3 vital things you didn’t know about the Relative Strength Index
The top link of an online search shows, that for a given online search, approximately 25% of users click the top link of a Google search, and more than 90% will never go past the first page. Usually, it is good to dig deeper, but with regard to the RSI indicator, if you actually expand your search, it wouldn’t change much, because you get the same information from all sources. Let’s take a fresh look at RSI. Hopefully, you will equally enjoy reading it, as I enjoyed writing.
1. Refreshing the basics
Let me make one thing clear: I like working with the Relative Strength Index. RSI is not a bad indicator. Nor it is the best answer to a trader’s problems. It is just a product of mathematical operations derived from price data, that can be interpreted by a trader or used in a trading strategy.
To start the dive into the RSI world, we have to go back to the basics. RSI is constrained between 0 and 100 points. Probably 99% of traders use a 14-period setting and 99% of them look for reversals below 30 or above 70.
OK, if RSI is constrained in the (0,100) zone it is not that hard to calculate, that the middle of this bracket is a 50-point line. Sticking to RSI(14) we get:
Sometimes RSI(14) is well above the 50-point line, sometimes it is well below it, and sometimes it crosses it frequently. If we create a simple strategy that holds a long position (1) when RSI(14) > 50 and a short position (-1) when RSI(14) < 50 then we will get:
Now, it gets interesting… Zooming in the period of the choppy market when RSI(14) crossed the 50-point line frequently, and comparing it with how price behaved in relation to 27-period exponential moving average (RSI is calculated using Wilder Moving Average (more here), so the TRUE period for exponential moving average smoothing is 2*14–1 = 27 bars), we can see that the RSI above/below 50-points signals take place at the same time as the crossovers of price and exponential moving average.
Is this coincidence? How close is the 50-point line to the exponential moving average of the corresponding period length? Can we calculate the difference? Can we calculate the 50-point line in terms of price value…?
To get the answers we have to get a little crafty. RSI indicator can be reversed, so we can create RSI Predictor (TradeStation & TradingView). The idea is quite simple:
Dear RSI Predictor,
Please tell me, (at the end of the bar) what price has to be reached (next bar close) for my RSI indicator to display (next bar close) the desired number.
Truly yours,
Trader Joe
Using RSI Predictor to calculate the desired price for RSI(14) to read 50 points, and comparing it to the exponential moving average (27) we notice something very interesting:
Wow! They both look the same… The only difference is the 1-bar offset (that is how RSI Predictor works) between RSI Predictor and Exponential Moving Average, which means that the RSI 50-point line IS the exponential moving average! So, any other number that RSI shows has to be interpreted as a distance from it.
To make a long story short: if RSI(14) is above 50-points then price (close) is above ExpMA(27), and if RSI(14) is below 50-points then price (close) is below ExpMA(27). It is not a magnificent discovery, but without it, we will not be able to properly understand the information we get from our charts and will fall prey to charlatans telling the fairy tales about magical properties that the Relative Strength Index supposedly has.
Here’s a short video showing it step by step:
2. Volatility & basic statistics
We just found out (mathematically) that when RSI crosses the 50-point line it means that the price crosses the exponential moving average of the corresponding length (2*period-1). Right now, it’s time to empirically check if it is really true.
As far as data we will stick to RSI(14) on daily S&P500 futures provided by the TradeStation platform.
Starting in 2011, we can find 25 occurrences when RSI(14) reading was between 49.75 points and 50.25 points, and we have one reading of RSI(14) being exactly 50 points, which is July 23rd, 2012.
Translating it to price (close) distance from 27-period exponential moving average (in percent) we see that our calculations were right, and the RSI 50-point line is indeed an exponential moving average (the average 0.01-point difference is negligible).
To fully understand what RSI is really showing we have to go back to the calculation behind one of the most popular indicators in the history of chart analysis. Without going into much detail, we can say that RSI is calculated as an (exponentially smoothed) ratio of how much price moved in one direction to how much price moved (in absolute terms) at all. In TradeStations’ EasyLanguage:
The key component that we will work with will be “TotChgAvg” which is the Exponential Moving Average of the absolute price movement (always positive numbers). The mentioned price movement is simply the difference between today’s and yesterday’s close, which is the most basic volatility measure. Note that, it’s not the Average True Range because it only takes closes and disregards the high and low, but in our case, it will be the volatility estimator that we will work with. With regard to volatility estimators, there are many more of them, but most of them share one thing in common — a scaling factor. For RSI(14) it will be 5.1961 which is the square root of 27 (moving average length). Therefore, we can draw an envelope around 27-period exponential moving average: upper boundary will be AvgExp(27) + 5,1961* TotChgAvg and lower boundary AvgExp(27) — 5,1961* TotChgAvg.
