Rate of Change Ratio 100 Scale (ROCR100)

The Rate of Change Ratio 100 Scale (ROCR100) is a momentum indicator that measures the ratio of the current price to the price n periods ago, multiplied by 100. This scaling makes it more intuitive to read and interpret compared to the standard ROCR. Values are centered around 100, where values above 100 indicate price increases and values below 100 indicate price decreases. The 100-scale format makes it immediately clear whether prices are rising or falling and by what percentage.

Usage

require 'sqa/tai'

prices = [44.34, 44.09, 44.15, 43.61, 44.33, 44.83, 45.10, 45.42, 45.84, 46.08, 46.03, 46.41]

# Calculate 10-period ROCR100
rocr100 = SQA::TAI.rocr100(prices, period: 10)

puts "Current ROCR100: #{rocr100.last.round(2)}"

# Values > 100 mean price is up, < 100 mean price is down
if rocr100.last > 100
  percent_change = rocr100.last - 100
  puts "Price is UP #{percent_change.round(2)}% from #{10} periods ago"
elsif rocr100.last < 100
  percent_change = 100 - rocr100.last
  puts "Price is DOWN #{percent_change.round(2)}% from #{10} periods ago"
else
  puts "Price is UNCHANGED from #{10} periods ago"
end

Parameters

Parameter	Type	Required	Default	Description
prices	Array	Yes	-	Array of price values
period	Integer	No	10	Lookback period for comparison

Returns

Returns an array of ROCR100 values centered around 100. The first period values will be nil.

Formula

ROCR100 = (Current Price / Price n periods ago) × 100

Where: - Current Price = Most recent price - Price n periods ago = Price from n periods back - Result is multiplied by 100 for the scaled format

Calculation Example

# Price today: $46.08
# Price 10 days ago: $44.34
# ROCR100 = (46.08 / 44.34) × 100 = 103.92

# This means:
# - Price is 3.92% higher than 10 periods ago
# - Value above 100 indicates upward momentum

Interpretation

ROCR100 Value	Interpretation
> 110	Strong upward momentum (10%+ gain)
102-110	Moderate upward momentum (2-10% gain)
100-102	Slight upward momentum (0-2% gain)
100	No change in price
98-100	Slight downward momentum (0-2% loss)
90-98	Moderate downward momentum (2-10% loss)
< 90	Strong downward momentum (10%+ loss)

Note: Array elements should be ordered from oldest to newest (chronological order)

Key Interpretation Points

• 100 is the center line: Unlike ROCR which centers at 1.0, ROCR100's 100 baseline is more intuitive
• Direct percentage reading: ROCR100 of 105 means 5% gain, 95 means 5% loss
• Easy mental math: Subtract 100 to get percentage change
• Momentum strength: Distance from 100 indicates momentum strength
• Trend direction: Rising ROCR100 shows strengthening momentum, falling shows weakening

The 100-Scale Advantage

1. Intuitive Reading

The 100-scale format is significantly more intuitive than the standard ROCR (centered at 1.0):

# Standard ROCR vs ROCR100 comparison
prices = [100, 105, 110, 115, 120]

rocr = SQA::TAI.rocr(prices, period: 2)
rocr100 = SQA::TAI.rocr100(prices, period: 2)

# ROCR values (centered at 1.0)
# [nil, nil, 1.05, 1.095, 1.091]
# Harder to interpret: Is 1.05 good? How much change is that?

