Relative Strength Index (RSI)

Introduction

J. Welles Wilder developed the Relative Strength Index (RSI) and introduced it in the June 1978 article for Commodities magazine, which is now Futures magazine. Wilder provided further detail in his classic book, New Concepts in Technical Trading Systems, which was also published in 1978. This book provides details on calculation, usage and signals for RSI and many of Wilder's other indicators including Average True Range, Parabolic SAR and ADX.

Even though the indicator is called the "Relative Strength Index", it does not measure relative strength in the traditional sense. The "relative strength comparative" shows the performance of one security against another with a ratio chart. John Murphy's relative strength charts compare the percentage change of 2 or more securities over a specific timeframe. RSI, on the other hand, uses price data from one security to compare its gains and losses over a period of time.

RSI is a momentum oscillator that measures the speed and change of price movements. RSI oscillates between zero and 100. Traditionally, and according to Wilder, RSI is considered overbought when above 70 and oversold when below 30. Signals can also be generated by looking for divergences, failure swings and centerline crossovers. RSI can also be used to identify the general trend.

RSI is an extremely popular momentum indicator that has been featured in a number of articles, interviews and books over the years. In particular, Constance Brown's book, Technical Analysis for the Trading Professional, features the concept of bull market and bear market ranges for RSI. Andrew Cardwell, Brown's RSI mentor, introduced positive and negative reversals for RSI. In addition, Cardwell turned the notion of divergence, literally and figuratively, on its head.

Calculation


                  100
    RSI = 100 - --------
                 1 + RS

    RS = Average Gain / Average Loss

To simplify the explanation, RSI has been broken down into its basic components: RS, Average Gain and Average Loss. This RSI calculation is based on 14 periods, which is the default suggested by Wilder in his book. Losses are expressed as positive values, not negative values.

The very first calculations for average gain and average loss are simple 14 period averages.

  • First Average Gain = Total of Gains during the past 14 periods / 14.
  • First Average Loss = Total of Losses during the past 14 periods / 14

The second, and subsequent, calculations are based on the prior averages and the current gain loss:

  • Average Gain = [(previous Average Gain) x 13 + current Gain] / 14.
  • Average Loss = [(previous Average Loss) x 13 + current Loss] / 14.

Taking the prior value plus the current value is a smoothing technique similar to that used in exponential moving average calculation. This also means that RSI values become more accurate as the total calculation period extends. SharpCharts uses at least 250 data points prior to the starting date of any chart (assuming that much data exists) when calculating its RSI values. To exactly replicate our RSI numbers, a formula will need at least 250 data points.

Wilder simply normalized RS with his formula and turned it into an oscillator that fluctuates between zero and 100. In fact, a plot of RS looks exactly the same as a plot of RSI. This normalization step makes it easier to identify extremes because RSI is range bound. RSI is 0 when the Average Gain equals zero. Assuming a 14-period RSI, this means prices moved lower all 14 periods. There were no gains to measure. RSI is 100 when the Average Loss equals zero. This means prices moved lower all 14 periods. There were no losses to measure.

Chart 1 - RSI RS Plots

Chart 2 - RSI Spreadsheet

Here's an Excel Spreadsheet that shows the start of an RSI calculation in action.

Parameters

The default look-back period for RSI is 14, but this can be lowered to increase sensitivity or raised to decrease sensitivity. 10-day RSI is more likely to reach overbought or oversold levels than 20-day RSI. The look-back parameters also depend on a security's volatility. 14-day RSI for internet retailer Amazon (AMZN) is more likely to become overbought or oversold than 14-day RSI for Duke Energy (DUK), a utility.

RSI is considered overbought when above 70 and oversold when below 30. These traditional levels can also be adjusted to better fit the security or the analytical requirements for the chartist. Raising overbought to 80 or lowering oversold to 20 will reduce the number of overbought/oversold readings. Short-term traders sometimes use 2-period RSI to look for overbought readings above 80 and oversold readings below 20.

Signals

Overbought-Oversold

Wilder considered RSI overbought above 70 and oversold below 30. Chart 3 shows McDonalds with 14-day RSI. This chart features daily bars in gray with a 1-day SMA in pink to highlight closing prices because RSI is based on closing prices. Working from left to right, the stock became oversold in late July and found support around 44. Notice that the bottom evolved after the oversold reading. The stock did not bottom as soon as the oversold reading appeared. Bottoming can be a process. From oversold levels, RSI moved above 70 in mid September to become overbought. Despite this overbought reading, the stock did not decline. Instead, the stock stalled for a couple weeks and then continued higher. Three more overbought readings occurred before the stock finally peaked in December. Momentum oscillators can become overbought (oversold) and remain so in a strong up (down) trend. The first three overbought readings foreshadowed consolidations. The fourth coincided with a significant peak. RSI then moved from overbought to oversold in January. The final bottom did not coincide with the initial oversold reading as the stock ultimately bottomed a few weeks later around 46.

