Relative strength index
From Wikipedia, the free encyclopedia
The Relative Strength Index (RSI) is a financial technical analysis oscillator showing price strength by comparing upward and downward close-to-close movements.
The RSI is popular because it is relatively easy to interpret. It was developed by J. Welles Wilder and published in Commodities magazine (now called Futures magazine) in June 1978, and in his New Concepts in Technical Trading Systems the same year.
Note that the term relative strength also refers to the strength of a security in relation to its sector or the overall market. For instance, XYZ might rise 2% when S&P 500 rises 1%.[1] This is sometimes called comparative relative strength to avoid confusion. It's unrelated to the Relative Strength Index described here.
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[edit] Calculation
For each day an upward change (U) or downward change (D) is calculated. "Up" days are characterized by the daily close being higher than yesterday's daily close, i.e.:
- U = closetoday − closeyesterday
- D = 0
Conversely, a down day is characterized by the close being lower than the previous day's (note that D is nonetheless a positive number),
- U = 0
- D = closeyesterday − closetoday
If today's close is the same as yesterday's, both U and D are zero. An average for U is calculated with an exponential moving average using a given N-days smoothing factor, and likewise for D. The ratio of those averages is the Relative Strength,
![RS = { EMA[N] \; of \; U \over EMA[N] \; of \; D }](http://upload.wikimedia.org/math/2/0/6/206954953516f2c520c586391a2cbc2f.png)
This is converted to a Relative Strength Index between 0 and 100,
This can be rewritten as follows to emphasise the way RSI expresses the up as a proportion of the total up and down (averages in each case),
![RSI = 100 \times { EMA[N]\;of\;U \over (EMA[N]\;of\;U) + (EMA[N]\;of\;D) }](http://upload.wikimedia.org/math/8/1/5/8153b94a437a2d27a0b2338e6ed33916.png)
The EMA, in theory, uses an infinite amount of past data. It's necessary either to go back far enough, or alternately at the start of data begin with a simple average of N days instead,
and then continue from there with the usual EMA formula,
(Similarly with D.)
[edit] Interpretation
Wilder recommended a smoothing period of 14. This is by his reckoning of EMA smoothing, ie. α=1/14 or N=27.
Wilder considered a security overbought if it reached the 70 level, meaning that the speculator should consider selling. Or conversely oversold at the 30 level. The principle is that when there's a high proportion of daily movement in one direction it suggests an extreme, and prices are likely to reverse. Levels 80 and 20 are also used, or may be varied according to market conditions (eg. a bull market may have an upward bias).
Large surges and drops in securities will affect RSI, but it could just be a false buy or sell. The RSI is best used as a complement with other technical analysis indicators.
The RSI should confirm price movement; therefore, if the stock price is moving up, the RSI should be moving up as well[2].
[edit] Cutler's RSI
A variation called Cutler's RSI is based on a simple moving average of U and D,[3] instead of the exponential average above.
![RS = { SMA[N] \; of \; U \over SMA[N] \; of \; D }](http://upload.wikimedia.org/math/d/f/c/dfc7eb500724b524266b4dd7dc97e835.png)
This is like the initial data point calculation shown above, but used on every day, not just the first. The divisor N in the SMAs in the numerator and denominator cancel out, so one needn't do those divisions, instead just a sum of U and a sum of D over the past N days can be made.
Cutler's RSI generally comes out slightly different from the normal Wilder RSI, but the two are similar, since SMA and EMA are similar.
[edit] References
- ^ Relative Strength, Comparative at MarketScreen.com
- ^ How to interpret RSI indicator
- ^ Cutler's RSI page at Aspen Graphics Technical Analysis Software
[edit] External links
[edit] See also
- MACD moving average convergence/divergence
[edit] Further reading
- New Concepts in Technical Trading Systems by J. Welles Wilder, ISBN 0-89459-027-8
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