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Williams’ Percent Range (%R)

Williams’ Percent Range Technical Indicator (%R) is a dynamic technical indicator, which determines whether the market is overbought/oversold. Williams’ %R is very similar to the Stochastic Oscillator. The only difference is that %R has an upside down scale and the Stochastic Oscillator has internal smoothing.

To show the indicator in this upside down fashion, one places a minus symbol before the Williams Percent Range values (for example -30%). One should ignore the minus symbol when conducting the analysis.

Indicator values ranging between 80 and 100% indicate that the market is oversold. Indicator values ranging between 0 and 20% indicate that the market is overbought.

As with all overbought/oversold indicators, it is best to wait for the security’s price to change direction before placing your trades. For example, if an overbought/oversold indicator is showing an overbought condition, it is wise to wait for the security’s price to turn down before selling the security.

An interesting phenomenon of the Williams Percent Range indicator is its uncanny ability to anticipate a reversal in the underlying security’s price. The indicator almost always forms a peak and turns down a few days before the security’s price peaks and turns down. Likewise, Williams Percent Range usually creates a trough and turns up a few days before the security’s price turns up.

Calculation:

TBelow is the formula of the %R indicator calculation, which is very similar to the Stochastic Oscillator formula:

%R = (HIGH(i-n)-CLOSE)/(HIGH(i-n)-LOW(i-n))*100

Where:
CLOSE — is today’s closing price;
HIGH(i-n) — is the highest high over a number (n) of previous periods;
LOW(i-n) — is the lowest low over a number (n) of previous periods.

Ultimate Oscillator

Usually oscillators compare the smoothened price of a financial tool and its value n periods ago. Larry Williams once noticed that the efficiency of such oscillator can vary and depends on the number of single periods you take for the calculation. So he created the Ultimate Oscillator that uses a weighted total of three oscillators with different calculation periods.
Larry Williams first described the oscillator in 1985 in the Technical Analysis of Stocks and Commodities magazine. The values of the indicator vary in a range from zero to 100 and the center is the 50 value. Values below 30 correspond with the overbought zone, and values between 70 and 100 - with the oversold zone.
The oscillator uses three time spaces that you can set manually. On default, they are equal to 7, 14 and 28 periods. Mind that longer periods comprise shorter ones. That means that 28-period values discount 14-period and 7-period values. Therefore, we use the values of the shortest period three times, so these values influence the result of the oscillator most of all.

Larry Williams recommended that you should open a position when a divergence appears. You should buy if:

• a bull divergence appeared: the prices have reached a lower minimum that hasn't been confirmed by a lower minimum of the oscillator;
• the oscillator fell below 30 when such bull divergence appeared;
• then the oscillator rose above the maximum level reached in the time of bull divergence forming. This is the moment when you should buy.

Close long positions if:

• the oscillator rose above 50 and then fell below 45;
• the oscillator rose above 70 (sometimes you'd better wait till it drops below 70);
• sale signals appeared.

Sell if:

• вa bear divergence appeared: the prices have reached a higher maximum that hasn't been confirmed by a higher maximum of the oscillator;
• the oscillator grew above 50 when at a bear divergence;
• the oscillator fell below the minimum level reached in the time of bear divergence forming.

Close short positions if:

• the oscillator grew above 65;
• the oscillator fell below 30
• purchase signals appeared.

Calculation:

1. Define current "True Low" (TL) — the least of two values: the current minimum and the precious closing price.

   TL (i) = MIN (LOW (i) || CLOSE (i - 1))

2. Find current "Buying Pressure" (BP). It is equal to the difference between current closing price and current True Low.
   

   BP (i) = CLOSE (i) - TL (i)

3. Define the "True Range" (TR). It is the greatest of the following differences: current maximum and minimum; current maximum and previous closing price; current minimum and previous closing price.
   

   TR (i) = MAX (HIGH (i) - LOW (i) || HIGH (i) - CLOSE (i - 1) || CLOSE (i - 1) - LOW (i))

4. Find the sum of BP values for all three periods of calculation:
   

   BPSUM (N) = SUM (BP (i), i)

5. Find the sum of TR values for all three periods of calculation:
   

   TRSUM (N) = SUM (TR (i), i)

6. Calculate the "Raw Ultimate Oscillator" (RawUO)

   RawUO = 4 * (BPSUM (1) / TRSUM (1)) + 2 * (BPSUM (2) / TRSUM (2)) + (BPSUM (3) / TRSUM (3))

7. Calculate the "Ultimate Oscillator" (UO) value according to the formula:
   

   UO = ( RawUO / (4 + 2 + 1)) * 100

Where:
MIN — means the minimum value;
MAX — the maximum value;
|| — a logical OR;
LOW (i) — the minimum price of the current bar;
HIGH (i) — the maximum price of the current bar;
CLOSE (i) — the closing price of the current bar;
CLOSE (i — 1) — the closing price of the previous bar;
TL (i) — the True Low;
BP (i) — the Buying Pressure;
TR (i) — the True Range;
BPSUM (N) — the mathematical sum of BP values for an n period (N equal to 1 corresponds with i=7 bars; N equal to 2 corresponds with i=14 bars; N equal to 3 corresponds with i=28 bars);
TRSUM (N) — the mathematical sum of TR values for an n period (N equal to 1 corresponds with i=7 bars; N equal to 2 corresponds with i=14 bars; N equal to 3 corresponds with i=28 bars);
RawUO — "Raw Ultimate Oscillator";
UO — stands for Ultimate Oscillator.

