Skip to main content
Track Exponential smoothing
13 / 41
Search the archiveLibrary
Library

1991issue C111

Equivalent relative-strength-index constructions from a ratio and from smoothed momentum

Two 14-period relative-strength-index constructions, one from a relative-strength ratio and one from exponentially smoothed up-move and down-move series, reduce without the smoother to the same identity. Substituting a equal to 2 and b equal to 5 produces 28.5714 on both sides.

  • A 14-period relative-strength index can be constructed as 100 minus 100 divided by one plus the relative-strength ratio.
  • The same 14-period index can be constructed as 100 times the 14-period exponentially smoothed up-move series divided by the sum of that series and the 14-period exponentially smoothed down-move series.
  • Without the smoother, both constructions reduce to the identity that 100 minus 100 over one plus a divided by b equals 100 times a over a plus b.
  • Substituting a equal to 2 and b equal to 5 produces 28.5714 on both sides of that identity, showing the two constructions are equivalent.
Entries in this reading2 entries
Current trackExponential smoothing183 readingsRelative Strength Index261 readings

Two constructions of the same index

A 14-period relative-strength index is a 100-scaled construction that reports the share of upward close-to-close movement relative to the combined upward and downward movement. One construction writes that index as 100 minus 100 divided by one plus the relative-strength ratio. In the ratio construction, relative strength is the quotient of up closes to down closes.

The same 14-period index can be constructed as 100 times the 14-period exponentially smoothed up-move series divided by the sum of that series and the 14-period exponentially smoothed down-move series.

Up-move, down-move, and exponential smoothing

The up-move input is today's close minus yesterday's lower close, and the down-move input is yesterday's higher close minus today's close.

Exponential smoothing is a recursive average applied separately to the up-move and down-move series. The 14-period exponential average applied to those series uses a smoothing constant of 2 divided by one plus the lookback length.

A shared identity without the smoother

Without the smoother, both constructions reduce to the identity that 100 minus 100 over one plus a divided by b equals 100 times a over a plus b.

Substituting a equal to 2 and b equal to 5 produces 28.5714 on both sides of that identity, showing the two constructions are equivalent.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
13 of 41 in the Exponential smoothing track
19911-1 pp.Next on Exponential smoothingConstructing the true strength index from double-smoothed momentumThe true strength index is constructed by exponentially smoothing one-period price changes, not by smoothing the price series itself.
All readings on this track · 41 readings
  1. 1984Matching average age across price filters
  2. 1984Residual-impact construction of exponential smoothers
  3. 1988Constructing simple and exponential moving averages as specified filters
  4. 1989Evaluating smoothed free reserves and funds-discount spreads
  5. 1990Integer construction of moving averages and exponential smoothing
  6. 1990Constructing incremental moving average filters
  7. 1991Constructing a double-smoothed stochastic oscillator
  8. 1991Constructing an exponential average from a smoothing weight
  9. 1991Constructing a double-smoothed momentum oscillator family
  10. 1991Competing certainty rules from exponential-average conditions
  11. 1991Hybrid construction of a mechanical timing system from smoothed signals
  12. 1991Constructing an exponential smoother from a moving-average length
  13. 1991Equivalent relative-strength-index constructions from a ratio and from smoothed momentum
  14. 1991Constructing the true strength index from double-smoothed momentum
  15. 1991True strength index from signed, double-smoothed momentum
  16. 1992Constructing exponential averages from simple lookbacks
  17. 1992Constructing exponential averages by the smoothing constant, startup length and lag
  18. 1992Nested range smoothing and windowed high-low damping
  19. 1992A weekly equity stance from the discount-bill spread
  20. 1993Double-smoothed stochastics momentum index construction
  21. 1993Constructing the true strength index with double exponential smoothing
  22. 1994Polarized fractal efficiency with a shared exponential smoother
  23. 1994Five-interval exponential smoothing of ten-interval signed path-efficiency
  24. 1994Hand-ranked price-volume series with stacked smoothing and stochastic
  25. 1995Range expansion filter on multi-horizon averages
  26. 1995The exponential smoothing constant from averaging lag
  27. 1997Construct a nested-average rainbow band and oscillator
  28. 1998Filter stacks that combine a moving average with exponential smoothing
  29. 2002Smoothed relative-strength construction from wilder-averaging and a price prefilter
  30. 2003Reverse-engineered RSI price targets
  31. 2004Piecewise trend quality from moving-average reversals
  32. 2004Nested smoothing recipes versus unaudited oscillator experiments
  33. 2008Weight construction beyond the N-day label
  34. 2010A consensus filter for objective RSI and smoothing construction
  35. 2012Sentiment-zone oscillator from signed closes
  36. 2012Classic RSI one-over-N smoothing versus the standard exponential average
  37. 2013Why exponential smoothing uses two over n plus one
  38. 2015Constructing ratio indicators with moving-average and exponential-smoothing weights
  39. 2015Slow relative-strength index from an exponentially smoothed price
  40. 2017Rebuilding the relative strength index as open-scale buy-sell pressure
  41. 2017Comparing Wilder and exponential smoothing inside a relative-strength index
By fieldIndicators and filters874 readingsBy year1991166 readings
All 183 readings tagged Exponential smoothing
Also on Exponential smoothing5 readings
1991Constructing a double-smoothed momentum oscillator family1991True strength index from signed, double-smoothed momentum1992Constructing true strength from double-smoothed momentum1995Explicit exponential weights and binary entry filters1995Adaptive length as a construction choice inside exponential smoothing