rescaled range analysis looks at a data series and determines the persistence or mean-reverting tendencies within that data. When H is greater than 0.5, the data is exhibiting a strong long-term trend, and when H is less than 0.5, it is likely to reverse trend over the time frame considered.

Rescaled Range Analysis  and Uses

The rickshaw man is a long candlestick with a doji body, centered between the high and low, that indicates indecision in the market.

The rickshaw man is a type of long-legged doji candlestick where the body can be found at or very near the middle of the candle. For example, if the price is in an overall uptrend but has experienced a recent pullback, a rickshaw man coupled with an oversold stochastic making a bullish crossover could signal a bottom to the pullback is near—once the price starts moving up the pattern and indicator signals are confirmed. Similarly, a trader could short or sell once the price moves below the rickshaw low, and place a stop loss (if going short) above the rickshaw man high. A trader could buy once the price moves above the rickshaw man high and set a stop loss below the rickshaw low. Despite the significant volatility indicated by the rickshaw man, it does not point to clear directional movement, and the price closes very near its opening price.

Rickshaw Man

Skewness refers to distortion or asymmetry in a symmetrical bell curve, or normal distribution, in a set of data.

Skewness refers to a distortion or asymmetry that deviates from the symmetrical bell curve, or normal distribution, in a set of data. S k 1 \= X ˉ − M o s ‾ S k 2 \= 3 X ˉ − M d s where: S k 1 \= Pearson’s first coefficient of skewness and  S k 2     the second s \= the standard deviation for the sample X ˉ \= is the mean value M o \= the modal (mode) value M d \= is the median value \\begin{aligned} &\\begin{gathered} Sk \_1 = \\frac {\\bar{X} - Mo}{s} \\\\ \\underline{\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad} \\\\ Sk \_2 = \\frac {3\\bar{X} - Md}{s} \\end{gathered}\\\\ &\\textbf{where:}\\\\ &Sk\_1=\\text{Pearson's first coefficient of skewness and }Sk\_2\\\\ &\\qquad\\ \\ \\ \\text{ the second}\\\\ &s=\\text{the standard deviation for the sample}\\\\ &\\bar{X}=\\text{is the mean value}\\\\ &Mo=\\text{the modal (mode) value}\\\\ &Md=\\text{is the median value} \\end{aligned} ​Sk1​\=sXˉ−Mo​​Sk2​\=s3Xˉ−Md​​where:Sk1​\=Pearson’s first coefficient of skewness and Sk2​    the seconds\=the standard deviation for the sampleXˉ\=is the mean valueMo\=the modal (mode) valueMd\=is the median value​
Pearson’s first coefficient of skewness is useful if the data exhibit a strong mode. Investors note skewness when judging a return distribution because it, like kurtosis, considers the extremes of the data set rather than focusing solely on the average. Short- and medium-term investors in particular need to look at extremes because they are less likely to hold a position long enough to be confident that the average will work itself out.
Investors commonly use standard deviation to predict future returns, but the standard deviation assumes a normal distribution. Investors note right-skewness when judging a return distribution because it, like excess kurtosis, better represents the extremes of the data set rather than focusing solely on the average.
Besides positive and negative skew, distributions can also be said to have zero or undefined skew. Pearson’s second coefficient of skewness, or Pearson median skewness, subtracts the median from the mean, multiplies the difference by three, and divides the product by the standard deviation.

Skewness , Formula, & Calculation

The State Street Investor Confidence Index measures institutional investor confidence. It is derived from looking at the risk taken by institutional investors.

Investor Confidence Index Historical Data

The State Street Investor Confidence Index is an index that measures institutional investor confidence. The Confidence Index figures are often used as a rationalization for past stock market movements or to predict future stock price movements. Unlike most measures of market sentiment, which measure attitudes, the State Street Investor Confidence Index measures actual holdings. The State Street Investor Confidence Index is an index that measures institutional investor confidence. The State Street index measures confidence by taking into account the changes in institutional investors' equity holdings.

State Street Investor Confidence Index  and Uses

StockCharts Technical Rank (SCTR) is a proprietary ranking for stocks within a group, created by John Murphy for the technical analysis site Stockcharts.com.

