The Relative Strength Index, or RSI, is a momentum indicator that depicts the price momentum of the asset you are trading. It is not related, in any way, to the concept of relative strength. Relative strength compares the returns of one stock or sector with other stocks/sectors (or in some cases an index). I use relative strength (not RSI) in my computer-based Model ETF Portfolio, and you can find an educational article on the subject of relative strength in our June 30, 2003 issue of The ETF Authority.

Introduced by J. Welles Wilder Jr. in his 1978 classic, New Concepts in Technical Trading Systems, RSI may very well be the best known of all technical indicators. If you do not already own this book, then I highly recommend it. In addition to RSI, he introduces the Parabolic System and Directional Movement (educational article on June 16, 20003) among several other well-known indicators and systems.

HOW TO COMPUTE RSI
RSI essentially shows the ratio of price movement on days the asset price rises as compared with price changes on days the asset price falls. It then normalizes these gains by forcing the index to hold between a level of "0" and "100."

The formula used to calculate RSI is as follows:

RSI = 100 – [100/(1+RS)]

where...

RS = Average of up day's closes / Average of down day's closes

The term average here is a bit confusing. This average is determined by summing up the total price gains on up days and dividing by how many total price changes you are examining for the up average. For the down average, add up the absolute value of the changes on the days prices fell, then divide that figure by the number of price changes.

For example, if I compute RSI using 11 days of prices, I will then have 10 price changes. If the sum of the gains on the up days is $1.50 and the sum of the losses on the down days is $1.00, then the RSI calculation would look something like this:

Average of up prices = $1.50/10 = 0.15
Average of down prices = $1.00/10 = 0.10

RS = .15/.10 = 1.5

RSI = 100 – [100/(1+1.5)] = 60

COMPUTING SUBSEQUENT RSI DATA
Wilder created the index at a time when computers were not widely available. Because of this, he chose a rather odd method to compute RSI for subsequent days. To calculate RSI on the next day, you would first multiply the average up day by nine and then add the current day's price change (if that day was positive). You would then divide that sum by 10 to get the new average up. For the average down figure, you would take the current average down, multiply that figure by nine, add the amount prices fell (if they did indeed fall), then divide that new result by 10.

For example, if the particular stock we used in the example above rose $0.50 the next day, then our calculations would be as follows:

Average up: (9 * 0.15 + 0.50) / 10 = 0.185
Average down: (9*0.10 + 0.00) / 10 = 0.09

RS = 0.185/0.09 = 2.0556

RSI = 100 – [100/(1+2.0556)] = 67

WARNING: YOUR CHARTING PACKAGE MIGHT COMPUTE RSI INCORRECTLY!
Many data vendors do not compute the Relative Strength Index (RSI) correctly. If prices do not change on any given day, then RSI should move towards 50. That is, if RSI was previously below 50, and prices do not change, then RSI should rise. If RSI was above 50 and prices remain unchanged, then RSI should slip towards 50. Many vendors leave RSI unchanged if prices do not change. This is incorrect!

The classic number used in the calculation for RSI is 14 days. Therefore, you'll need 15 days of prices to compute a 14-day RSI. Note also that once the first set of average up and average down figures are computed, you'll need to multiply those numbers by 13 (as opposed to nine, which we merely used as an example above), then add the price gain or price loss, then divide by 14 to get the new average up or average down figures.

LET YOUR RSI AGE A BIT BEFORE USING IT IN TRADING SYSTEMS
Notice that RSI essentially has a memory. You never throw out the old price data. The previous average becomes a factor in the new average. This means that if you and a friend compute RSI, but start the computation on different days, your actual RSI levels will be slightly different. This is very important if you are trying to write a system that uses RSI for trading decisions. I would not make any decisions based on your RSI calculation until you've had at least five times as many days passed compared to the number of days you use in your model. Therefore, if you use a 14-day RSI, then you should not use that type of system to generate any trading signals until you have at least 70 days of RSI history (which means you must have 85 days of price data).

OVERBOUGHT AND OVERSOLD
Two of the most overused terms in this business are "overbought" and "oversold." RSI is often used as a way of determining when something is overbought or oversold. The term "overbought" is supposed to mean that the product you are tracking is at risk of reversing lower, at least for a correction, because its price has risen too far, too fast. Meanwhile, "oversold" stocks are supposedly in position to reverse higher because their prices have fallen too far, too fast.

RSI offers you one way of quantifying overbought and oversold. When I'm using a 14-day RSI, then I generally consider the 70 level to be overbought and the 30 level to be oversold. If I use an 8-day measure, then I would use 75 or 80 for overbought and 20 or 25 for oversold, as the smaller the number of days, the more volatile the RSI indicator will be.

Unfortunately, these "rules of thumb" will probably get you into a whole lot of trouble. RSI is what is known as a "momentum oscillator." If you attempt to use the indicator to sell when momentum is high or buy when it is low, you may very well be trading against the trend. By definition, the market will tend to be overbought in a strong uptrend and oversold in a strong downtrend. Buying and selling at oversold and overbought levels works only in a non-directional (range trading, or non-trending) market.

Some traders will still try to sell when RSI gets high or buy when it is very low. However, they will adjust for the market's overall trend. For example, if the trend is up, then many traders will only sell when RSI moves above, then falls below, the 80 mark. If the trend is up, they will buy if RSI falls below and then moves back above 40. Likewise, in a bear market, they will often buy only when RSI drops below and then moves back above 20 and will sell on a move above, and then back below, 60. (Note: All of these levels are based on a 14-day RSI measure.)

I have found that you are far better off buying when RSI moves above 70 (with an intelligent stop, of course) and selling when RSI falls below 30. In the past, I've created profitable trading systems in the U.S. bond market based on these ideas, coupled with the Directional Movement Index.

DIVERGENCES
I am not going to spend a whole lot of time on divergences here, although they are very important when studying momentum indicators. I've already written a full educational article on the subject, which you can find in our issue archives (June 23, 2003 ETF Authority issue).

Divergences are often a warning of an impending change in trend. If the security you're examining is in an uptrend, then a divergence occurs when prices reach a new high, but RSI does not. If the security you're examining is in a downtrend, then a divergence occurs if prices fall to a new low, but RSI does not manage a new low.

A word of warning: markets can diverge for a very long time. Take a look at the chart of Intel Corp. (INTC, $31.66) above. RSI peaked in early September with INTC trading at $28.22. If you had shorted the stock or had stayed on the sidelines at that point, then you would have missed a rally of nearly +15%! I would never short against an uptrend just because I noticed a momentum divergence. Absent at least a fall below important support, or a break of an up trendline, there is no sell signal. Also, if the fall in RSI sees its down trendline break (see the red down trendline in the chart above), then I would get very nervous about using the divergence as a sign of impending doom.

SUMMARY
The Relative Strength Index (RSI) is one of the most widely used technical indicators. It is well suited as part of a computer-based trading system. However, blindly following the crowd by selling when the market is overbought, or buying when it is oversold, is a strategy that is nearly guaranteed to lose you money in the long run. I have explained in the preceding paragraphs how to use this indicator in a more profitable manner as well as how to compute it. Understanding how the indicator is calculated will help you to better understand what a change in its level truly represents.

Good trading!

Steven Poser
Editor
The ETF Authority
New York, NY

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