RSI is probably J. Welles Wilder Jr.'s best-known indicator. It can be found on virtually every technical analysis website and is included with almost all software packages. RSI stands for Relative Strength Index, but the name is misleading. Most relative strength calculations compare a stock against an index -- such as comparing Intel (INTC) to the Semiconductor or $SOX index. Wilder's RSI compares a stock's gains to its losses over a set period of time. The result is an RSI graph usually presented as a panel above or below the price chart.

When Wilder first articulated RSI in his 1978 book, New Concepts in Technical Analysis (ISBN 0-894959-027-8), his methodology involved the use of a Hewlett-Packard programmable calculator. The swing trader of that time would have had to follow the logic of a 10-column spreadsheet to understand how the indicator was constructed. The swing trader of 2004 has a noticeable advantage. With a stroke of the computer key, presto, RSI appears above or below the price chart.

On reflection, however, this ability to effortlessly conjure up RSI can also be a disadvantage. Without understanding the mathematical construction of the indicator, it is easy to use it mechanically. Worse, its implications can be misinterpreted, which may lead to poor trading decisions. In future articles I will devote attention to a detailed discussion of how RSI can:

-- Serve as a leading indicator of an upcoming reaction or reversal by limning out "a failure swing."
-- Trace out price patterns difficult to detect on the underlying price chart.
-- Signal bearish or bullish momentum divergence and therefore the probability of trend reversal.
-- Mimic trendlines on the underlying price chart by establishing key support and resistance levels.

Many times during these discussions, I will refer back to the mathematical reasoning behind RSI and I will now explain that calculation.

The formula for RSI is:

RSI = 100 – [100/1 +RS]

RS = Average of n periods closes up/Average of n periods closes down.

RSI provides meaningful information on a chart of any length, and I have used it on 5 minute, hourly, daily, weekly and monthly charts. "N" in the RS formula is the number of periods used in the calculation. Wilder himself suggested 14 periods as the default, but a 9 and 21 period RSI are also commonly used by traders.

If you're not mathematically inclined, finding RS can sound daunting, but is actually simple. The first step is to assemble 14 periods of data for any stock or index. In the example below of Intel, I started my RSI calculation on November 1st and collected 14 days of closing prices, since I wanted to do a daily RSI computation. 

The next step was to total all the up closes, or daily gains, during the 14 days. As the spreadsheet below shows, Intel gained 17 cents on November 2nd, 6 cents on November 3rd, 21 cents on November 4th etc. The sum of these gains for all fourteen days was $2.77. To find out the average gain for the period, one simply divides $2.77 by 14 to get 19.8 cents.

The same process is repeated for the down days. Total declines in the 14-day period were 50 cents, making the average decline 3.6 cents.

Next, you need to figure out RS. RS is calculated by dividing the average up closes (19.8) by the average down closes 
(3.6). This simple calculation (19.8/3.6) yields a result of 5.50.

The formula asks us to then add 1.0 to 5.5, giving us a result of 6.5. To resolve the brackets we divide 100/6.5 and find that the answer is 15.38.

The final step is to subtract 15.38 from 100. The 100 is included in the formula to insure that the final result always oscillates between zero and 100. When 15.38 is deducted from 100, we have calculated the RSI of 84.62. That RSI indicates Intel is extremely overbought and is prone to profit taking or a "reaction." (Note that Stockcharts further smoothes this raw RSI number by adding additional data points so its RSI and the one you calculate will be slightly different.)

One of Wilder's goals in creating RSI was to eliminate unnecessary calculations. Once the 14th day's numbers were established, he used a 10-column spreadsheet to compute subsequent RSI values. An example of the 10- column spreadsheet with RSI calculations is provided below. The math takes some practice. The logic itself, however, doesn't change. RSI for days 15-19 (November 19-26) is presented in the spreadsheet. 

Below is a chart of Intel covering the period of the spreadsheet, November 1st -26th. In addition to RSI, I have also placed parabolic SAR and ADX, two of Wilder's other popular indicators, on the chart. Note that on November 12th RSI went above the overbought 70 level. That warned the swing trader INTC was significantly overbought. By itself, it was not a sell signal, because a stock can get and stay overbought for a long period of time when a strong uptrend is in place. It did caution, however, to be very alert for a reaction and be prepared to nail down profits.

Intel stayed overbought for several days and reached a closing peak of $24.80 on November 18th. RSI at that point was an extreme 84.62. Note how the large series of up days and the very small number of down days led to this extreme reading. 

On November 19th, Intel declined 64 cents, creating a large black candle. RSI gave a sell signal as it declined from above 70 to below that level. The slower moving ADX, while remaining on a buy signal, saw +DI fall below the black ADX line, often signaling a peak. The following day INTC lost another 6 cents. The parabolic SAR dots switched from below the share price to above it, signifying that profits should immediately be taken on INTC (the Swing Trader exited its position in INTC on this day with an 8.1% gain). According to Wilder's indicators, however, since ADX was on a buy signal, INTC should not be shorted.

Note how the RSI declined on subsequent days as the price fell. As the average gains in the last fourteen days approached the average losses, RSI trended down toward the 50 level, the point at which gains and losses over the 14 days are in perfect balance. 

Understanding how RSI is constructed leads to more effective use of the indicator.

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