Table of Contents
StockCharts Technical Rank (SCTR)
Understanding the SCTR
Example of How to Use the SCTR
SCTR vs. Relative Strength
Limitations of the SCTR Some traders may wish to buy strong stocks, or stocks with an increasing SCTR ranking, while selling or shorting stocks that have a weak or deteriorating SCTR ranking. An increasing SCTR means the stock's price performance is showing strength relative to the group of stock being analyzed. The StockCharts Technical Rank is a numerical ranking for individual stocks in different groups—large-capitalization (cap), mid-cap, small-cap, U.S. non-leveraged, and non-inverse exchange-traded funds (ETFs), and Canadian stocks—showing the stock's overall strength based on six technical indicators covering various time frames.

StockCharts Technical Rank (SCTR)

Symmetrical distribution is evident when values of variables occur at a regular interval. In addition, the mean, median and mode occur at the same point.

A symmetrical distribution occurs when the values of variables appear at regular frequencies and often the mean, median, and mode all occur at the same point. This also holds in other symmetric distributions such as the uniform distribution (where all values are identical; depicted simply as a horizontal line) or the binomial distribution, which accounts for discrete data that can only take on one of two values (e.g., zero or one, yes or no, true or false, etc.).
On rare occasions, a symmetric distribution may have two modes (neither of which are the mean or median), for instance in one that would appear like two identical hilltops equidistant from one another.
The median describes the point at which 50% of data values lie above, and 50% lie below. The central limit theorem states that the distribution of sample approximates a normal distribution (i.e., becomes symmetric) as the sample size becomes larger, regardless of the population distribution—including asymmetric ones.
Symmetrical distribution is most often used to put price action into context. Symmetrical distribution is a core concept in technical trading as the price action of an asset is assumed to fit a symmetrical distribution curve over time. In a symmetrical distribution, all three of these descriptive statistics tend to be the same value, for instance in a normal distribution (bell curve).

Symmetrical Distribution

Tail risk is portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution.

Tail risk is a form of portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution. Tail risk is a form of portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution. The normal distribution curve has a kurtosis equal to three and, therefore, if a security follows a distribution with kurtosis greater than three, it is said to have fat tails. The assumption that market returns follow a normal distribution is key to many financial models, such as Harry Markowitz's modern portfolio theory (MPT) and the Black-Scholes Merton option pricing model. When a portfolio of investments is put together, it is assumed that the distribution of returns will follow a normal distribution.

Tail Risk

Three inside up and three inside down are three-candle reversal patterns. They show current momentum is slowing and the price direction is changing.

Three inside up and three inside down are three-candle reversal patterns that appear on candlestick charts. The three inside up pattern is a bullish reversal pattern composed of a large down candle, a smaller up candle contained within the prior candle, and then another up candle that closes above the close of the second candle. The three inside down pattern is a bearish reversal pattern composed of a large up candle, a smaller down candle contained within the prior candle, and then another down candle that closes below the close of the second candle. 3.  The second candle is a white (up) candle with a small real body that opens and closes within the real body of the first candle. 3.  The second candle is a black candle with a small real body that opens and closes within the real body of the first candle.

Three Inside Up/Down

Three outside up/down are patterns of three candlesticks that often signal a reversal in trend.

The three outside up is a bullish candlestick pattern with the following characteristics:
1.  The market is in a downtrend.
2.  The first candle is black.
3.  The second candle is white with a long real body and fully contains the first candle. The first candle marks the beginning of the end for the prevailing trend as the second candle engulfs the first candle. The three outside up and three outside down are three-candle reversal patterns that appear on candlestick charts. The security continues to post losses, seeing its price drop below the range of the first candle, completing a bearish outside day candlestick.

Three Outside Up/Down

The three stars in the south is a three-candle bullish reversal pattern, following a decline, that appears on candlestick charts.

The three stars in the south is an extremely rare three-candle bullish reversal pattern that appears on candlestick charts. It indicates a bullish reversal, although the price should ultimately move in the expected direction before taking a trade.
The three stars in the south is a bullish reversal pattern with four characteristics:
1.  The market is in a downtrend.
2.  The first candle is black with a long real body, long lower shadow, and no upper shadow.
3.  The second candle is black with a shorter real body and a higher low than the first candle's low.
4.  The third candle is black with a short real body, no shadows, and a close that's within the high-low range of the second candle.
These strict requirements make the pattern rare. The pattern is formed by three long black (down) candles, with the second and third candles opening within the real body of the prior candle and closing lower than they opened and below the prior close.
Suppose a security is engaged in an active downtrend, with confident bears looking for lower prices. The three stars in the south candlestick pattern is a very rare pattern that doesn't typically precede large price moves. If the price drops following the pattern, it is not a bullish reversal, but rather a bearish continuation pattern.

