TECHNICAL INDICATORS
On-Balance Volume
On-balance volume (OBV) is a technical analysis indicator intended to relate price and volume in the stock market. OBV is based on a cumulative total volume.[1]
Because OBV is a cumulative result, the value of OBV depends upon the starting point of the calculation.
Total volume for each day is assigned a positive or negative value depending on prices being higher or lower that day. A higher close results in the volume for that day to get a positive value, while a lower close results in negative value.[2] So, when prices are going up, OBV should be going up too, and when prices make a new rally high, then OBV should too. If OBV fails to go past its previous rally high, then this is a negative divergence, suggesting a weak move.[3]
The technique, originally called "continuous volume" by Woods and Vignola, was later named "on-balance volume" by Joseph Granville who popularized the technique in his 1963 book Granville's New Key to Stock Market Profits.[1] The index can be applied to stocks individually based upon their daily up or down close, or to the market as a whole, using breadth of market data, i.e. the advance/decline ratio.[1]
OBV is generally used to confirm price moves.[4] The idea is that volume is higher on days where the price move is in the dominant direction, for example in a strong uptrend there is more volume on up days than down days.[5]
https://en.wikipedia.org/wiki/On-balance_volume
Other price × volume indicators:
Accumulation/Distribution Line
The accumulation/distribution line or accumulation/distribution index in the stock market, is a technical analysis indicator intended to relate price and volume, which supposedly acts as a leading indicator of price movements.[1]
This ranges from -1 when the close is the low of the day, to +1 when it's the high. For instance if the close is 3/4 the way up the range then CLV is +0.5. The accumulation/distribution index adds up volume multiplied by the CLV factor, i.e.
The starting point for the acc/dist total, i.e. the zero point, is arbitrary, only the shape of the resulting indicator is used, not the actual level of the total.
The name accumulation/distribution comes from the idea that during accumulation buyers are in control and the price will be bid up through the day, or will make a recovery if sold down, in either case more often finishing near the day's high than the low. The opposite applies during distribution.
The accumulation/distribution index is similar to on balance volume, but acc/dist is based on the close within the day's range, instead of the close-to-close up or down that the latter uses.
A Chaikin oscillator is formed by subtracting a 10-day exponential moving average from a 3-day exponential moving average of the accumulation/distribution index. Being an indicator of an indicator, it can give various sell or buy signals, depending on the context and other indicators.
Dimensional analysis - explains why volume and price are multiplied (not divided) in such indicators
https://en.wikipedia.org/wiki/Accumulation/distribution_index
Average Directional Index
The average directional movement index (ADX) was developed in 1978 by J. Welles Wilder as an indicator of trend strength in a series of prices of a financial instrument.[1] ADX has become a widely used indicator for technical analysts, and is provided as a standard in collections of indicators offered by various trading platforms.
Calculations
The ADX is a combination of two other indicators developed by Wilder, the positive directional indicator (abbreviated +DI) and negative directional indicator (-DI).[2] The ADX combines them and smooths the result with a smoothed moving average.
To calculate +DI and -DI, one needs price data consisting of high, low, and closing prices each period (typically each day). One first calculates the directional movement (+DM and -DM):
UpMove = today's high − yesterday's high
DownMove = yesterday's low − today's low
if UpMove > DownMove and UpMove > 0, then +DM = UpMove, else +DM = 0
if DownMove > UpMove and DownMove > 0, then -DM = DownMove, else -DM = 0
After selecting the number of periods (Wilder used 14 days originally), +DI and -DI are:
+DI = 100 times the smoothed moving average of (+DM) divided by average true range
-DI = 100 times the smoothed moving average of (-DM) divided by average true range
The smoothed moving average is calculated over the number of periods selected, and the average true range is a smoothed average of the true ranges. Then:
ADX = 100 times the smoothed moving average of the absolute value of (+DI − -DI) divided by (+DI + -DI)
Variations of this calculation typically involve using different types of moving averages, such as an exponential moving average, a weighted moving average or an adaptive moving average.[3]
Interpretation
The ADX does not indicate trend direction or momentum, only trend strength.[4] It is a lagging indicator; that is, a trend must have established itself before the ADX will generate a signal that a trend is under way. ADX will range between 0 and 100. Generally, ADX readings below 20 indicate trend weakness, and readings above 40 indicate trend strength. An extremely strong trend is indicated by readings above 50. Alternative interpretations have also been proposed and accepted among technical analysts. For example it has been shown how ADX is a reliable coincident indicator of classical chart pattern development, whereby ADX readings below 20 occur just prior to pattern breakouts.[5] The value of the ADX is proportional to the slope of the trend. The slope of the ADX line is proportional to the acceleration of the price movement (changing trend slope). If the trend is a constant slope then the ADX value tends to flatten out.[6]
Timing
Various market timing methods have been devised using ADX. One of these methods is discussed by Alexander Elder in his book Trading for a Living. One of the best buy signals is when ADX turns up when below both Directional Lines and +DI is above -DI. You would sell when ADX turns back down.[7]
https://en.wikipedia.org/wiki/Average_directional_movement_index
MACD
MACD, short for moving average convergence/divergence, is a trading indicator used in technical analysis of securities prices, created by Gerald Appel in the late 1970s.[1] It is designed to reveal changes in the strength, direction, momentum, and duration of a trend in a stock's price.