This particular volatility band does not differentiate much from others of this kind like Bollinger Band or Keltner Band. What stands out are the red/blue arrows showing moments when RSI was close to 70 points (red arrow) or 30 points (blue arrow). At the same time, the price was really close to the upper or lower boundary of our volatility channel. To check how close we will translate the volatility band into a standard score histogram:
Now, we’re onto something…
I don’t know if this was the intention of the RSI creator to highlight 30/70 point levels because they are +1 and -1 (scaled) volatility zones, but that is what it really is. When RSI(14) equals 70 then the price is (almost) exactly at the upper volatility band, and when RSI(14) equals 30 then the price is (almost) exactly at the lower volatility band.
3. Changing shape changes all
Right now, using the same logic for constructing the volatility bands, it’s time to check the behavior of other period lengths used for RSI calculation.
Any numbers are equally good, but we will use numbers from the Fibonacci sequence (geometric growth) instead of any fixed interval (linear growth). We will start with RSI(2), RSI(3), RSI(5) … and finish with RSI(89). And, yes — I know — no one uses RSI(89). Well, we’re about to find out why.
There is one thing that is consistent with previous discoveries: No matter the period length for RSI, the 50-point line is still an exponential moving average of the corresponding length. But when we compare how Z-score translates into levels that the RSI indicator reaches, then we see, that the +1 and -1 Z-score is never reached by RSI(2) and RSI(3), and is really quickly reached by RSI(55) or RSI(89). So even when RSI(2) drops to 1 point or goes as high as 99 points the Z-score is still way above -1 or below 1. On the other hand, RSI(89) moving to 58-points already translated into +1 Z-score, and dropping to 42-points translates to -1 Z-score. This means that any attempt to average or compare RSIs of different lengths in order to get the full picture of the market situation is a wasted effort.
But this is not the only problem we have with the behavior of RSI of different lengths. Even from the above chart, we see that RSI(2) can take pretty much any number between 0 and 100, and RSI(89) will barely reach 70-points and in the last 10 years (S&P500 futures) did not drop below 37-points. The asymmetry in positive and negative extremes is caused by the current bull market, so the next pictures will be built using almost 20 years of data for the S&P500 index.
The picture shows the distributions of RSI readings depending on the period length. Starting from the shortest period we get a bimodal distribution (RSI(2) will most of the time be in a 5–10 or 90–95 point bin) that through almost uniform distribution of RSI(3) transforms into platykurtic distribution (RSI(5) and RSI(8)). After that, we finally go to something that we know and are used to: normal distribution aka “the bell curve”. This happens when the RSI length is set to 13 or 21. Once we move into “long-term territory” (34,55,89) the density function gets more and more leptokurtic.
So, this is another view of the same problem with RSI. The trader, without dropping its habits, just can’t get a good deal of valuable information from short or long term period RSIs, because only mid-term lengths (the one and only RSI(14)) show the picture of the market through the lens that we are used to: the bell curve.
The mistakes that come from using the normal distribution with financial data is a longer and more complex story, so for now, let’s just stick to the main subject — the RSI indicator.
We just discussed that the RSI indicator is badly calibrated. It shows one kind of property for short-term settings, other properties for medium-term settings, and totally different properties for long-term settings. The best visualization we get is by looking at the heat map, where we plot 50 different RSI lengths at once. The idea is simple — saturate with more and more red when RSI is high (>80), and saturate with more and more green when RSI is low(<20):
The first row (horizontal lines) from the bottom is RSI(2) and the top one is RSI(100). The information we get from this chart is not a surprise. The bottom rows change colors from bright red (overbought) to bright green (oversold) really frequently, which is consistent with the previous chart, where RSI(2) has a bimodal distribution. And the top rows, where long period RSIs are plotted, barely get affected by the price movements. The only things that change are the pale shades of red or green. And of course, this is also expected, because long-term RSIs rarely break from the 40- to 60-point range.
Well, we pretty much deciphered RSI. We know that:
- When RSI(period) crosses the 50-point line, price crosses the exponential moving average of a corresponding length (2*period — 1)
- For RSI(14) 70-point line equals +1 volatility (scaled) from ExpMov(27) and 30-point line equals -1 volatility (scaled) from ExpMov(27)
- RSI is a Z-score (distance) between price and the exponential moving average, for which the scaling factor (square root of the period) is not working properly
The wrong calibration of the scaling factor makes it impossible to average or compare RSIs of different lengths. If you want to stay with RSI(14) only, you’re fine. If not — you either need a solution or are forced to work with constraints that cannot be overcome.
From now on, if you encounter the RSI indicator ever again you will know exactly what you see. You will be immune to supposedly magical properties of RSI trading systems, or secret patterns that few know. Hopefully, it will make you a better trader.