Three Stars in the South

The thrusting pattern is a candlestick formation that can result in either a continuation or reversal of the prevailing short-term trend. The pattern is quite common.

A thrusting pattern is a type of price chart pattern used by technical analysts. A thrusting pattern is a long black candle followed by a white candle that closes near the midpoint of the black candle's real body.
The pattern is thought to act as a continuation pattern, but in reality, it acts as a reversal pattern about half the time.
Thrusting patterns are fairly common, don't necessarily result in large price moves, and are most useful when combined with other types of evidence.
A thrusting pattern occurs when a black candle is followed by a white candle. The thrusting pattern is also similar to the piercing pattern, in which the white candle closes above the midpoint of the previous black candle. Since the price can break higher or lower following the pattern, traders will watch for the price to move above the high of the first candle to signal a potential long trade or a drop below the second candle low to signal a short trade. For example, if a stock pulls back within a long-term uptrend and then forms a thrusting pattern along a rising trendline, it could signal the pullback is over and the uptrend is resuming if the price breaks the pattern to the upside.

Thrusting Pattern  and Example

Time-varying volatility refers to the fluctuations in volatility over different time periods. 

Time-varying volatility refers to the fluctuations in volatility over different time periods. Over time a security is expected to have varying volatility subject to large swings in price, with stocks and other financial instruments exhibiting periods of high volatility and low volatility at various points in time. Implied volatility differs from historical volatility in that it is not based on historical data but rather a mathematical calculation that provides a measure of the market’s estimated volatility based on current market factors. Time-varying volatility describes how the price volatility of an asset may change given different time periods. Overall, options with a longer time to expiration will have a higher volatility while options expiring in a shorter amount of time will have a lower implied volatility.

Time-Varying Volatility

Today's high refers to a security's intraday high trading price or the highest price at which a stock traded during the course of the day.

Today's high refers to a security's intraday highest trading price. There are numerous intraday strategies, which include scalping, where traders attempt to profit from incremental changes in price; range trading, which essentially uses support and resistance levels to determine buy and sell decisions; and news-based trading, which typically uses heightened volatility around news events that may create trading opportunities.
The biggest advantage of intraday trading is that positions are not affected by the possibility of negative overnight news that have the potential to materially impact the price of a security. One way that day traders and technical analysts use today's high, along with today's low, is to help them identify gaps or sudden jumps up or down in a stock's price with no trading in between those two prices. The price movements of any stock are posted throughout the trading day and summarized at the end of the trading day. Today's high is the highest price at which a stock traded during the course of the trading day and is typically higher than the closing or equal to the opening price.

Today's High

Time segmented volume (TSV) is a technical analysis indicator developed by Worden Brothers Inc. that segments a stock's price and volume by intervals.

Time segmented volume (TSV) is a technical analysis indicator developed by Worden Brothers Inc. that segments a stock's price and volume according to specific time intervals. The price and volume data is then compared to uncover periods of accumulation (buying) and distribution (selling).
Time segmented volume (TSV) is a technical analysis indicator that segments a stock's price and volume by intervals. Time segmented volume (TSV) is a technical analysis indicator developed by Worden Brothers Inc. that segments a stock's price and volume according to specific time intervals. Now you can calculate a moving average of an already smoothed TSV and use it much in the same way the MACD (moving average convergence divergence) indicator is used. While TSV is an indicator of money moving into and out of a stock, it's not a standalone price-gauging tool.

Time Segmented Volume

The unique three river is a candlestick pattern composed of three specific candles, and it may lead to a bullish reversal or a bearish continuation.

The unique three river is a candlestick chart pattern that predicts a bullish reversal, although there is some evidence that it could act as a bearish continuation pattern. The unique three river pattern is composed of three candlesticks, in a specific sequence: a long downward real body, a hammer that makes a new low, and a third candle with a small upward real body that stays within the range of the hammer. Traders often use the direction of a confirmation candle, which is the fourth candle, to signal which direction the price is likely to move following the pattern. If the price moves higher on the confirmation candle, this helps confirm the bullish reversal and a trader could take a long position with a stop loss below the low of the second candle. The long real body of the first candle shows that bears control the prevailing trend while the hammer in the second candle suggests that bulls are regaining strength following a protracted decline.