Chart 3 - RSI Overbought Oversold

Like many momentum oscillators, overbought and oversold readings for RSI work best when prices move sideways within a range. Chart 4 shows MEMC Electronics (WFR) trading between 13.5 and 21 from April to September 2009. The stock peaked soon after RSI reached 70 and bottomed soon after the stock reached 30.

Chart 4 - RSI Overbought Oversold

Divergences

According to Wilder, divergences signal a potential reversal point because directional momentum is weakening. In general, a bullish divergence occurs when an indicator makes a higher high and the underlying security makes a lower low. A bearish divergence forms when the indicator records a lower low and the security records a lower high. Chart 5 shows Ebay (EBAY) with a bearish divergence in August-October. The stock moved to new highs in September-October, but RSI formed lower highs for a bearish divergence. The subsequent breakdown in mid October confirmed weakening momentum.

Chart 5 - RSI Divergences

A bullish divergence formed in January-March. The bullish divergence formed with Ebay moving to new lows in March and RSI holding above its prior low. RSI reflected less downside momentum during the February-March decline. The mid March breakout confirmed improving momentum. Divergences tend to be more robust when they form after an overbought or oversold reading.

Before getting too excited about finding divergences for great trading signals, it must be noted that divergences are misleading in a strong trend. A strong uptrend can show numerous bearish divergences before a top actually materializes. Conversely, bullish divergences can appear in a strong downtrend - and yet the downtrend continues. Chart 6 shows the S&P 500 ETF (SPY) with three bearish divergences and a continuing uptrend. These bearish divergences may have warned of a short-term pullback, but there was clearly no major trend reversal.

Chart 6 - RSI Divergences

Failure Swings

Wilder also considered failure swings as strong indications of an impending reversal. Failure swings are independent of price action. In other words, failure swings focus solely on RSI for signals and ignore the concept of divergences. A bullish failure swing forms when RSI moves below 30 (oversold), bounces above 30, pulls back, holds above 30 and then breaks its prior high. It is basically a move to oversold levels and then a higher low that holds above oversold levels. Chart 7 shows Research in Motion (RIMM) with 10-day RSI forming a bullish failure swing.

Chart 7 - RSI Failure Swing

A bearish failure swing forms when RSI moves above 70, pulls back, bounces, fails to exceed 70 and then breaks its prior low. It is basically a move to overbought levels and then a lower high that fails to exceed overbought levels. Chart 8 shows Texas Instruments (TXN) with a bearish failure swing in May-June 2008.

Chart 8 - RSI Failure Swing

Trend ID

In Technical Analysis for the Trading Professional, Constance Brown suggests that oscillators do not travel between 0 and 100. This also happens to be the name of the first chapter. Brown identifies a bull market range and a bear market for RSI. RSI tends to fluctuate between 40 and 90 in a bull market (uptrend) with the 40-50 zones acting as support. These ranges may vary depending on RSI parameters, strength of trend and volatility of the underlying security. Chart 9 shows 14-week RSI for SPY during the bull market from 2003 until 2007. RSI surged above 70 in late 2003 and then moved into its bull market range (40-90). There was one overshoot below 40 in July 2004, but RSI held the 40-50 zone the rest of the time. In fact, notice that pullbacks to this zone provided lower risk entry points.

Chart 9 - RSI Trend ID

On the flip side, RSI tends to fluctuate between 10 and 60 in a bear market (downtrend) with the 50-60 zone acting as resistance. Chart 10 shows 14-day RSI for the US Dollar Index ($USD) during its 2009 downtrend. RSI moved to 30 in March to signal the start of a bear range. The 40-50 zone subsequently marked resistance until a breakout in December.

