Relative strength index
From Wikipedia, the free encyclopedia
The Relative Strength Index (RSI) is a financial technical analysis momentum oscillator measuring the velocity and magnitude of directional price movement by comparing upward and downward close-to-close movements.
Momentum measures the rate of the rise or fall in stock price. Is the momentum increasing in the "up" direction, or is the momentum increasing in the "down" direction.
A simple way to picture momentum: Imagine a ball rolling down a hill. It starts off pretty slow and then as it gets further down the hill it picks up momentum and starts rolling faster.
The RSI 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 posited that when price moves up very rapidly, at some point it is considered overbought. Likewise, when price falls very rapidly, at some point it is considered oversold. In either case, Wilder felt a reaction or reversal is imminent. The slope of the RSI is directly proportional to the velocity of the move. The distance traveled by the RSI is proportional to the magnitude of the move.
As a result, Wilder believed that tops and bottoms are indicated when RSI goes above 70 or drops below 30. Traditionally, RSI readings above 70 are considered overbought, and below 30 are considered oversold.
Wilder further believed that divergence between RSI and price action is a very strong indication that a market turning point is imminent. Bearish divergence occurs when price makes a new high but the RSI makes a lower high, thus failing to confirm. Bullish divergence occurs when price makes a new low but RSI makes a higher low.
Wilder thought that "failure swings" above 70 and below 30 on the RSI are strong indications of market reversals. For example, assume the RSI hits 76, pulls back to 72, then rises to 77. If it falls below 72, Wilder would consider this a "failure swing" above 70.
Finally, Wilder wrote that chart formations and areas of support and resistance could sometimes be more easily seen on the RSI chart as opposed to the price chart. The center line for the relative strength index is 50, which is often seen as both the support and resistance line for the indicator.
If the relative strength index is below 50, it generally means that the stock's losses are greater than the gains. When the relative strength index is above 50, it generally means that the gains are greater than the losses.
In addition to Wilder's original theories of RSI interpretation, Andrew Cardwell has developed several new interpretations of RSI to help determine and confirm trend. First, Cardwell noticed that uptrends generally traded between RSI 40 and 80, while downtrends usually traded between RSI 60 and 20. Cardwell observed when securities change from uptrend to downtrend and vice versa, the RSI will undergo a "range shift."
Next, Cardwell noted that bearish divergence: 1) only occurs in uptrends, and 2) mostly only leads to a brief correction instead of a reversal in trend. Therefore bearish divergence is a sign confirming an uptrend. Similarly, bullish divergence is a sign confirming a downtrend.
Finally, Cardwell discovered the existence of positive and negative reversals in the RSI. Reversals are the opposite of divergence. For example, a positive reversal occurs when an uptrend price correction results in a higher low compared to the last price correction, while RSI results in a lower low compared to the prior correction. A negative reversal happens when a downtrend rally has results in a lower high compared to the last downtrend rally, but RSI makes a higher high compared to the prior rally.
In other words, despite stronger momentum as seen by the higher high or lower low in the RSI, price could not make a higher high or lower low. This is evidence the main trend is about to resume. Cardwell noted that positive reversals only happen in uptrends while negative reversals only occur in downtrends, and therefore their existence confirms the trend.
[edit] Cutler's RSI
A variation called Cutler's RSI is based on a simple moving average of U and D,[2] 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
- ^ Cutler's RSI page at Aspen Graphics Technical Analysis Software
[edit] External links
- Trading options with the RSI
- How to interpret RSI buy and sell signals
- Cardwell Techniques with the RSI
[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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