The MACD indicator[2] (or "oscillator") is a collection of three time series calculated from historical price data, most often the closing price. These three series are: the MACD series proper, the "signal" or "average" series, and the "divergence" series which is the difference between the two. The MACD series is the difference between a "fast" (short period) exponential moving average (EMA), and a "slow" (longer period) EMA of the price series. The average series is an EMA of the MACD series itself.
The MACD indicator thus depends on three time parameters, namely the time constants of the three EMAs. The notation "MACD(a,b,c)" usually denotes the indicator where the MACD series is the difference of EMAs with characteristic times a and b, and the average series is an EMA of the MACD series with characteristic time c. These parameters are usually measured in days. The most commonly used values are 12, 26, and 9 days, that is, MACD(12,26,9). As true with most of the technical indicators, MACD also finds its period settings from the old days when technical analysis used to be mainly based on the daily charts. The reason was the lack of the modern trading platforms which show the changing prices every moment. As the working week used to be 6-days, the period settings of (12, 26, 9) represent 2 weeks, 1 month and one and a half week. Now when the trading weeks have only 5 days, possibilities of changing the period settings cannot be overruled. However, it is always better to stick to the period settings which are used by the majority of traders as the buying and selling decisions based on the standard settings further push the prices in that direction.
The MACD and average series are customarily displayed as continuous lines in a plot whose horizontal axis is time, whereas the divergence is shown as a bar chart (often called a histogram).
MACD indicator showing vertical lines (histogram)
A fast EMA responds more quickly than a slow EMA to recent changes in a stock's price. By comparing EMAs of different periods, the MACD series can indicate changes in the trend of a stock. It is claimed that the divergence series can reveal subtle shifts in the stock's trend.
Since the MACD is based on moving averages, it is a lagging indicator. As a future metric of price trends, the MACD is less useful for stocks that are not trending (trading in a range) or are trading with unpredictable price action. Hence the trends will already be completed or almost done by the time MACD shows the trend.
The formula for the MACD line is based on two exponential moving averages of the close prices, usually with the periods of 12 and 26:[5]
The signal line is then built as the exponential moving average of the MACD line:
Mathematical interpretation
In signal processing terms, the MACD series is a filtered measure of the derivative of the input (price) series with respect to time. (The derivative is called "velocity" in technical stock analysis.) MACD estimates the derivative as if it were calculated and then filtered by the two low-pass filters in tandem, multiplied by a "gain" equal to the difference in their time constants. It also can be seen to approximate the derivative as if it were calculated and then filtered by a single low pass exponential filter (EMA) with time constant equal to the sum of time constants of the two filters, multiplied by the same gain.[6] So, for the standard MACD filter time constants of 12 and 26 days, the MACD derivative estimate is filtered approximately by the equivalent of a low-pass EMA filter of 38 days. The time derivative estimate (per day) is the MACD value divided by 14.
The average series is also a derivative estimate, with an additional low-pass filter in tandem for further smoothing (and additional lag). The difference between the MACD series and the average series (the divergence series) represents a measure of the second derivative of price with respect to time ("acceleration" in technical stock analysis). This estimate has the additional lag of the signal filter and an additional gain factor equal to the signal filter constant.
Classification
The MACD can be classified as an absolute price oscillator (APO), because it deals with the actual prices of moving averages rather than percentage changes. A percentage price oscillator (PPO), on the other hand, computes the difference between two moving averages of price divided by the longer moving average value.
While an APO will show greater levels for higher priced securities and smaller levels for lower priced securities, a PPO calculates changes relative to price. Subsequently, a PPO is preferred when: comparing oscillator values between different securities, especially those with substantially different prices; or comparing oscillator values for the same security at significantly different times, especially a security whose value has changed greatly.
