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1993issue C101

Constructing a relative momentum index from the relative strength index

A relative momentum index reuses the relative strength index smoother and 0-to-100 ratio map. TradersWeek editorial reading: change only what counts as an up or down observation, and a one-bar close change can be compared with a multi-bar momentum difference as a single design choice.

  • The relative strength index turns a ratio of smoothed up closes to smoothed down closes into a bounded reading by multiplying that ratio, divided by one plus the same ratio, by 100.
  • Each smoothed total is refreshed by subtracting one lookback share of the prior total and adding the current one-bar up close, the absolute one-bar down close, or zero when that side is absent.
  • The relative momentum index uses that same bounded-ratio mapping, but forms the ratio from smoothed multi-bar up momentum and smoothed multi-bar down momentum.
  • A spreadsheet construction used a five-bar comparison span and a 20-bar smoothing span, seeding the first totals as simple sums and then subtracting one-twentieth of the prior total on later bars.
Entries in this reading2 entries
Current trackMomentum strategy103 readingsRelative Strength Index186 readings

A two-layer recipe

TradersWeek editorial reading: treat oscillator construction as two layers. Keep the same smoother and the same 0-to-100 ratio map. Change only what counts as an up or down observation.

The archive facts below describe each layer in turn. The teaching split itself is editorial.

The shared smoother and ratio map

The relative strength index turns a ratio of smoothed up closes to smoothed down closes into a bounded reading. It multiplies that ratio, divided by one plus the same ratio, by 100.

Each smoothed up-close and down-close total is refreshed by subtracting one lookback share of the prior total and adding the current one-bar up close, the absolute one-bar down close, or zero when that side is absent. That update is average-off smoothing.

Changing only the up and down observation

The relative momentum index uses the same bounded-ratio mapping as the relative strength index, but the ratio is formed from smoothed multi-bar up momentum and smoothed multi-bar down momentum.

Up momentum is the positive difference between the current close and the close a chosen number of bars earlier, or zero. Down momentum is the absolute value of a negative difference over that same span, or zero. That chosen length is the momentum span.

TradersWeek editorial reading: a one-bar close change and a multi-bar momentum difference are then the same observation rule at two spans. The map does not change.

Five-day up and down momentum on the S&P 500

The December rally is counted almost entirely as five-day gains, so down-momentum stays at zero until 10 January, when the first five-day loss appears and the worksheet RMI eases from the mid-90s. Every point is an exact column C or D cell from the sidebar Excel table, not a redrawn curve.
The December rally is counted almost entirely as five-day gains, so down-momentum stays at zero until 10 January, when the first five-day loss appears and the worksheet RMI eases from the mid-90s. Every point is an exact column C or D cell from the sidebar Excel table, not a redrawn curve.S&P 500 · daily · 1991-12-06T00:00:00.000Z to 1992-01-10T00:00:00.000Z

The sidebar fixes the momentum lookback at y = 5 sessions and the smoother at x = 20. This pair is only the raw up and down observation layer; the first RMI prints after the 20-day seed on 6 January 1992.

Seeding the first totals

A spreadsheet construction of the relative momentum index used a five-bar comparison span and a 20-bar smoothing span. TradersWeek editorial note: the comparison span is the momentum span used to form each signed difference.

The first 20-bar up-momentum and down-momentum totals can be seeded as simple sums of the first 20 signed momentum observations. Later bars subtract one-twentieth of the prior total and add the current observation.

After smoothing, the momentum ratio is the up-momentum total divided by the down-momentum total. That ratio is then scaled with the same 100-times-ratio-over-one-plus-ratio step used for the relative strength index.

