## Relative Strength Index (RSI)

##### Published: Oct 2006

The Relative Strength Index (RSI) is a form of technical analysis that calculates the price strength of a security by comparing its consecutive end of day share prices. The RSI is a momentum indicator that measures the speed at which a security’s price is changing. High RSI values of over 70 on a scale of 0 to 100 often indicate overbought shares, whereas RSI values of lower than 30 often indicate oversold shares. RSI is therefore used to identify trading entry and exit points.

The RSI is calculated as follows. For each trading day both the upwards (U) and downwards (D) change of the closing share prices is calculated.

If the share price closes higher than on the previous day U and D are:

U = closetoday – closeyesterday
D = 0
If the share price is down compared to the previous day:

D = closeyesterday – closetoday
U = 0
Should the current share price remain unchanged both U and D will be zero.

The ratio of the U and D averages for a given time period is the Relative Strength of the security. In order to calculate the Average U and D we need to divide all Us and Ds respectively by the number of trading days(N). The lower the number of periods (N) used, the more sensitive or faster the RSI will be. The RSI is usually more accurate when using a 14-day period.

$$Average\: D=\frac {D1\:+\:D2\:+\:D3……+DN}{n}$$
$$Average \:U=\frac{U1\:+\:U2\:+\:U3\:+\:UN}{N}$$

Note that the average is not a true average as the sum of U and D is divided by the total number of days and not by the number of gaining or losing days only.

The ratio of average U and average D is the initial relative strength value:

$$Initial\: RS=\frac{Average\: U}{Average\: D}$$

This first relative strength value is then converted into the Relative Strength Index (RSI) using the formula:

$$RS=100 \:-\:\frac{100}{1\:+\:Initial\: RS}$$

For the following days the Average U and D of the previous day is used as a moving average smoothing factor for the following RSIs. The smoothing factor takes into account all of the values in the data set.

$$Smoothed\: RS=\frac{\frac{Average\:U_{yesterday}\:N\:-1\:+\:U_{today}}{N}}{\frac{Average\:D_{yesterday}\:N\:-\:1\:+\:D_{today}}{N}}$$

$$RSI=100\:-\:\frac{100}{1\:+\:Smoothed\: RS}$$
The RSI result is a number between 0 and 100. Investors use the RSI to look for bullish or bearish signals. In an RSI chart, the RSI oscillates around a centreline of 50. Any value above 50 indicates that average gains are higher than average losses, whereas a value of below 50 signals that average losses outweigh average gains.

Often RSI values of 70 and 30 are used to indicate overbought or oversold shares, so that a share falling below 70 is seen as a sign for falling share price trend in the future and a share rising above 30 is regarded as a bullish signal. Some traders will look for extreme RSI values in combination with corresponding longterm trends.

Other investors will look for a divergence between the share price development and the RSI curve to identify potential entry or exit points.