Relative Strength Index

Bull / Bear Dichotomy Indicator v 1.0 (BBD)

The purpose of a trading or investing model is to move probability in your favour. One can be considered worthwhile if it can consistently produce risk adjusted returns in excess of the broad market over any period greater than 2 years. A mechanical trading model can be considered worthwhile if in addition to this it can:

Remove emotion from decisions.
Do the hard work so you have the time freedom to enjoy your profits.

Regardless of the time domain of your preferred trading style, being able to clearly slice the market into high probability bullish and bearish periods is of great advantage. So far during the Technical Indicator Fight for Supremacy we have identified three very effective and different ways of doing this:

The True Golden Cross
Relative Strength Index
Stochastic Oscillator

Below I will cover a quick summary of the previous research or you can jump straight to the latest findings.

The True Golden Cross

EMA Crossover 13/48 EOD Long

Using a simple 13 / 48 Day EMA crossover; 62% of the time the 13 Day EMA was above the 48 Day EMA. During this time the average trade duration was 93 days and there was an annual return of 10.17% vs 6.32% for the global average during our test period. During the balance of time there was an annual return of -3.48% (see full tests and research).

Conclusion:

EMA(13) > EMA(48) = Bullish
EMA(13) < EMA(48) = Bearish

Relative Strength Index

126 Day RSI EOW, Long

Using a 126 Day RSI (with an EMA instead of Wilder’s Smoothing, it would be 63.5 instead of 126 on a standard RSI) and End OF Week (EOW) signals; 63% of the time the RSI was above 50. During this period the average trade duration was 97 days and there was an annual return of 8.73% vs 6.32% for the global average during our test period. During the balance of time there was an annual return of -2.77% (see full tests and research).

Conclusion:

RSI(126) > 50 = Bullish
RSI(126) < 50 =Bearish

Stochastic Oscillator

252 Day Stochastic Oscillator EOD, Long

Using a 252 Day Stochastic Oscillator (SO); 66% of the time the SO was above 50. During this period the average trade duration was 104 days and there was an annual return of 8.43% vs 6.32% for the global average during our test period. During the balance of time there was an annual return of -2.05% (see full tests and research).

Conclusion:

SO(252) > 50 = Bullish
SO(252) < 50 = Bearish

The Bull and Bear Dichotomy v 1.0 (BBD)

The EMA crossover shows us that there is value in measuring shorter term momentum vs longer term momentum. The RSI shows us that there is value in a measure of declines vs advances. While the Stochastic Oscillator shows us that there is value in being long a market when it is in the top half of its range. The trade profile for each indicator is desirable but their signals are often in conflict.

Don Beasley of Trademark Capital has been an inspiration of mine for many years and has been kind enough on several occasions to share his insight and experience. He likes to combine the RSI and Stochastic Oscillator by taking an average of the two. This is straight forward because both move between the same 0-100 range.

Including the EMA crossover is not as straight forward however; it is not limited to a scale at all. But because the percentage distance between the EMA(13) and EMA(48) should be normally distributed we decided to force it into a 0-100 range by using the cumulative distribution of a bell curve. It has a SD of 2.17% when EMA(13) > EMA(48) and SD of 2.35% when EMA(13) < EMA(48):

Bull / Bear Dichotomy v1 Example

Above you can see the readings from each indicator during a randomly selected 2.5 year period on the Australian All Ordinaries Index. The thick red line is an equally weighted average of the RSI, SO and MA Cross, smoothed with a EMA(10). This we are calling the Bull / Bear Dichotomy or BBD Indicator v1. By combining all three indicators, a greater level of stability and robustness is achieved. See below the full trade profile:

In looking at the trade profile the signal stability is clear with an average trade duration of 170 days, an average profit of 21.81% and a probability of profit sitting at 48%! The other statistics are not dissimilar to the component indicators. The only thing missing from the BBD is a measure of volume. We plan to include this in v2 and this will hopefully improve the stability further.

