# RSI

The **Relative Strength Index (RSI)** is one of the most popular technical indicators that can help you determine overbought and oversold price levels as well as generate buy and sell signals.

RSI was developed by J. Welles Wilder, Jr. and published in a 1978 book, *New Concepts in Technical Trading Systems*, and in *Commodities* magazine (now *Futures* magazine) in the June 1978 issue. It is a **momentum oscillator** and as such it measures the rate of change of a given security’s price. Since it is also a **bounded oscillator**, it allows to spot overbought and oversold areas on the price chart.

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## Identifying overbought/oversold levels and basic buy and sell signals

The fact that RSI is a bounded oscillator (it takes on values from 0 to 100) allows us to identify overbought and oversold levels quite easily. Wilder considered RSI values over 70 overbought and values below 30 oversold, but these values can be adjusted to suit particular needs and markets. For instance, 80 could be used as overbought line in a strong uptrend and 20 as oversold line in a strong downtrend.

The simplest **buy signals are generated when RSI crosses the oversold line** – it can be a crossing from above and from below, depending on the version we choose. Conversely, the simplest **sell signals are generated when RSI crosses the overbought line** – here it also can be a crossing from above and from below, again – depending on the version we choose. Becoming overbought or oversold does not necessarily signal a trend reversal – in strong trends a security can become overbought or oversold many times before the trend reverses. It may, nevertheless, be a good opportunity to either take profits or enter the market.

Some investors also pay attention to **centerline crossovers**, i.e. situations when the RSI line crosses the 50 lin. The cross from above is considered bearish, while the cross from below – bullish. The chart below illustrates the idea of overbought/oversold levels as well as centerline crossovers:

GDX became overbought at the end of April, as well as in the first two weeks of May. Bearish centerline crossovers (i.e. from above) took place in the middle of January, in the second half of February, March and May. It became oversold at the end of January and in the first week of February. Bullish centerline crossovers (i.e. from below) appeared in the middle of February, as well as at the beginning and at the end of March. Virtually all of these signals were accurate.

## RSI and Gold

RSI is a very universal indicator. In this section we would like to present some of its successful applications on the gold market.

During the whole presented period RSI in conjunction with a 50-day moving average gave very reliable buying signals, as described on the chart. What is more, the usual line-crossovers (overbought and oversold line, centerline) signals proved quite reliable as well.

## RSI and Silver

This section is dedicated to the presentation of RSI applications on the silver market. We focus on one type of repeating pattern on the RSI chart that flashed very strong sell signals.

As we can see, throughout the whole analyzed period RSI gave very strong sell signals on the formation of major tops: first, there was a crest above or at the 70 line, and then another top above the 80 line that heralded the forthcoming price fall.

## Divergences

Divergences between RSI and price give one of the strongest buy and sell signals. Since divergences are present on the charts of many indicators and are a more general phenomenon, we have decided to dedicate separate articles to both **bullish** and **bearish divergences** . As they occur quite often on the charts of many assets, we encourage you to familiarize yourself with these terms.

## Failure swings

Failure swings are patterns formed solely on the RSI chart, i.e. they do not take the security’s price into consideration. According to Wilder, they provide very strong buy and sell signals. The following diagram depicts the idea of both bearish and bullish failure swings:

**Bearish Failure Swing** takes place when RSI forms a new high **above the overbought line**, then bounces back below it, forms a lower high **below the overbought line** and then goes down even further below the previous low, which is called the **sell point**.

**Bullish Failure Swing** takes place when RSI forms a new low **below the oversold line**, then bounces up above it, forms a higher low **above the oversold line** and then goes up even further **above the previous high**, which is called the **buy point**.

The following chart provides an example of both bearish and bullish failure swings:

Bullish failure swing took place in the last week of January and in the first week of February. Bearish failure swing formed in the middle of May. Both gave accurate buy and sell signals.

## Parameters Optimization

When using RSI we need to answer various questions: how many days should we include for calculation? What values should be considered overbought and oversold? These values are called **parameters**. Even though the author of RSI suggested one set of parameters: 14 days look-back period and 30 and 70 as oversold and overbought lines, respectively, **it seems really unlikely that these values are optimal for every market and every investor**. For instance, long-term investors could prefer a less sensitive version with a relatively long look-back period and higher overbought and lower oversold levels, to eliminate accidental whipsaws. What is more, **these optimal parameters may change over time** as the markets evolve.

The process of finding optimal parameters is called **optimization**. While one can (at least in theory) perform such an optimization by visually inspecting various combinations of parameters, such a process would probably yield inaccurate results and would certainly be cumbersome. Moreover, using this “manual” approach, it would be impossible to find and monitor optimum values for many markets, let alone other indicators. Hence it is usually carried out automatically using computers.