Another member of the price oscillator family is the detrended price oscillator (DPO), which ignores long term trends while emphasizing short term patterns.
Trading interpretation
Exponential moving averages highlight recent changes in a stock's price. By comparing EMAs of different lengths, the MACD series gauges changes in the trend of a stock. The difference between the MACD series and its average is claimed to reveal subtle shifts in the strength and direction of a stock's trend. It may be necessary to correlate the signals with the MACD to indicators like RSI power.
Some traders attribute special significance to the MACD line crossing the signal line, or the MACD line crossing the zero axis. Significance is also attributed to disagreements between the MACD line or the difference line and the stock price (specifically, higher highs or lower lows on the price series that are not matched in the indicator series).
Signal-line crossover
A "signal-line crossover" occurs when the MACD and average lines cross; that is, when the divergence (the bar graph) changes sign. The standard interpretation of such an event is a recommendation to buy if the MACD line crosses up through the average line (a "bullish" crossover), or to sell if it crosses down through the average line (a "bearish" crossover).[7] These events are taken as indications that the trend in the stock is about to accelerate in the direction of the crossover.
Zero crossover
A "zero crossover" event occurs when the MACD series changes sign, that is, the MACD line crosses the horizontal zero axis. This happens when there is no difference between the fast and slow EMAs of the price series. A change from positive to negative MACD is interpreted as "bearish", and from negative to positive as "bullish". Zero crossovers provide evidence of a change in the direction of a trend but less confirmation of its momentum than a signal line crossover.
Divergence
A "positive divergence" or "bullish divergence" occurs when the price makes a new low but the MACD does not confirm with a new low of its own. A "negative divergence" or "bearish divergence" occurs when the price makes a new high but the MACD does not confirm with a new high of its own.[8] A divergence with respect to price may occur on the MACD line and/or the MACD Histogram.[9]
Timing
The MACD is only as useful as the context in which it is applied. An analyst might apply the MACD to a weekly scale before looking at a daily scale, in order to avoid making short term trades against the direction of the intermediate trend.[10] Analysts will also vary the parameters of the MACD to track trends of varying duration. One popular short-term set-up, for example, is the (5,35,5).
False signals
Like any forecasting algorithm, the MACD can generate false signals. A false positive, for example, would be a bullish crossover followed by a sudden decline in a stock. A false negative would be a situation where there is bearish crossover, yet the stock accelerated suddenly upwards.
A prudent strategy may be to apply a filter to signal line crossovers to ensure that they have held up. An example of a price filter would be to buy if the MACD line breaks above the signal line and then remains above it for three days. As with any filtering strategy, this reduces the probability of false signals but increases the frequency of missed profit.
Analysts use a variety of approaches to filter out false signals and confirm true ones.
A MACD crossover of the signal line indicates that the direction of the acceleration is changing. The MACD line crossing zero suggests that the average velocity is changing direction.
Relative Strength Index
The relative strength index (RSI) is a technical indicator used in the analysis of financial markets. It is intended to chart the current and historical strength or weakness of a stock or market based on the closing prices of a recent trading period. The indicator should not be confused with relative strength.
The RSI is classified as a momentum oscillator, measuring the velocity and magnitude of price movements. Momentum is the rate of the rise or fall in price. The relative strength RS is given as the ratio of higher closes to lower closes, with closes here meaning averages of absolute values of price changes. The RSI computes momentum as the ratio of higher closes to overall closes: stocks which have had more or stronger positive changes have a higher RSI than stocks which have had more or stronger negative changes.
The RSI is most typically used on a 14-day timeframe, measured on a scale from 0 to 100, with high and low levels marked at 70 and 30, respectively. Short or longer timeframes are used for alternately shorter or longer outlooks. High and low levels—80 and 20, or 90 and 10—occur less frequently but indicate stronger momentum.