A defined momentum input

TradersWeek editorial reading: with the smoother and the ratio map held fixed, the momentum span is the remaining design choice. A momentum strategy can treat that multi-bar close-to-close difference as an explicit, testable rule input rather than as a narrative label.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
16 of 51 in the Momentum strategy track
19941-8 pp.Next on Momentum strategyConstructing daily advance-decline breadth toolsA daily advance-decline series is a running total of advancing issues minus declining issues, which may be negative, and is read as a second dimension beside price.
All readings on this track · 51 readings
  1. 1984Half-cycle differencing for momentum signals
  2. 1987Relative strength evaluation under competing optimization criteria
  3. 1988Weekly MACD as a two-clock momentum confirmation stack
  4. 1989Equal-weight zero-cross from smoothed spreads
  5. 1989Testing relative-strength-index reversal rules against trend continuation
  6. 1989Smoothed three-day futures filter for index option bounces
  7. 1989Cycle-length windows for momentum, Relative Strength Index, and stochastic construction
  8. 1991Filtered rally magnitude as a bull-regime breakout
  9. 1992Constructing true strength from double-smoothed momentum
  10. 1992Constructing a double-smoothed true strength index
  11. 1993When momentum structure and breadth break together
  12. 1993Constructing double-smoothed range and momentum oscillators
  13. 1993Constructing a two-parameter relative momentum index
  14. 1993Building a bounded momentum oscillator with RSI smoothing
  15. 1993Two-speed oscillators with divergence and trendline gates
  16. 1993Constructing a relative momentum index from the relative strength index
  17. 1994Constructing daily advance-decline breadth tools
  18. 1994Building a composite regime score from monetary climate and weekly trend
  19. 1994Averaging Relative Strength Index and the stochastic oscillator into one reversal oscillator
  20. 1995Dividend-yield regression as a hold versus momentum gate
  21. 1996Jump and hold filters for long-term Treasury yield direction
  22. 1997Constructing extendedness from a 10 percent swing filter
  23. 1997A range-expansion oscillator that can refuse its own stretch
  24. 1997RSI trend permission and Fibonacci pullback rules
  25. 1998Nested midpoint construction for a range-normalized oscillator
  26. 1999Evaluating Relative Strength Index momentum with zero-line and threshold rules
  27. 1999Treat RSI and momentum as three mechanical procedures
  28. 2000Thrust strength figure from moving-average swings
  29. 2001Constructing a non-range-bound balance of market power score
  30. 2004Cleaned breadth oscillator and new-high divergence: a swing-market case file
  31. 2004Evaluating advance-issues-momentum on a fixed-symbol-basket
  32. 2004Constructing a trend filter from two adjacent high-low windows
  33. 2006A dollar-versus-commodity extreme as a regime case
  34. 2008Zero-centered stochastic bands and bracket stops
  35. 2012Evaluating engulfing momentum across hold windows
  36. 2012Staged stops as one mechanical entry and exit procedure
  37. 2012Stacking a relative-strength-index forecast, a trend filter, and long-only momentum
  38. 2013Constructing fair-value filters from averages and momentum
  39. 2014Constructing a multi-window slope divergence entry
  40. 2015Bandedge trend filter construction with inverse crossover rules
  41. 2017Opposite rules for index price and volatility momentum
  42. 2018A three-state overlay that colors a trend only after the line clears the bar
  43. 2018Half-cycle relative-strength index with a Fisher map for cyclic reversals
  44. 2018Emotion as a rule input when momentum breaks
  45. 2018Two-bar body expansion as a momentum breakout construction
  46. 2019Pair a two-day high breakout with a volume-weighted exit on the same chart
  47. 2020Building reflex and trendflex cross and extreme entry rules
  48. 2020Construct a dual-series price momentum oscillator overlay
  49. 2020A multi-timeframe stochastic as a panel of weekly voters
  50. 2020Centerline crossovers that compare index momentums
  51. 2020Multi-timeframe stochastic voting as one mechanical rule
By fieldIndicators and filters682 readingsBy year199376 readings
All 103 readings tagged Momentum strategy
Also on Momentum strategy5 readings
1987Relative strength evaluation under competing optimization criteria1989Cycle-length windows for momentum, Relative Strength Index, and stochastic construction1989Testing relative-strength-index reversal rules against trend continuation1992Constructing true strength from double-smoothed momentum1993Building a bounded momentum oscillator with RSI smoothing