## New Approach to Generating Signals

We have already mentioned that basic buy and sell signals are generated by the RSI line crossing overbought and oversold lines. When we want to use RSI this way, not only do we need to choose parameters (as was discussed above), but we also need to choose the way of generating signals, i.e. whether we want to generate signal when RSI crosses a particular line from above or from below. The first question that comes to mind is: “Which one should I use?”. The answer – in our opinion – is pretty straightforward and simple: “The one that works best!”. Now, how would we find that one? To answer this question, we have carried out extensive research and slightly refined the methodology of generating line-crossover signals – instead of always using many lines at a time (overbought, oversold, centerline), for each type of signals (buy, sell) we consider only one line – a buy line or a sell line, depending on the signal – and then automatically find the best (i.e. yielding the highest ROI) parameters. At this point computer’s work is over, but we believe that before this new “best” indicator is put into use, the parameters and the final shape of the indicator should be examined by a professional in order to make sure that the computer didn’t make mistakes. While computers good at making calculations, they don’t have “common sense” that should be used before putting one’s (or somebody else’s) money on the table. In this case, computers might for example suggest only one buying point at the beginning of a bull market and no other points – which is one of the profitable strategies, but not too satisfactory for short-term traders. Naturally, the best parameters vary for different kinds of investors: short-, medium-, and long-term ones. Bearing in mind that markets can change rapidly, we also constantly monitor the parameters to ensure that the obtained results are always up to date.

## Calculation

RSI is calculated using the following formula:

Where

The original version proposed by Wilder used 14 days and this is still considered a “standard” value. This parameter can be changed depending on one’s needs and the market itself. The shorter the time span used, the more sensitive the indicator becomes, flashing more signals.

At least two remarks must be made regarding the calculation of average closes up and down. First of all, a close up means the **difference** between today’s close price and yesterday’s close price if the security **closed higher than yesterday**. So if today’s price is $62 and yesterday’s is $60, the close up is $2 (= $62 - $60). Conversely, a close down means the **difference** between yesterday’s close price and today’s close price if the security **closed lower than yesterday**. So if today’s price is $58 and yesterday’s $60, the close down is again $2 (= $60 - $58). Since close price change can only be in one direction then if close up is positive then close down is zero and if close down is positive then close up is zero. If close price did not change then both close up and close down are zero. Please note that both close up and close down are **nonnegative numbers**.

Secondly, to compute RS we calculate the averages of up and down closes only once. The following **smoothing formulas** are used from then on:

For instance, if we want to use standard x=14, then we would get an average of 14 day’s closes up by multiplying its previous value by 13, adding current close up and dividing it all by 14.

This technique was proposed by Wilder himself and allows us to use only the data from the previous day. Should you ever need to compute RSI manually (or using a spreadsheet) and wish to use this technique, please keep in mind that – since it is not a precise way of calculation – RSI values obtained this way become more accurate as the computation period extends. You should then also use some days before the start of the period you would like to analyze as an input for the calculation to make it more reliable.

RSI is a **bounded** indicator – thanks to its construction it takes on values between 0 and 100. If there was no single day when price increased during the look-back period of x days, then average of x day’s closes up = 0. Then RS = 0 and hence RSI = 100 – [100/(1+RS)] = 100 – 100/1 = 100 – 100 = 0.

If the price did not decrease during the x-day look-back period, then the average of x day’s closes down = 0. Since we cannot divide 0 into average of x day’s closes up, we assume that RS = infinity and hence RSI = 100 (100 – 100/infinity = 100). All other cases with nonnegative average closes up a and down fall into these boundaries. Below you will find an example of RSI step-by-step calculation:

First of all, we need to determine the difference between today’s and yesterday’s close price, which is done in the “Change” column. If the difference is positive it gets copied into the “Close up” column and a 0 is inserted in the corresponding field in the “Close down” column. Conversely, if it is negative then it is copied **as a positive value** into the “Close down” column and a 0 goes into the “Close up” column. After a chosen number of periods (we use the standard 14-day period in the above example) we are able to calculate RS and RSI.

## Conclusion

RSI is one of the most popular and widely used technical indicators that provides us with many ways to generate buy and sell signals. These include automatic line-crossover signals as well as more sophisticated visual ones, based on divergences and failure swings. It can also be used to tell the general state of the market in question by identifying areas where the market is overbought and oversold. However, one needs to keep in mind, that it is not (as any other technical indicator for that matter) a fully automatic tool – there are always choices to be made with regard to parameters. Even if there are always the default, pre-defined sets of parameters, no one can guarantee that they will always work and – what is more – that they will generate the highest profits. In order to mitigate the risk of using wrong indicator, we suggest using optimized, checked and monitored indicators.

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