# ROCR100 values (centered at 100)
# [nil, nil, 105.0, 109.5, 109.1]
# Immediately clear: 5% gain, 9.5% gain, 9.1% gain

2. Mental Math Simplicity

With ROCR100, calculating percentage change is trivial:

rocr100 = SQA::TAI.rocr100(prices, period: 10)
current = rocr100.last

# Simple subtraction gives percentage change
percent_change = current - 100

puts "Price change: #{percent_change.round(2)}%"
# ROCR100 = 107.5 → 7.5% gain
# ROCR100 = 94.3 → 5.7% loss

3. Better Visualization

The 100 baseline is easier to visualize on charts:

# Chart reference levels are more intuitive
rocr100 = SQA::TAI.rocr100(prices, period: 10)

# Common reference levels
puts "Overbought zone (>110):" if rocr100.last > 110
puts "Moderate bullish (100-110):" if rocr100.last.between?(100, 110)
puts "Neutral (98-102):" if rocr100.last.between?(98, 102)
puts "Moderate bearish (90-98):" if rocr100.last.between?(90, 98)
puts "Oversold zone (<90):" if rocr100.last < 90

4. Easier Threshold Setting

Setting trading thresholds is more natural:

prices = load_historical_prices('AAPL')
rocr100 = SQA::TAI.rocr100(prices, period: 10)

# Clear percentage-based thresholds
OVERBOUGHT_THRESHOLD = 110   # 10% gain
OVERSOLD_THRESHOLD = 90      # 10% loss
NEUTRAL_UPPER = 102          # 2% gain
NEUTRAL_LOWER = 98           # 2% loss

case rocr100.last
when (OVERBOUGHT_THRESHOLD..)
  puts "Overbought: #{(rocr100.last - 100).round(2)}% above baseline"
when (...OVERSOLD_THRESHOLD)
  puts "Oversold: #{(100 - rocr100.last).round(2)}% below baseline"
when (NEUTRAL_LOWER..NEUTRAL_UPPER)
  puts "Neutral: Within 2% of baseline"
else
  puts "Trending: #{(rocr100.last - 100).round(2)}% from baseline"
end

Example: Basic Momentum Signals

prices = load_historical_prices('AAPL')
rocr100 = SQA::TAI.rocr100(prices, period: 10)

current = rocr100.last
previous = rocr100[-2]

# Crossover signals at 100 (baseline)
if current > 100 && previous <= 100
  puts "BULLISH SIGNAL: ROCR100 crossed above 100"
  puts "Price momentum turning positive"
  puts "Gain: #{(current - 100).round(2)}%"
elsif current < 100 && previous >= 100
  puts "BEARISH SIGNAL: ROCR100 crossed below 100"
  puts "Price momentum turning negative"
  puts "Loss: #{(100 - current).round(2)}%"
end

# Momentum strength
momentum_strength = (current - 100).abs
case momentum_strength
when 0...2
  puts "Weak momentum (#{momentum_strength.round(2)}%)"
when 2...5
  puts "Moderate momentum (#{momentum_strength.round(2)}%)"
when 5...10
  puts "Strong momentum (#{momentum_strength.round(2)}%)"
else
  puts "Extreme momentum (#{momentum_strength.round(2)}%)"
end

Example: Trend Confirmation

prices = load_historical_prices('MSFT')
rocr100 = SQA::TAI.rocr100(prices, period: 10)

# Confirm trend strength with ROCR100
current = rocr100.last
recent_avg = rocr100[-5..-1].sum / 5.0

puts "Current ROCR100: #{current.round(2)}"
puts "5-period average: #{recent_avg.round(2)}"

# Sustained momentum above 100
if rocr100[-5..-1].all? { |v| v && v > 100 }
  puts "Strong uptrend: ROCR100 above 100 for 5 periods"
  avg_gain = recent_avg - 100
  puts "Average gain: #{avg_gain.round(2)}%"
elsif rocr100[-5..-1].all? { |v| v && v < 100 }
  puts "Strong downtrend: ROCR100 below 100 for 5 periods"
  avg_loss = 100 - recent_avg
  puts "Average loss: #{avg_loss.round(2)}%"
else
  puts "Mixed momentum: No clear trend"
end

