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Relative Strength Index (RSI)

Indicator Name: Relative Strength Index, or RSI

Indicator Type: Bounded Oscillator

Description: The Relative Strength Index is one of the most common indicators in use today. It is difficult to find a chartist that doesn't have RSI pasted to the bottom of his or her chart. It was developed in 1978 in order to resolve two specific problems with momentum indicators of the time. The first problem was that momentum lines often became erratic due to sharp changes being dropped out of the calculation as time passed. For example if we were constructing a 14 day momentum line, and there was a sharp decline 14 days ago, then that value would contribute a significant sum to our momentum calculation, until the 15th day after it, when it would suddenly and completely disappear from the calculations. This would then cause the momentum value to rise sharply on the 15th day after the sharp decline. There was an obvious need to smooth the momentum. The other problem was that there was a need to get the indicator to display a consistent range so that different instruments and timeframes could be compared.

The Relative Strength Index solved both problems brilliantly, by providing the necessary smoothing AND by limiting its range to oscillations between 0 and 100 (hence the name "bounded" oscillators for all such indicators). We can see in the Calculation section below how this is accomplished mathematically.

Calculation: The formula for calculating RSI is fairly simple. The only parameter is the period (N) over which it is to be calculated. Using that, we go back through the chart and make an "average gain" (g) and an "average loss" (l) calculation, with each Gn being the individual gain price and each Ln being the individual loss price, and i the number of gain bars (bars where the close is higher than the open):

Average gain calculation AND Average Loss equation

It should be noted that a bar where the open and close prices are exactly equal is not considered a gain or a loss and should not be included in the calculation. Once we have calculated the average loss (l) and average gain (g), we can go on to plug them into our main RSI equation as follows:


We can easily see from this equation that as l gets very large, l/g+l approaches 1, so the RSI value approaches 0. This can be interpreted as:

A large average loss relative to the average gain reduces the RSI values until it approaches 0, but it can never reach 0, because g > 0, making l/g+l < 1. Our minimum value is RSI > 0 as the average gain g approaches 0 (g = 0 is impossible).

We saw earlier that the g = 0 condition is not possible, since bars which open and close at the same price cannot be considered gain bars.

Conversely, If the average gain (g) gets very large, l/g+l approaches 0, so RSI approaches 100. In other words:

As the average gain becomes very large relative to the average loss, we get an RSI value that approaches, but never reaches 100. Our maximum value is RSI < 100 if the average loss l approaches 0 (l = 0 is impossible).

So we see that RSI is bounded by 0 on the downside and by 100 on the upside. Mathematically, we run into problems if all the bars in our range closed at the exact same price that they opened at. In the unlikely event that it does happen, the RSI value for that bar is undefined.

Example: Let's say we are calculating the Daily RSI(5) value, for the sake of simplicity. So we look at the last 5 days' price action and extract the open and close information for each day:

Day 1
Open: 100.00
Close: 101.00
Change: +1.00

Day 2
Open: 101.00
Close: 102.00
Change: +1.00

Day 3
Open: 102.00
Close: 103.00
Change: +1.00

Day 4
Open: 103.00
Close: 101.00
Change: -2.00

Day 5
Open: 101.00
Close: 99.00
Change: -2.00

We see that days 1, 2 and 3 are "gain days", and days 4 and 5 are "loss days". We have g = (1+1+1)/3 = 1, and l = (2+2)/2 = 2. Substituting these values into our main RSI equation we get:

RSI example


Uses: The Relative Strength Index is a measure of how oversold or how overbought a financial instrument is. RSI values below 30 indicate and oversold condition, while RSI values above 70 indicate overbought. The most basic use of RSI relies on these trade signals - once RSI is overbought, and curls downward towards breaking out of the overbought territory it's time to short the pair, and vica versa with the oversold condition.

Another popular use is to determine bullish or bearish divergence. For example, if the currency is making a new high, while the RSI is not, this is an indication that the up trend may be ending soon (bearish divergence). The signal usually comes when the RSI line drops below its most recent trough.

There are a wide range of other uses for the Relative Strength Index indicator.

Most Common Settings: The most common period is N=14. Other popular settings are N=9, 7, and 5 which work to increase the volatility of the RSI chart. Some technical analysts use longer periods like N=21 or 28 in order to smooth the RSI curve in hopes of achieving more reliable signals. Some trading platforms also allow you to set the bounds as parameters, so if you would like RSI to move between 0 and 200 instead of 0 and 100, you can change it. This can be marginally useful when running comparisons with other indicators. It is also possible to apply additional smoothing to the RSI indicator, which is beyond the scope of this article.

Strengths: The RSI has the advantage of being a very elegant indicator, in that it's movements are smooth, and it can fit into a neat package between 0 and 100. It has the added advantage of being used by many traders out there, which is not only a testament to its abilities, but it also makes its signals self-fulfilling at times. When used to indicate divergences, it can be quite powerful.

Weaknesses: Doesn't take into account how many up days vs. down days there are in the range, so one single big decline could offset a large number of gain periods and vica versa. The RSI is also notoriously weak in strongly trending markets because it can remain oversold/overbought for a long time during strong trends. Avoid using RSI in strongly trending markets unless trading in the direction of the trend.

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