The relative strength index of a stock is a technical indicator that is used to calculate whether a security is currently in an overbought or oversold state. This is a very important and fundamental indicator that has been used by traders since it was developed in 1978 by J. Welles Wilder, Jr., an American mechanical engineer who is known for his groundbreaking work in technical indicator development.

## Calculation

Relative strength index, or RSI for short, is calculated as follows:

**RSI = 100 – 100/(1+RS)**

RS= the average of x up days closes (AU)/the average of x down day closes (AD).

AU= sum of previous x days up closes value (SU)/x

AD= sum of previous x days down closes value (SD)/x

X normally is set to a 14 period but users can most often edit this is charting software.

**An up day value is calculated as follows:**

Current close – previous close= up day value

down day value is assigned as 0 on an up day

**A down day value is calculated as follows:**

previous close – current close = down day value

up day value is assigned as 0 on a down day.

## Example

Over the previous 14 trading days, stock ABC has a sum of up day values of 20. During the same 14 day time period the sum of down day values is 10.

AU = 20/14 = 1.4

AD = 10/14 = .7

RS = 1.4/.7 = 2

RSI = 100 – 100/(1+2) = 100- 33 = 77

As you can see a higher relative up day average results in a higher RSI value, while the opposite is true of greater relative down day averages.

A longer time period will result in a calculation that is less sensitive to moves and is more likely to result in RSI values closer to 50, while a shorter time period will result in a more volatile indicator which is more likely to show extreme values.

* It should be noted that current calculations of RSI often use exponential moving averages for AU and AD values. The math for this is even more complex but essentially results in higher weighting being placed on more recent values. If you understand this framework the logic behind using exponential moving averages is not hard to grasp, even if the actual calculations are. It is rare that a trader would actually have to calculate a relative strength index by hand since it is included on almost any charting software.

## Application as an Indicator

After obtaining a value from the relative strength index calculation, normally the value is plotted on a graph which is either superimposed over a price chart or placed underneath. Due to the construct of the RSI formula, values are bound between 0 and 100. Normally a value of 30 or lower is considered oversold, while a value of greater than 70 is considered overbought. Sometimes the thresh hold level is adjusted to 25-75 or even 20-80 to increase the rarity of the indicator threshold being met. A trader may use the meeting of the indicator with a top threshold to mean a short or sell signal, while the meeting of a bottom threshold may be used as a buy indicator. Let’s take a look at how an RSI appears on charting software.

The S&P 500 has been trending steadily up over this time period, but you can see that even in this strong uptrend oftentimes when the upper 70 level threshold is met short term selling has followed the majority of the time.

While it may not be the only technical indicator a trader uses for entries and exits, every good trader is aware of RSI levels as they are a tried and true method of identifying overbought and oversold conditions.

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