# Accelerating vs decelerating momentum
if current > recent_avg && current > 100
  puts "Momentum accelerating to the upside"
elsif current < recent_avg && current < 100
  puts "Momentum accelerating to the downside"
elsif current < recent_avg && current > 100
  puts "Uptrend but momentum decelerating"
elsif current > recent_avg && current < 100
  puts "Downtrend but momentum decelerating"
end

Example: Overbought/Oversold Conditions

prices = load_historical_prices('TSLA')
rocr100_10 = SQA::TAI.rocr100(prices, period: 10)
rocr100_20 = SQA::TAI.rocr100(prices, period: 20)

current_10 = rocr100_10.last
current_20 = rocr100_20.last

puts "10-period ROCR100: #{current_10.round(2)}"
puts "20-period ROCR100: #{current_20.round(2)}"

# Overbought conditions (percentage thresholds)
if current_10 > 110 && current_20 > 105
  puts "OVERBOUGHT across multiple timeframes"
  puts "10-period: #{(current_10 - 100).round(2)}% gain"
  puts "20-period: #{(current_20 - 100).round(2)}% gain"
  puts "Consider taking profits or waiting for pullback"

  # Extreme overbought
  if current_10 > 120
    puts "EXTREME OVERBOUGHT: 20%+ gain in 10 periods"
    puts "High probability of mean reversion"
  end

# Oversold conditions
elsif current_10 < 90 && current_20 < 95
  puts "OVERSOLD across multiple timeframes"
  puts "10-period: #{(100 - current_10).round(2)}% loss"
  puts "20-period: #{(100 - current_20).round(2)}% loss"
  puts "Potential buying opportunity"

  # Extreme oversold
  if current_10 < 80
    puts "EXTREME OVERSOLD: 20%+ loss in 10 periods"
    puts "High probability of bounce"
  end
end

Example: Divergence Detection

prices = load_historical_prices('NVDA')
rocr100 = SQA::TAI.rocr100(prices, period: 10)

# Find recent highs
price_high_1 = prices[-20..-10].max
price_high_2 = prices[-9..-1].max

# Find corresponding ROCR100 values
rocr100_high_1 = rocr100[-20..-10].compact.max
rocr100_high_2 = rocr100[-9..-1].compact.max

# Bearish divergence
if price_high_2 > price_high_1 && rocr100_high_2 < rocr100_high_1
  puts "BEARISH DIVERGENCE detected"
  puts "Price: #{price_high_1.round(2)} -> #{price_high_2.round(2)}"
  puts "ROCR100: #{rocr100_high_2.round(2)} -> #{rocr100_high_1.round(2)}"
  puts "Momentum weakening despite higher prices"

  # Calculate divergence magnitude
  price_change = ((price_high_2 / price_high_1 - 1) * 100).round(2)
  momentum_decline = (rocr100_high_2 - rocr100_high_1).round(2)

  puts "Price gained: #{price_change}%"
  puts "Momentum lost: #{momentum_decline.abs} points"
end

# Bullish divergence
price_low_1 = prices[-20..-10].min
price_low_2 = prices[-9..-1].min

rocr100_low_1 = rocr100[-20..-10].compact.min
rocr100_low_2 = rocr100[-9..-1].compact.min

if price_low_2 < price_low_1 && rocr100_low_2 > rocr100_low_1
  puts "BULLISH DIVERGENCE detected"
  puts "Price: #{price_low_1.round(2)} -> #{price_low_2.round(2)}"
  puts "ROCR100: #{rocr100_low_1.round(2)} -> #{rocr100_low_2.round(2)}"
  puts "Momentum strengthening despite lower prices"

  # Calculate divergence magnitude
  price_change = ((1 - price_low_2 / price_low_1) * 100).round(2)
  momentum_gain = (rocr100_low_2 - rocr100_low_1).round(2)

  puts "Price lost: #{price_change}%"
  puts "Momentum gained: #{momentum_gain} points"
end

Example: Multi-Period Analysis

prices = load_historical_prices('SPY')