It is highly likely that that we are reaching the upper limits of what is possible, as far as returns, from a long term indicator applied to a blind selection of broad market indices. To improve on these results it will be necessary to do one or a combination of the following:

Have a selection process for the assets to be traded.
Apply a secondary trading system specifically designed to perform during the bullish or bearish environments identified by the BBD.

How do think these results could be improved? What other long term measures would be worth researching for inclusion in v2 of The Bull / Bear Dichotomy Indicator?

Please note: These returns are the result of evenly allocating funds between 16 different global test markets. If only one market was on a buy signal then only 1/16th of the capital was exposed to the market. Some markets performed better than others and lifted the returns. All were profitable and the strategy outperformed on an absolute basis on 15/16 of the test markets. A further explanation of the methodology can be found here.

Relative Strength Index (RSI) – Test Results

The RSI is a staple indicator of the technical analysis community but how good is it, really? What are the best settings? What does its trade profile look like? Ask around and no one can tell you… Does it not seem strange that so many traders can be using an indicator without solid data on its performance? Well we are on a mission to change that. We tested 3800 different RSI settings through 300 years of data across 16 different global markets~ to reveal the facts.

Download A FREE Spreadsheet With Data, Charts

And Results For all 3,800 RSIs Tested

RSI Conclusion

Our Testing Strategy Explained

noʊtɑ bɛnɛ (Note Well) we use an EMA when calculating the RSI instead of a WS-MA. This is not just to be difficult, please read more about the RSI for an explanation. The formula to convert the EMA Look Back period to the identical equivalent WS-MA used by your charting programs when calculating the RSI is (Period + 1)/2. Below is a table with all the Look Back Periods we tested and how they convert to the original RSI:

RSI Period Conversions

Now there are many different ways that signals can be taken from the RSI but to start with we wanted to see how the market behaved when the RSI was in different ‘zones’. We also wanted to find out which RSI Look Back period is the most desirable. But this presents a problem because changing the Look Back period alters the range of an RSI.

For instance during our tests across 16 different markets and 300 years of data the range for the RSI(5) was 89.96 – 10.04 while for the RSI(100) it was 70.77 – 29.23. Clearly a direct level comparison between two RSIs of different look back periods is not suitable.

To overcome this challenge we identified the range for each RSI across all different look back periods tested. Then divided each range by 10 and advanced from the mid line (50) in 1/10th increments specific for each different RSI. The normalisations were numbered based on how many 1/10th of their range they were from 50 (with the exception of the final increment at each end which was extended to 100 or 0 respectively).

Here is a table of the normalisations used which will hopefully clarify:

RSI Normalisations

For instance, lets say we wanted to see how the market performed within a 0 – 3 Normalised RSI range on a RSI(15) vs. an RSI(55). Using the table above as a guide we would test the RSI(15) from 50 – 78.30 and the RSI(55) from 50 – 70.91; in doing so we should be comparing apples with apples.

Next it was necessary to exclude some data because it was taken from a sample too small to be conclusive. Lets say you were to buy every time that an RSI(35) was in the -4 to -5 RSI range, in our tests your annualized return during exposure was 248377165801.21%… sounds great right? Yes and no; the average trade did return 1.16% per day… but the average trade duration was only 1 day and you would have only been exposed to the market 3 days a year. Statistics like this are invalid so we excluded anything that didn’t result in market exposure of at least 6%.

We tested all combinations of increment ranges:

Range of 1 = -5 to -4, -4 to -3 … 3 to 4, 4 to 5

Range of 2 = -5 to -3, -4 to -2 … 2 to 4, 3 to 5

Range of 3 = -5 to -2, -4 to -1 … 1 to 4, 2 to 5

Range of 4 = -5 to -1, -4 to -0 … 1 to 4, 2 to 5

Range of 5 = -5 to 0, -4 to 1 … -1 to 4, 0 to 5

The key findings are published below, to see all the results download the full results spreadsheet.

