Relative Strength Index (RSI): Calculation

In June 1978, Welles Wilder introduced the Relative Strength Index to the trading community in an article for Commodities Magazine. The Relative Strength Index (RSI) is one of the most popular momentum oscillators used by traders. It is so popular that every charting software package and professional trading system anywhere in the world has it as one of its primary indicators.

The calculated value for Wilder's RSI oscillates between 0 and 100. This value represents a ratio of the average recent time period price 'gains' to the average recent time period price 'losses' calculated over a number of time periods. There are two equations that are involved in solving the formula. The first component equation obtains the initial Relative Strength (RS) value, which is the ratio of the average UP closes to the average DOWN closes over 'N' periods represented in the following formula:

RS = Average of 'N' day's closes UP/Average of 'N' day's closes DOWN

The actual RSI value is calculated by indexing the indicator to 100 through the use of the following formula:

RSI = 1 00 - (100 /1 + RS)

In calculating for the value for RSI on succeeding days, the 'sum of gain' in price in 'N' time and the 'sum of loss' in price in 'N' time is multiplied by one less than the fixed period of time 'N'. The gain or loss for the next subsequent bar is added and the resulting number is divided by the fixed period of time 'N'. We can see this in the following formula.

RSI = 1 00 - (100/1 +[((Sum of gain in price in 'N-I ' past intervals· 'NI ')+Gain this bar) / 'N' / ((Sum of loss in price in 'N-l' past intervals· 'N-I ' ) + Loss this bar) / 'N']

Where: RSl = Initial RSI value.

'N' is the length of time intervals that is referenced in the past. For example, 14 of the prior bars.

Under Table #3 is a spreadsheet that shows the relationships between the Gain average and the Loss average as a ratio.

By carefully studying the ratio relationships in Table # 3, we can glean the following information about the Relative Strength Index:

1. When the RSI is above 50, the indicator is telling us that the average gain exceeds the average loss.

2. When the RSI is below 50, the indicator is telling us that the average loss exceeds the average gain.

3. The RSI behaves like a logarithmic curve.

4. Anytime the ratio exceeds 10:1, the market has been experiencing a very strong move up.

5. Anytime the ratio exceeds 1:10, the market has been experiencing a very strong down move.

6. The largest increase or decrease in the RSI value occurs when the ratio changes from 1: 1 to the next whole number (2: 1 or 1 :2).

7. The RSI value experiences its largest changes in value as it oscillates between the index values of 40 and 60. In other words the RSI is most sensitive to price change when the RSI is oscillating between 40 and 60.