# Calculate multiple timeframes
rocr100_5 = SQA::TAI.rocr100(prices, period: 5)
rocr100_10 = SQA::TAI.rocr100(prices, period: 10)
rocr100_20 = SQA::TAI.rocr100(prices, period: 20)

puts "5-period ROCR100: #{rocr100_5.last.round(2)} (#{(rocr100_5.last - 100).round(2)}%)"
puts "10-period ROCR100: #{rocr100_10.last.round(2)} (#{(rocr100_10.last - 100).round(2)}%)"
puts "20-period ROCR100: #{rocr100_20.last.round(2)} (#{(rocr100_20.last - 100).round(2)}%)"

# All timeframes aligned above 100 = strong bullish
if rocr100_5.last > 100 && rocr100_10.last > 100 && rocr100_20.last > 100
  puts "\nSTRONG BULLISH: All timeframes above 100"
  puts "Short-term momentum: #{(rocr100_5.last - 100).round(2)}%"
  puts "Medium-term momentum: #{(rocr100_10.last - 100).round(2)}%"
  puts "Long-term momentum: #{(rocr100_20.last - 100).round(2)}%"

  # Check if momentum is accelerating
  if rocr100_5.last > rocr100_10.last && rocr100_10.last > rocr100_20.last
    puts "Momentum ACCELERATING across timeframes"
  end

# All timeframes aligned below 100 = strong bearish
elsif rocr100_5.last < 100 && rocr100_10.last < 100 && rocr100_20.last < 100
  puts "\nSTRONG BEARISH: All timeframes below 100"
  puts "Short-term decline: #{(100 - rocr100_5.last).round(2)}%"
  puts "Medium-term decline: #{(100 - rocr100_10.last).round(2)}%"
  puts "Long-term decline: #{(100 - rocr100_20.last).round(2)}%"

  # Check if decline is accelerating
  if rocr100_5.last < rocr100_10.last && rocr100_10.last < rocr100_20.last
    puts "Decline ACCELERATING across timeframes"
  end

# Mixed signals
else
  puts "\nMIXED SIGNALS: Timeframes diverging"

  # Potential reversal patterns
  if rocr100_5.last < 100 && rocr100_20.last > 100
    puts "Short-term pullback in long-term uptrend"
    puts "Potential buying opportunity"
  elsif rocr100_5.last > 100 && rocr100_20.last < 100
    puts "Short-term bounce in long-term downtrend"
    puts "Potential selling opportunity"
  end
end

Example: Trading Strategy with ROCR100

prices = load_historical_prices('AAPL')
rocr100 = SQA::TAI.rocr100(prices, period: 10)

# Define thresholds
STRONG_BUY = 90      # 10% decline
BUY = 95             # 5% decline
NEUTRAL_LOW = 98     # 2% decline
NEUTRAL_HIGH = 102   # 2% gain
SELL = 105           # 5% gain
STRONG_SELL = 110    # 10% gain

current = rocr100.last
price = prices.last

case current
when (...STRONG_BUY)
  puts "STRONG BUY SIGNAL at $#{price.round(2)}"
  puts "ROCR100: #{current.round(2)} (#{(100 - current).round(2)}% below baseline)"
  puts "Price down significantly, extreme oversold"

when (STRONG_BUY...BUY)
  puts "BUY SIGNAL at $#{price.round(2)}"
  puts "ROCR100: #{current.round(2)} (#{(100 - current).round(2)}% below baseline)"
  puts "Price declining, oversold condition"

when (BUY...NEUTRAL_LOW)
  puts "Weak sell at $#{price.round(2)}"
  puts "ROCR100: #{current.round(2)} (#{(100 - current).round(2)}% below baseline)"
  puts "Slight decline, approaching neutral"

when (NEUTRAL_LOW..NEUTRAL_HIGH)
  puts "NEUTRAL at $#{price.round(2)}"
  puts "ROCR100: #{current.round(2)} (near baseline)"
  puts "No clear momentum signal"