Unique Three River  and Example

The up/down gap side-by-side white lines is a rare three-candle continuation pattern that occurs on candlestick charts.

Table of Contents
What Is Up/Down Gap Side-by-Side White Lines? The down gap side-by-side white lines is a bearish continuation pattern with the following characteristics:
1.  The market is in a downtrend.
2.  The first candle is a black candle.
3.  The second candle is a white candle that opens below the close of the first candle (gap down).
4.  The third candle is a white candle with a real body that's the same length as the second candle and opens at the same level or lower than the real body of the first candle.
The side-by-side white lines pattern is moderately accurate in predicting a continuation of the current trend, but it is somewhat uncommon. Understanding Up/Down Gap Side-by-Side White Lines
Up/Down Gap Side-By-Side White Lines Psychology
Up Gap Side-By-Side White Lines Example
Up/Down Gap Side By Side White Lines Limitations
The up/down gap side-by-side white lines is a three-candle continuation pattern that occurs on candlestick charts. The pattern has moderate reliability in terms of the trend continuing after the pattern, but quite often the price move after the pattern will be muted, indicating it is not a highly significant pattern.
The up version is a large up (white or green) candle followed by a gap and then two more white candles of similar size to each other. The difference between up/down gap side-by-side white lines and a three outside up/down candlestick pattern is that, unlike the former pattern, the latter is a reversal pattern, not a continuation pattern.

Up/Down Gap Side-by-Side White Lines

The gap three methods is a three-bar Japanese candlestick pattern that indicates a continuation of the current trend.

The Gap Three Methods is a three-bar Japanese candlestick pattern that indicates a continuation of the current trend. 4.  The third bar is a black candle that has an open within the real body of the first candle and a close within the real body of the second candle. 4.  The third bar is a white candle that has an open within the real body of the second candle and a close within the real body of the first candle. The Downside Gap Three Methods pattern suggests a bearish continuation of the trend.
The Upside Gap Three methods is a bullish continuation pattern with the following characteristics:
1.  The market is in an uptrend. 3.  The second bar is a white candle with a long real body where the shadows over both candles don’t overlap.

Upside/Downside Gap Three Methods  and Example

Weak form efficiency is one of the degrees of efficient market hypothesis that claims all past prices of a stock are reflected in today's stock price. 

A Random Walk Down Wall Street: The Time-tested Strategy for Successful Investing

The book, in addition to touching on random walk theory, describes the efficient market hypothesis and the other two degrees of efficient market hypothesis: semi-strong form efficiency and strong form efficiency. Advocates of weak form efficiency believe all current information is reflected in stock prices and past information has no relationship with current market prices. Weak form efficiency claims that past price movements, volume and earnings data do not affect a stock’s price and can’t be used to predict its future direction. Unlike weak form efficiency, the other forms believe that past, present and future information affects stock price movements to varying degrees.

Weak Form Efficiency

A Wolfe Wave is a pattern used in technical analysis to time trades around a breakout.

A Wolfe Wave is a chart pattern composed of five wave patterns in price that imply an underlying equilibrium price. Levels of support correspond to prices low enough to attract enough demand to stabilize and raise share prices, while levels of resistance correspond to prices high enough to cause shareholders to sell shares and take profits, reducing demand levels and causing prices to level off or drop. According to the theory behind the pattern, a line drawn from the point at the beginning of the first wave and passing through the beginning of the fourth wave predicts a target price for the end of the fifth wave. A Wolfe Wave is a chart pattern composed of five wave patterns in price that imply an underlying equilibrium price. When technical analysts look for patterns such as Wolfe Waves, they attempt to profit off of a breakout, where share prices move outside of the channel formed by support and resistance levels.

Wolfe Wave

The Worden Stochastics indicator plots the percentile rank of the latest closing price compared to other closing values in the lookback period.

The Worden Stochastics indicator represents the percentile rank of the most recent closing price compared to all of the other closing values over a specified lookback period. Traders use the indicator to determine if a particular security is overbought or oversold, to provide trade signals, and spot divergences that could signal a price reversal. If the price is making higher peaks while the stochastic is making lower peaks, that could signal a potential downside reversal in the price. The Worden Stochastics indicator represents the percentile rank of the most recent closing price compared to all of the other closing values over a specified lookback period. Like other stochastics, the Worden version provides overbought and oversold levels, as well as potential trade signals using signal line crossovers.

Advanced Technical Analysis Concepts

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Terms in Advanced Technical Analysis Concepts