Return to Top

RSI: ANY, Range = 1

First, to see how the market behaved in each increment; a long position was taken ANY time the test market was in the corresponding RSI range:

RSI, ANY, Increment Range 1, Annualized Return During Exposure, Long

Above 0 (50 on the RSI) and the returns are positive, below zero and the returns were negative, you don’t often see such a clear edge over the market as that (see the results when going Short). The blank cells, (if you were wondering) are where data was excluded because the market exposure < 6%.

Return to Top

RSI: ANY > 0, Range = 1, 2, 3, 4, 5

So we now know that RSI > 50 = Good and RSI < 50 = Bad. Lets now look at how far above 50 (the 0 increment) we can go and capture the best profits. A Long position was open ANY time the test market was in the corresponding RSI range:

RSI ANY - Long, Increment Range 1, 2, 3, 4, 5 > 0

From the above table we can see that the most gains on the Long side occur when the RSI is between the 0 and 4 increment (see results going short). The Look Back period makes surprisingly little difference although around 55 days we see the most gains captured over all:

55 Day RSI EOW, 50 - 77.88 Range, Long Any

Above are the results from an RSI(55) with a open Long position any time that the RSI was in in the 50 – 77.88 range (0 – 4 increment). The positions were only opened and closed at the End Of the Week (EOW) because switching from EOD to EOW almost doubled the average trade duration and the probability of profit (see the results EOD). While the trade profile is quite good, the MA Crossover or FRAMA are still both more desirable.

Note – our RSI(55) using an EMA is equivalent to an RSI(28) in your charting programs which use Wilder’s Smoothing.

Return to Top

RSI, ENTRY > 0, Range = 1, 2, 3, 4, 5

What if we only opened a Long position when the RSI was rising? In these tests a position was only initiated when the RSI went from being below 50 (the 0 increment) to above 50. It was then held as long as the RSI remained in the corresponding range:

RSI ENTRY - Long, Increment Range 1, 2, 3, 4, 5 > 0

By introducing entry criteria to the RSI trades the market exposure decreased and with it the returns in most areas (see results going short). One area that does stands out however; the Annualized Return During Exposure when the RSI(5) moves through the 0 – 1 increment. Lets take a look at the trade profile:

5-day-rsi-eod-0-1-l-entry

Above are the results from an RSI(5) with a position opened Long only when the RSI raised above 50. The position was then held until the RSI moved above 55.99 or back below 50 (the 0 – 1 increment). The resulting trade profile doesn’t suit my style but I will entertain the idea because it may suit yours…

You don’t have to look far in the quant blogosphere to find examples of systems based on holding a position for only one day following an fed announcement when the VIX is above a certain level etc. Anyway, be this a practical system or not, it does have a rather smooth looking equity curve and a high probability of profit. Just for fun, lets look at what happens if we add 4X leverage and only go Long when the 13 / 48 MA Crossover is confirming the RSI signal:

13 EMA > 48 EMA + 5 Day RSI, EOD, 50 - 60 Range, Long + Entry, 4X

You must admit, once you crank up the leverage and remove the bear markets by confirming the signals with the 13 / 48 MA Crossover; this is an impressive looking equity curve. The best part is that you are only exposed to the market 7% of the time! Realistic in the real market? Questionable…

Perhaps with the use of futures this could be a workable strategy. It was profitable on 15/16 global indices we tested and showed a 54% probability of profit through 3837 trades (a nice large sample). What do you think?

Return to Top

RSI Conclusion

Never before have I seen such a dichotomy of profitable and unprofitable trades when an indicator is above or below a level as is the case with the RSI being above or below 50. This proves that momentum is a strong and valuable predictor of market direction and the theory behind the RSI is sound. For this reason it would be worth testing your system with entry signals confirmed by the RSI(55) being on the appropriate side of 50. (Remember to use the conversion table; our RSI(55) will be an RSI(28) in your charting program.)

While the RSI clearly provides valuable information, unfortunately we are yet to identify a method of use that presents a more desirable trade profile than the simple effectiveness of the MA Crossover or the FRAMA.