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Stochastic Oscillator

The Stochastic Oscillator Technical Indicator compares where a security’s price closed relative to its price range over a given time period. The Stochastic Oscillator is displayed as two lines. The main line is called %K. The second line, called %D, is a Moving Average of %K. The %K line is usually displayed as a solid line and the %D line is usually displayed as a dotted line.

There are several ways to interpret a Stochastic Oscillator. Three popular methods include:

• Buy when the Oscillator (either %K or %D) falls below a specific level (e.g., 20) and then rises above that level. Sell when the Oscillator rises above a specific level (e.g., 80) and then falls below that level;
• Buy when the %K line rises above the %D line and sell when the %K line falls below the %D line;
• Look for divergences. For instance: where prices are making a series of new highs and the Stochastic Oscillator is failing to surpass its previous highs.

Calculation:

The Stochastic Oscillator has four variables:

• %K periods. This is the number of time periods used in the stochastic calculation;
• %K Slowing Periods. This value controls the internal smoothing of %K. A value of 1 is considered a fast stochastic; a value of 3 is considered a slow stochastic;
• %D periods. his is the number of time periods used when calculating a moving average of %K;
• %D method. The method (i.e., Exponential, Simple, Smoothed, or Weighted) that is used to calculate %D.

The formula for %K is:

%K = (CLOSE-LOW(%K))/(HIGH(%K)-LOW(%K))*100

Where:
CLOSE — is today’s closing price;
LOW(%K) — is the lowest low in %K periods;
HIGH(%K) — is the highest high in %K periods.

The %D moving average is calculated according to the formula:

%D = SMA(%K, N) 

Where:
N — is the smoothing period;
SMA — is the Simple Moving Average.

Relative Vigor Index (RVI)

The main point of Relative Vigor Index Technical Indicator (RVI) is that on the bull market the closing price is, as a rule, higher, than the opening price. It is the other way round on the bear market. So the idea behind Relative Vigor Index is that the vigor, or energy, of the move is thus established by where the prices end up at the close. To normalize the index to the daily trading range, divide the change of price by the maximum range of prices for the day. To make a more smooth calculation, one uses Simple Moving Average. 10 is the best period. To avoid probable ambiguity one needs to construct a signal line, which is a 4-periodsymmetrically weighted moving average of Relative Vigor Index values. The concurrence of lines serves as a signal to buy or to sell.

Calculation:

RVI = (CLOSE-OPEN)/(HIGH-LOW) 

Where:
OPEN — is the opening price;
HIGH — is the maximum price;
LOW — is the minimum price;
CLOSE — is the closing price.

Relative Strength Index (RSI)

The Relative Strength Index Technical Indicator (RSI) is a price-following oscillator that ranges between 0 and 100. When Wilder introduced the Relative Strength Index, he recommended using a 14-day RSI.. Since then, the 9-day and 25-day Relative Strength Index indicators have also gained popularity.
A popular method of analyzing the RSI is to look for a divergence in which the security is making a new high, but the RSI is failing to surpass its previous high. This divergence is an indication of an impending reversal. When the Relative Strength Index then turns down and falls below its most recent trough, it is said to have completed a "failure swing". The failure swing is considered a confirmation of the impending reversal.
Ways to use Relative Strength Index for chart analysis:

• Tops and bottoms
  The Relative Strength Index usually tops above 70 and bottoms below 30. It usually forms these tops and bottoms before the underlying price chart;
• Chart Formations
  The RSI often forms chart patterns such as head and shoulders or triangles that may or may not be visible on the price chart;
• Failure swing ( Support or Resistance penetrations or breakouts)
  This is where the Relative Strength Index surpasses a previous high (peak) or falls below a recent low (trough);
• Support and Resistance levels
  The Relative Strength Index shows, sometimes more clearly than price themselves, levels of support and resistance.
• Divergences
  As discussed above, divergences occur when the price makes a new high (or low) that is not confirmed by a new high (or low) in the Relative Strength Index. Prices usually correct and move in the direction of the RSI.

Calculation:

RSI = 100-(100/(1+U/D))

Where:
U — is the average number of positive price changes;
D — is the average number of negative price changes.