The relative strength index was developed by J. Welles Wilder and published in a 1978 book, New Concepts in Technical Trading Systems, and in Commodities magazine (now Modern Trader magazine) in the June 1978 issue.[1] It has become one of the most popular oscillator indices.[2]
The RSI provides signals that tell investors to buy when the security or currency is oversold and to sell when it is overbought. [3]
RSI with recommended parameters and its day-to-day optimization was tested and compared with other strategies in Marek and Šedivá (2017). The testing was randomised in time and companies (e.g., Apple, Exxon Mobil, IBM, Microsoft) and showed that RSI can still produce good results; however, in longer time it is usually overcome by the simple buy-and-hold strategy. [4]
For each trading period an upward change U or downward change D is calculated. Up periods are characterized by the close being higher than the previous close:
D = 0
Conversely, a down period is characterized by the close being lower than the previous period's close (note that D is nonetheless a positive number),
U = 0
If the last close is the same as the previous, both U and D are zero. The average U and D are calculated using an n-period smoothed or modified moving average (SMMA or MMA) which is an exponentially smoothed Moving Average with α = 1/period. Some commercial packages, like AIQ, use a standard exponential moving average (EMA) as the average instead of Wilder's SMMA.
Wilder originally formulated the calculation of the moving average as: newval = (prevval * (period - 1) + newdata) / period. This is fully equivalent to the aforementioned exponential smoothing. New data is simply divided by period which is equal to the alpha calculated value of 1/period. Previous average values are modified by (period -1)/period which in effect is period/period - 1/period and finally 1 - 1/period which is 1 - alpha.
The ratio of these averages is the relative strength or relative strength factor:
If the average of D values is zero, then according to the equation, the RS value will approach infinity, so that the resulting RSI, as computed below, will approach 100.
The relative strength factor is then converted to a relative strength index between 0 and 100:[1]
The smoothed moving averages should be appropriately initialized with a simple moving average using the first n values in the price series.
Interpretation
Basic configuration
Relative strength index 7-period
Bitcoin, RSI-14, bearish divergence occurs
The RSI is presented on a graph above or below the price chart. The indicator has an upper line, typically at 70, a lower line at 30, and a dashed mid-line at 50. Wilder recommended a smoothing period of 14 (see exponential smoothing, i.e. α = 1/14 or N = 14).
Principles
Wilder posited[1] that when price moves up very rapidly, at some point it is considered overbought. Likewise, when price falls very rapidly, at some point it is considered oversold. In either case, Wilder deemed a reaction or reversal imminent.
The level of the RSI is a measure of the stock's recent trading strength. The slope of the RSI is directly proportional to the velocity of a change in the trend. The distance traveled by the RSI is proportional to the magnitude of the move.
Wilder believed that tops and bottoms are indicated when RSI goes above 70 or drops below 30. Traditionally, RSI readings greater than the 70 level are considered to be in overbought territory, and RSI readings lower than the 30 level are considered to be in oversold territory. In between the 30 and 70 level is considered neutral, with the 50 level a sign of no trend. [5]
Divergence
Wilder further believed that divergence between RSI and price action is a very strong indication that a market turning point is imminent. Bearish divergence occurs when price makes a new high but the RSI makes a lower high, thus failing to confirm. Bullish divergence occurs when price makes a new low but RSI makes a higher low.[1]: 68
Overbought and oversold conditions
Wilder thought that "failure swings" above 50 and below 50 on the RSI are strong indications of market reversals.[6] For example, assume the RSI hits 76, pulls back to 72, then rises to 77. If it falls below 72, Wilder would consider this a "failure swing" above 70.
Finally, Wilder wrote that chart formations and areas of support and resistance could sometimes be more easily seen on the RSI chart as opposed to the price chart. The center line for the relative strength index is 50, which is often seen as both the support and resistance line for the indicator.
If the relative strength index is below 50, it generally means that the stock's losses are greater than the gains. When the relative strength index is above 50, it generally means that the gains are greater than the losses.
Uptrends and downtrends
In addition to Wilder's original theories of RSI interpretation, Andrew Cardwell has developed several new interpretations of RSI to help determine and confirm trend. First, Cardwell noticed that uptrends generally traded between RSI 40 and 80, while downtrends usually traded between RSI 60 and 20. Cardwell observed when securities change from uptrend to downtrend and vice versa, the RSI will undergo a "range shift."
Example of RSI Indicator Divergence
Next, Cardwell noted that bearish divergence: 1) only occurs in uptrends, and 2) mostly only leads to a brief correction instead of a reversal in trend. Therefore, bearish divergence is a sign confirming an uptrend. Similarly, bullish divergence is a sign confirming a downtrend.
Reversals
Finally, Cardwell discovered the existence of positive and negative reversals in the RSI. Reversals are the opposite of divergence. For example, a positive reversal occurs when an uptrend price correction results in a higher low compared to the last price correction, while RSI results in a lower low compared to the prior correction. A negative reversal happens when a downtrend rally results in a lower high compared to the last downtrend rally, but RSI makes a higher high compared to the prior rally.