when (NEUTRAL_HIGH..SELL)
  puts "Weak buy at $#{price.round(2)}"
  puts "ROCR100: #{current.round(2)} (#{(current - 100).round(2)}% above baseline)"
  puts "Slight gain, approaching overbought"

when (SELL..STRONG_SELL)
  puts "SELL SIGNAL at $#{price.round(2)}"
  puts "ROCR100: #{current.round(2)} (#{(current - 100).round(2)}% above baseline)"
  puts "Price advancing, overbought condition"

when (STRONG_SELL..)
  puts "STRONG SELL SIGNAL at $#{price.round(2)}"
  puts "ROCR100: #{current.round(2)} (#{(current - 100).round(2)}% above baseline)"
  puts "Price up significantly, extreme overbought"
end

# Additional context
trend = rocr100[-5..-1].compact
if trend.all? { |v| v > current }
  puts "Warning: Momentum declining"
elsif trend.all? { |v| v < current }
  puts "Note: Momentum building"
end

Common Settings

Period	Use Case	Typical Range
5	Very short-term, day trading	95-105
10	Standard, short-term trends	90-110
14	Swing trading	90-110
20	Intermediate trends	85-115
30	Long-term momentum	80-120

Advanced Techniques

1. Rate of Change of ROCR100

Monitor how quickly momentum is changing:

rocr100 = SQA::TAI.rocr100(prices, period: 10)

# Calculate ROC of ROCR100 itself
roc_of_rocr100 = []
rocr100.each_cons(5) do |window|
  if window.all?
    change = window.last - window.first
    roc_of_rocr100 << change
  end
end

if roc_of_rocr100.last > 2
  puts "Momentum accelerating rapidly"
elsif roc_of_rocr100.last < -2
  puts "Momentum decelerating rapidly"
end

2. ROCR100 Bands

Create bands around 100 for trading zones:

# Calculate average distance from 100
deviations = rocr100.compact.map { |v| (v - 100).abs }
avg_deviation = deviations.sum / deviations.length

upper_band = 100 + avg_deviation
lower_band = 100 - avg_deviation

puts "ROCR100 Bands: #{lower_band.round(2)} - 100 - #{upper_band.round(2)}"

3. Comparative ROCR100

Compare momentum across different assets:

spy_rocr100 = SQA::TAI.rocr100(spy_prices, period: 10)
qqq_rocr100 = SQA::TAI.rocr100(qqq_prices, period: 10)

if spy_rocr100.last > qqq_rocr100.last
  puts "SPY showing stronger momentum than QQQ"
  puts "SPY: #{spy_rocr100.last.round(2)} vs QQQ: #{qqq_rocr100.last.round(2)}"
end

Key Differences from Related Indicators

Feature	ROCR100	ROCR	ROC	ROCP
Baseline	100	1.0	0	0
Formula	(P/Pn) × 100	P/Pn	((P-Pn)/Pn) × 100	(P-Pn)/Pn
Reading	105 = 5% gain	1.05 = 5% gain	5 = 5% gain	0.05 = 5% gain
Intuitive	Most intuitive	Less intuitive	Intuitive	Least intuitive
Best For	General use	Academic	Charts	Calculations

Why Choose ROCR100?

1. Most User-Friendly: 100 baseline is universally understood
2. Quick Mental Math: Simply subtract 100 for percentage
3. Clear Visualization: 100 line is obvious reference on charts
4. Easy Thresholds: Round numbers (100, 105, 110) are natural
5. Better Communication: "ROCR100 is 107" is clearer than "ROCR is 1.07"

Related Indicators

• ROC - Rate of Change (percentage)
• ROCR - Rate of Change Ratio (ratio format)
• ROCP - Rate of Change Percentage (decimal)
• MOM - Momentum (absolute change)
• RSI - Relative Strength Index

See Also

• Back to Indicators
• Basic Usage
• Momentum Indicators Overview