# Relative Strength Index (RSI)

**RELATIVE STRENGTH INDEX (RSI)**

a momentum oscillator

J. Welles Wider developed the RSI and published it in a 1978 book, “New Concepts in Technical Trading Systems”. It was also published in Commodities magazine (now Futures magazine) in June of the same year.

**Purpose**

The RSI is used as a trading indicator in the technical analysis of financial markets. Based on the closing prices of completed trading periods, one of its purpose is to indicate the current and historical strength of a market. In a RSI, it is assumed that prices close higher in strong market periods, while in weaker periods it closes lower. It then calculates this as a ratio of the number of additionally higher closes to the additionally lower closes. The RSI method may be classified as a momentum oscillator that measures the velocity and magnitude of directional price movements. (Momentum is defined here as the rate of the increase or decrease in price.)

**Calculation**

To calculate, an upward change (U) or downward change (D) must be done for each trading period. Up periods are usually seen as the close now being higher than the previous close,

U = closenow − closeprevious

D = 0

A down period is characterized by the close now being lower than the previous period’s. The D below should be a positive number,

U = 0

D = closeprevious − closenow

Both U and D are zero if the last close is the same as the previous one. Using a given N-period smoothing factor, an average for U is calculated with an exponential moving average. The calculation for D is the same. The ratio of those averages is the Relative Strength,

RS = { EMA[N] of U / EMA[N] of D }

This is converted to a Relative Strength Index between 0 and 100,

RSI = 100 – 100 * { 1 / 1 + RS }

This can be rewritten as follows to emphasize the way RSI expresses the up as a proportion of the total up and down (averages in each case),

RSI = 100 * { EMA[N] of U / (EMA[N] of U) + (EMA[N] of D) }

In theory, the EMA uses an infinite amount of past data. There are 2 ways. First is to go back far enough, and second, at the start of data begin with a simple average of N periods,

AvgUinitial = { U1 + U2 + … + UN / N }

and continue from there with the usual EMA formula,

AvgUtoday = α * Utoday + (1-α) * AvgUyesterday

The calculation of D is similar.

**Interpretation**

The RSI is usually plotted as lines along with two moving averages connecting the relevant values for each period. It is presented in a graph below the price chart of a market.

By Wilders reckoning of EMA smoothing, i.e. α=1/14 or N=27, he recommended a smoothing period of 14. He proposed that when price moves up very fast, at some point it is considered overbought. And when price falls very fast, it is considered oversold. In either case, Wilder felt a reaction or reversal is about to happen. Note the 2 following facts:

(a) the slope of the RSI is directly proportional to the velocity of the move,and

(b) the distance traveled by the RSI is proportional to the magnitude of the move.

**Overbought and Oversold Territories**

As a result, Wilder believed that tops are indicated when RSI is higher than 70 or bottoms are formed when RSI goes below 30. Greater than 70 RSI readings are considered to be in overbought territory, traditionally, while lower than 30 RSI readings are considered to be in oversold. The neutral level is between the 30 and 70 level.

Wilder also believed that divergence between RSI and price action is a very strong indication that a market turning point is looming. Bearish divergence occurs when price makes a new high. The RSI however makes a lower high and thus fails to confirm. Bullish divergence occurs when price makes a new low but RSI makes a higher low instead.

**Failure Swings**

Strong indications of market reversals according to Wilder are “failure swings” above 70 and below 30 on the RSI. Consider this, assume that the RSI hits 76, pulls back to 72, then rises to 77. Wilder would consider this a “failure swing” above 70 if it falls below 72.

Lastly, Wilder believed that chart formations and areas of support and resistance could sometimes be easily seen on the RSI chart rather than on the price chart. At 50, the center line for the relative strength index, this is often seen as both the support and resistance line for the indicator.

It would mean that the stock’s losses are greater than the gains when the relative strength index is below 50. However, if the relative strength index is above 50, this simply means that the gains are greater than the losses.

**Cardwell’s New Interpretations**

Aside from Wilder’s original theories of RSI interpretation, Andrew Cardwell has developed several new interpretations of RSI to help determine and confirm trend. First, Cardwell noticed that uptrends generally traded between RSI 40 and 80, while downtrends usually traded between RSI 60 and 20. He observed when securities change from uptrend to downtrend and vice versa, the RSI will undergo a “range shift.”

Cardwell noted that bearish divergence: 1) only happens in uptrends, and 2) leads to a brief correction instead of a reversal in trend most of the time. Therefore bearish divergence is a sign confirming an uptrend, whereas bullish divergence is a sign confirming a downtrend.

The existence of positive and negative reversals in the RSI was discovered by Cardwell. Reversals are the opposite of divergence. An example of a positive reversal is when an uptrend price correction results in a higher low compared to the last price correction, while RSI results in a lower low compared to the prior correction. For a negative reversal to happen, a downtrend rally results in a lower high compared to the last downtrend rally, but RSI makes a higher high compared to the prior rally.

**Final Note**

So, even with the stronger momentum as seen by the higher high or lower low in the RSI, price could not make a higher high or lower low. This proves that the main trend is about to resume. Positive reversals only occur in uptrends, while negative reversals only happen in downtrends as noted by Cardwell. Therefore, their existence confirms the trend.