In other words, despite stronger momentum as seen by the higher high or lower low in the RSI, price could not make a higher high or lower low. This is evidence the main trend is about to resume. Cardwell noted that positive reversals only happen in uptrends while negative reversals only occur in downtrends, and therefore their existence confirms the trend.
Cutler's RSI
A variation called Cutler's RSI is based on a simple moving average of U and D,[7] instead of the exponential average above. Cutler had found that since Wilder used a smoothed moving average to calculate RSI, the value of Wilder's RSI depended upon where in the data file his calculations started. Cutler termed this Data Length Dependency. Cutler's RSI is not data length dependent, and returns consistent results regardless of the length of, or the starting point within a data file.
{\displaystyle RS={\frac {{\text{SMA}}(U,n)}{{\text{SMA}}(D,n)}}}
Cutler's RSI generally comes out slightly different from the normal Wilder RSI, but the two are similar, since SMA and SMMA are also similar.
MACD, moving average convergence/divergence
True strength index, a similar momentum-based indicator
Stochastic oscillator
In technical analysis of securities trading, the stochastic oscillator is a momentum indicator that uses support and resistance levels. George Lane developed this indicator in the late 1950s.[1] The term stochastic refers to the point of a current price in relation to its price range over a period of time.[2] This method attempts to predict price turning points by comparing the closing price of a security to its price range.
The 5-period stochastic oscillator in a daily timeframe is defined as follows:
where
{High} _{5}}
and
{Low} _{5}}
are the highest and lowest prices in the last 5 days respectively, while %D is the N-day moving average of %K (the last N values of %K). Usually this is a simple moving average, but can be an exponential moving average for a less standardized weighting for more recent values. There is only one valid signal in working with %D alone — a divergence between %D and the analyzed security.[3]
The calculation above finds the range between an asset's high and low price during a given period of time. The current security's price is then expressed as a percentage of this range with 0% indicating the bottom of the range and 100% indicating the upper limits of the range over the time period covered.[citation needed] The idea behind this indicator is that prices tend to close near the extremes of the recent range before turning points. The Stochastic oscillator is calculated:
Where
{Price} } is the last closing price
{Low} _{N}} is the lowest price over the last N periods
{High} _{N}} is the highest price over the last N periods
%D} is a 3-period simple moving average of %K, {SMA} _{3}(\%K)}
{-Slow} } is a 3-period simple moving average of %D, {SMA} _{3}(\%D)}
A 3-line Stochastics will give an anticipatory signal in %K, a signal in the turnaround of %D at or before a bottom, and a confirmation of the turnaround in %D-Slow.[4] Typical values for N are 5, 9, or 14 periods. Smoothing the indicator over 3 periods is standard.
According to George Lane, the Stochastics indicator is to be used with cycles, Elliott Wave Theory and Fibonacci retracement for timing. In low margin, calendar futures spreads, one might use Wilders parabolic as a trailing stop after a stochastics entry. A centerpiece of his teaching is the divergence and convergence of trendlines drawn on stochastics, as diverging/converging to trendlines drawn on price cycles. Stochastics predicts tops and bottoms.
Interpretation
The signal to act is when there is a divergence-convergence, in an extreme area, with a crossover on the right hand side, of a cycle bottom.[3] As plain crossovers can occur frequently, one typically waits for crossovers occurring together with an extreme pullback, after a peak or trough in the %D line. If price volatility is high, an exponential moving average of the %D indicator may be taken, which tends to smooth out rapid fluctuations in price.
Stochastics attempts to predict turning points by comparing the closing price of a security to its price range. Prices tend to close near the extremes of the recent range just before turning points. In the case of an uptrend, prices tend to make higher highs, and the settlement price usually tends to be in the upper end of that time period's trading range. When the momentum starts to slow, the settlement prices will start to retreat from the upper boundaries of the range, causing the stochastic indicator to turn down at or before the final price high.[5]
Stochastic divergence.
An alert or set-up is present when the %D line is in an extreme area and diverging from the price action. The actual signal takes place when the faster % K line crosses the % D line.[6]
Divergence-convergence is an indication that the momentum in the market is waning and a reversal may be in the making. The chart below illustrates an example of where a divergence in stochastics, relative to price, forecasts a reversal in the price's direction.
An event known as "stochastic pop" occurs when prices break out and keep going. This is interpreted as a signal to increase the current position, or liquidate if the direction is against the current position.[7]
Williams %R – Equivalent of %K, mirrored around the 0%-axis