We also tried using an EMA signal line on the RSI but the results where not worth writing about (download all the results in a spreadsheet to see for yourself.) However I feel that there will be other worthwhile ways to test the RSI. Perhaps it could be used as a breadth indicator where the number of higher highs from the RSI is compared to the number of higher highs from the stocks within an ETF?

How would you like to see the RSI tested? Ideas?

More in this series:

We have conducted and continue to conduct extensive tests on a variety of technical indicators. See how they perform and which reveal themselves as the best in the Technical Indicator Fight for Supremacy.

Return to Top

~The data used for these tests is included in the results spreadsheet and more details about our methodology can be found here.
No interest was earned while in cash and no allowance has been made for transaction costs or slippage. Trades were tested using End Of Day (EOD) signals on Daily data except where otherwise noted.

Relative Strength Index (RSI)

The Relative Strength Index (RSI) is a very popular Momentum Oscillator and was created by J. Welles Wilder, Jr. who first presented it in his landmark book New Concepts in Technical Trading Systems (June 1978).

The RSI moves within a range from 0 to 100 and typically has an upper extreme zone above 70 and a lower extreme zone below 30. When in the upper extreme zone a stock is considered overbought and when in the lower extreme zone a stock is considered oversold. At such extremes the RSI suggests that a recent stock movement is likely to slow or reverse. Welles recommended a 14 period RSI but increasing the RSI period will decrease its volatility (and vice versa) as seen in the example below where three different RSI periods are overlaid:

RSI Example

The Relative Strength Index measures declines relative to advances over a specified period. This is done by averaging out the amount that a stock advanced on the days that it moved higher and the amount that stock declined on the days it moved lower. A modified ratio of these two averages is then charted creating a visual Relative Strength Index of bulls and bears.

Wells used his own smoothing method in the RSI known as Wilder’s Smoothing (WS-MA). Despite having a unique calculation method, WS-MA is actually identical to an EMA with a period of (2 * RSI Period) – 1. So an RSI(14) actually has an EMA period of 27 = (14 * 2) -1. Why care? Because it helps to maintain constancy between methods and measures when comparing indicators as we are in the Technical Indicator Fight for Supremacy.

For instance if we were to compare the Relative Momentum Index (RMI) to the RSI it would be helpful to compare them over equivalent look back periods so any patterns become evident. For this reason we use the EMA instead of the WS-MA in the Relative Strength Index.

How to Calculate the RSI

RSI = 100 – (100 / 1 + RS)

RS = EMA of Gains / EMA of Declines

EMA = EMA(1) + α * (Current change – EMA(1))

Where:

α = 2 / (N + 1)

N = (2 * RSI Period) – 1

RSI Period = User selected value but typically 14

Note:

Declines are expressed as their absolute value (all as positive).

Each EMA can be seeded with a SMA of the relevant Gains or Losses.

Free RSI Excel Download

To make life easy we have built a free Excel Spreadsheet for you to download containing an RSI that will automatically adjust to the look back period you set. You will find it at the following link under Technical Indicators.

How to use the RSI

Overbought/Oversold: Wilder suggested the upper and lower extremes of 70 and 30 as an indication of turning points. He said that when the RSI rises above 30 this is a bullish sign, with the opposite indication when the RSI falls below 70. Some traders, after identifying the long term trend of a stock will use extreme readings from the RSI as an entry point.

Divergences: Confirmation of the strength of a medium term bullish trend can be gained by looking for higher highs from the stock confirmed by higher highs from the RSI. In a similar fashion; a stock that is declining and making lower lows while the RSI is making higher lows may become a buying opportunity.

Centreline Crossover: The centreline on an RSI is 50, above this level we know that the average gain has been larger than the average decline over the look back period. Many traders look to see the RSI above or below 50 as confirmation before opening a long or short position.

Is the RSI a good indicator?

That is a great question, at a guess I would say yes but rather than guess we tested it through 300 years of data across 16 different global markets – See the Results.