Chart 10 - RSI Trend ID

Positive-Negative Reversals

Andrew Cardwell developed many new methods for interpreting RSI that include positive and negative reversals, which are the opposite of bearish and bullish divergences. Cardwell's books are out of print, but he does offer seminars detailing these methods. Constance Brown credits Andrew Cardwell for her RSI enlightenment. Before discussing the reversal technique, it should be noted that Cardwell's interpretation of divergences differs from Wilder. Cardwell considered bearish divergences as bull market phenomenon. In other words, bearish divergences form in uptrends. Similarly, bullish divergences are considered bear market phenomenon indicative of a downtrend. A positive reversal forms when RSI forges a lower low and the security forges a higher high. This lower low is not at oversold levels, but usually somewhere between 30 and 50. Chart 11 shows MMM with a positive reversal forming in June 2009. MMM broke resistance a few weeks later and RSI moved above 70. Despite weaker momentum (lower low in RSI), MMM held above its prior low and showed underlying strength. This signaled that the bigger uptrend was about to resume.

Chart 11 - RSI Reversals

A negative reversal is the opposite of a positive reversal. RSI forms a higher high, but the security forms a lower high. Again, the higher high is not usually in overbought territory, but somewhere in the 50-70 area. Chart 12 shows Starbucks (SBUX) forming a lower high as RSI forms a higher high. This negative reversal foreshadowed the big support break in late June and sharp decline. Even though RSI forged a new high and momentum was strong, the security failed to follow suit and formed a lower high. This shows weakness in the price action that foreshadowed the decline.

Chart 12 - RSI Reversals

Conclusions

RSI is a versatile momentum oscillator that has stood the test of time. Despite changes in volatility and the markets over the last 10 years, RSI remains as relevant now as it was in Wilder's days. While Wilder's original interpretations are useful to understanding the indicator, the work of Brown and Cardwell takes RSI interpretation to a new level. Adjusting to this level takes some rethinking on the part of the traditionally schooled chartist. Wilder considers overbought conditions ripe for a reversal, but overbought can also be a sign of strength. Bearish divergences still produce some good sell signals, but chartists must be careful in strong trends when bearish divergences are actually normal. Even though the concept of positive and negative reversals may seem to undercut Wilder's interpretation, the logic makes sense and Wilder would hardly dismiss the value of underlying price action. Positive and negative reversals put price action of the underlying security first and the indicator second, which is the way it should be. Bearish and bullish divergences place the indicator first and price action second. By putting more emphasis on price action, the concept of positive and negative reversals challenges our thinking towards momentum oscillators.

Using with SharpCharts

RSI is available as an indicator for SharpCharts. Once selected, users can place the indicator in a window above, below or on the price plot. Placing RSI directly on top of the price plot accentuates the indicator's movements relative to price action of the underlying security. Users can apply "advanced options" to smooth the indicator with a moving average or add a horizontal line to mark overbought or oversold levels.

Chart 13 - RSI SharpCharts

Chart 14 - RSI SharpCharts

Chart 15 - RSI SharpCharts

Suggested Scans

In the traditional sense, RSI can be used to identify short-term oversold stocks in long-term uptrends. The 200-day simple moving average is used to identify the long-term trend because it is a trend following indicator. A stock is in a long-term uptrend when above the 200-day and a long-term downtrend when below. RSI is used to identify overbought and oversold levels because it is a momentum oscillator. RSI is considered overbought when above 70 and oversold when below 30. 5-period RSI was chosen to insure an adequate supply of results. A longer RSI timeframe can be used to generate fewer results. Alternatively, overbought and oversold levels can be adjusted to 20 and 80 to tighten the scan.

RSI Oversold Scan (click here)

  • For the last market close:
  • United States Stocks with…
  • 20-day Simple Moving Average of Volume for today is greater than 40000
  • 60-day Simple Moving Average of Close for today is greater than 20
  • Daily Close for today is greater than 200-day SMA for today
  • Daily RSI(5) for today is less than or equal to 30

RSI Overbought Scan (click here)

  • For the last market close:
  • United States Stocks with…
  • 20-day Simple Moving Average of Volume for today is greater than 40000
  • 60-day Simple Moving Average of Close for today is greater than 20
  • Daily Close for today is less than 200-day SMA of Close for today
  • Daily RSI(5) for today is greater than or equal to 70

Further Study

Book: New Concepts in Technical Trading Systems by Welles Wilder. From the creator, this book features a chapter on RSI that discloses the formula and five things RSI can tell us. This classic also covers the Parabolic SAR, the Average Directional Index (ADX), Average True Range (ATR) and more.

Book: Technical Analysis for the Trading Professional By Constance Brown. Brown takes RSI to a new level with bull market and bear market ranges, positive and negative reversals, and projections based on RSI. Some methods of Andrew Cardwell, her RSI mentor, are also explained and refined in this book.



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