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### 10.34 Relative Strength Index

The Relative Strength Index (RSI) by J. Welles Wilder compares average upward close-to-close movement against all close-to-close movement, each smoothed by an EMA (see Exponential Moving Average).

For each day an upward or downward movement is calculated. On an up day

U = close[today] - close[yesterday]
D = 0

or on a down day as follows (notice D is a positive amount),

U = 0
D = close[yesterday] - close[today]

The sequence of U values over time is averaged with an EMA (see Exponential Moving Average) and likewise the D values. The ratio is the “relative strength”,

EMA[N] of U
RS = -----------
EMA[N] of D

This is turned into an index between 0 and 100,

1
RSI = 100 * ------
1 + RS

This can also be written as follows, emphasising the way the RSI measures up movement as a proportion of the two up and down,

EMA[N] of U
RSI = 100 * -----------------------------
(EMA[N] of U) + (EMA[N] of D)

Wilder recommended a smoothing period of N=14, and that’s the default in Chart. Note also that the period is interpreted by Wilder’s reckoning of EMA smoothing (see Wilder EMA period).

An index value of 70 is considered overbought and 30 oversold; those levels are shown as dashed lines. The principle is that after a large proportion of movement in one direction, a reaction the other way becomes likely. On the other hand it’s easy to see from the formula that a steady progressive trend (every day up, or every day down) can push the RSI to an extreme and hold it there.

The term “relative strength” also refers to a comparison between a stock and the overall market. This is sometimes called “relative strength comparative” to avoid confusion. This is unrelated to the relative strength and relative strength index described in this section.

See also CMO (see Chande Momentum Oscillator) which is an RSI with SMA smoothing, and TSI (see True Strength Index) which is an RSI with double-EMA smoothing.

#### 10.34.1 Stochastic RSI

The stochastic RSI is an N-day unsmoothed %K stochastic applied to the RSI line. The position of today’s RSI is expressed as a fraction 0 to 1 of its overall range (lowest to highest) in the past N days, the same N as used for the RSI calculation,

RSI[today] - RSI[Nday low]
Stoch RSI =  ------------------------------
RSI[Nday high] - RSI[Nday low]

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