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A comprehensive guide to the Relative Strength Index (RSI)

The maths behind trading

In this piece, we will delve into the essential concepts surrounding the Relative Strength

Index (RSI). The RSI serves as a gauge for assessing the strength of price momentum and

offers insights into whether a particular stock is in an overbought or oversold condition.

Throughout this exploration, we will demystify the underlying calculations of RSI, explore its

significance in evaluating market momentum, and unveil its practical applications for traders.

From discerning opportune moments to buy or sell based on RSI values to identifying

potential shifts in market trends, we will unravel the mathematical intricacies that underpin

this critical trading indicator.

Please note that none of the below content should be used as financial advice, but for

educational purposes only. This article does not recommend that investors base their

decisions on technical analysis alone.

As indicated in the name, RSI measures the strength of a stock's momentum and can be used to show when a stock can be considered over- or under-bought, allowing us to make a more informed decision as to whether we should enter a position or hold off until a bit longer.

It’s all very well and good to know that ‘you should buy when RSI is under 30 and sell when

RSI is over 70', but in this article, I will attempt to explain why this is the case and what RSI is really measuring.

The calculations

The relative strength index is an index of the relative strength of momentum in a market. This

means that its values range from 0 to 100 and are simply a normalised relative strength. But

what is the relative strength of momentum?

Initial Average Gain = Sum of gains over the past 14 days / 14

Initial Average Loss = Sum of losses over the past 14 days / 14

Relative strength is the ratio of higher closes to lower closes. Over a fixed period of usually

14 days (but sometimes 21), we measure how much the price of the stock has increased in

each trading day and find the mean average between them.

We then repeat and do the same to find the average loss.

The subsequent average gains and losses can then be calculated:

Average Gain = [(Previous Avg. Gain * 13) + Current Day's Gain] / 14

Average Loss = [(Previous Avg. Loss * 13) + Current Day's Loss] / 14

With this, we can now calculate relative strength!

Therefore, if our stock gained more than it lost in the past 14 days, then our RS value would

be >1. On the other hand, if we lost more than we gained, then our RS value would be <1.

Relative strength tells us whether buyers or sellers are in control of the price. If buyers were

in control, then the average gain would be greater than the average loss, so the relative

strength would be greater than 1. In a bearish market, if this begins to happen, we can say that there is an increase in buyers’ momentum; the momentum is strengthening.

We can normalise relative strength into an index using the following equation:

Relative Strength=Average Gain / Average Loss

Traders then use the RSI in combination with other techniques to assess whether to buy or

sell. When a market is ranging, which means that price is bouncing between support and

resistance (has the same highs and lows for a period), we can use the RSI to see when we

may be entering a trend.

When the RSI is reaching 70, it is an indication that the price is being overbought, and in a

ranging market, there is likely to be a correction and the price will fall so that the RSI stays at

around 50. The opposite is likely to happen when the RSI dips to 30. Price action is deemed

to be extreme, and a correction is likely.

It should, however, be noted that this type of behaviour is only likely in assets presenting

mean-reversion characteristics.

In a trending market, RSI can be used to indicate a possible change in momentum. If prices

are falling and the RSI reaches a low and then, a few days later, it reaches a higher low

(therefore, the low is not as low as the first), it indicates a possible change in momentum; we

say there is a bullish divergence.

Divergences are rare when a stock is in a long-term trend but is nonetheless a powerful


In conclusion, the relative strength index aims to describe changes in momentum in price

action through analysing and comparing previous day's highs and lows. From this, a value is generated, and at the extremes, a change in momentum may take place. RSI is not supposed to be predictive but is very helpful in confirming trends indicated by other techniques.

Written by George Chant

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