- Bocconi Students Options Club

# Relative Strength Index & Bollinger Bands

## Relative Strength Index

The Relate Strength Index (RSI) is one of the most popular indicators used for technical analysis by traders alike. The RSI predicts the price action of the specific stock ahead of time by indicating the price momentum of a stock.

### Who invented it?

The RSI was invented and developed in 1978 by J. Welles Wilder. Born in the 1930s Mr. Wilder was a mechanical engineer who became a real estate developer and later on a technical analyst. He designed some of the most common technical indicators used today such as the Average True Range, Relative Strength Index (RSI), Parabolic SAR, the __Average Directional index__ and many more.

### How does it work?

There are two conditions where the RSI is relevant to traders: overbought and oversold. A stock is said to be overbought when it has increased sharply in percentage in just a few days and this increase in price is larger than normal. A stock can even be considered overbought when it has just been increasing in price for a significant number of consecutive days. Analysts will deem the stock price as too expensive for what it's worth and this generally signals a fall in price to come in the near future. Oversold is the same but for when a stock has been decreasing in price. If there is a big fall in price over a number of consecutive days the stock will be considered oversold and in this case labelled as cheap for what it’s worth, many analysts will recommend to buy at this point and then it will rebou nd and increase again.

### The Mathematics Behind

The way the RSI shows these two conditions is by using the formula below:

To calculate the RSI we use a time-period for the data used. The standard time-period used is 14 periods, this is the past 14 trading days. This time-period can be changed to one’s personal preferences for their trading strategies/methods (mainly determined by the time frame of their trade) , but for simplicity reasons I will use 14 as the standard time-period. The average gain will be the average of the 14 days’ up closes. Say there were 7 days in the 14 days where the stock closed up and the average gain was 1% and there were 7 days where the stock closed down and the average loss was -0.9% – we don’t put the negative for the loss – then we put these values in the average gain and average loss and calculate the RSI.

The standard parameters and reference points for the RSI that are used by most traders throughout the world are:

- Period (trading days): 14

- Overbought: 70 (and above)

- Oversold: 30 (and under)

- Price: Close

The *Price* parameter is which price is put into the RSI formula from each day of the period. In the standard case it is the price at the close of the market.

### Example

Figure 1 shows Twitters ($TWTR) daily candle stick graph over about 3 months. On the 26th of June, the RSI dips under the 30 limit that was set. This indicates that the stock is oversold, meaning it is worth more than what it is trading at currently (ceteris paribus). On the candlestick graph we see that price action reverses and there is a rally (or a "correction"), meaning a strong increase in price of the stock. On the 22nd of July the RSI breaks the 70 limit after some strong gains over the last month. This means the stock is overbought, and might undergo a decrease or a "correction". There is a sell-off and the stock price decreases as shown in the graph above.

### Conclusion and Notes

The RSI is a great indicator and is among the most commonly used indicators in the trading world. It is incredibly useful for traders and investors alike, notably in better timing when they close or open a position. It can notably offer signals for traders to open positions, for example, if a stock is oversold a trader could buy a short-dated call, or sell a put.

However, using it becomes even more powerful and delivers better results when it is paired up with solid fundamental analysis and other indicators, one of which is the Bollinger Bands.

## Bollinger Bands

Bollinger Bands are another very commonly used technical indicator. It uses standard deviations to calculate the volatility of a stock. It can help traders alike predict rallies, corrections, large price movements and ultimately whether a stock is oversold or overbought.

### Who invented it?

The Bollinger Bands were developed by John Bollinger. John Bollinger is a renowned financial analyst, author and technical analyst who was notably involved in the in the seminal stages of computer-driven technical analysis. His most famous work are the Bollinger Bands which are widely used in the technical analysis field.

### The Mathematics Behind

Bollinger Bands consist of a centerline with two bands above and below it. The centerline is a simple moving average (SMA) which is simply the sum of the price points in a given period divided by the number of periods (trading days). The two other bands are the standard deviations of the stock.

The standard deviation measures the average amount by which a price point deviates from the mean price of the stock. To calculate the standard deviation, first one subtracts the mean price from the previous price points over a certain time-period, each of these values is then squared and the results are added up. These values are then averaged by dividing by the number of price points we want. This is the variance, to get the standard deviation which is what is useful to traders, one takes the square root of the variance.

The standard parameters for the Bollinger Bands that are used by most traders throughout the world are:

- Period (trading days): 20

- Standard Deviation: 2

- Price: Close

The number of standard deviations means that from the simple moving average we add or subtract – in this case two – standard deviations and plot the points that give us the upper and lower bands.

### How it is used and Examples

The same concept of overbought and oversold is also seen in Bollinger Bands. When the candlesticks start reaching the upper band, the stock is generally overbought, when it starts reaching the lower band, the stock is generally oversold. If the price hits the lower band and crosses the middle, 20 day SMA, this signals an uptrend. If the price hits the lower band and crosses the middle, 20 day SMA, this signals a downtrend.

If the Bollinger Bands become very narrow, this signals a strong reversal either in the upward or downward direction.

Figure 2 shows Honeywells ($HON) daily candle stick graph over 3 months. Around the 13th of June the price hit and went under the lower band and over the next couple of weeks there was a strong upward rally and the price got even higher after the 20 day SMA was crossed. After a couple weeks of very solid growth, on the 4th of June it crossed the upper band and the stock was then considered overbought, over the next week or so there was a sharp decline in the price.

Figure 3 shows General Electrics ($GE) 3 month candlestick graph at the end of 2019. For most of October the price action wasn’t very volatile and as a result the Bollinger Bands contracted and were very narrow, this signals an incoming ‘explosion’ in the price (either in an upward or downward trend). The 20 day SMA is a good indicator to help identify in which way the price will go. Here the candlesticks were above the 20 day SMA signaling a strong upward trend and that is exactly what happened.

## Using RSI and Bollinger Bands together

Since both these indicators do a good job showing the trader when a stock is overbought or oversold, combining the RSI and Bollinger Bands gives the trader even higher accuracy signals.

Figure 4 shows McDonalds ($MCD) 3 month candlestick graph. In this graph, both the RSI and the Bollinger Bands are being used. Around the 13th of July if only the Bollinger bands were being used the trader would think that since it crossed the upper band then the stock was overbought but by adding the RSI, it showed the stock hadn’t broken the upper 70 line and therefore according to the RSI wasn’t fully overbought. Later on in the month – 23rd of July – both the Bollinger Bands and the RSI indicate that the stock is overbought and a sell off is incoming and that is indeed what happened.

**Concluding notes on RSI and Bollinger Bands **

Both these tools are very simple to set up and the trader doesn’t even need to be able to do the math behind the indicators. It is just a matter of understanding what these indicators tell you. It takes a lot practice to be able to be able to read these tools accurately. Even if the trader does understand them perfectly there are often other factors that influence the price and the indicators can be inaccurate. A combination of certain technical indicators (such as RSI and Bollinger Bands) is an effective way to get more accurate signals and better time trades supported by consequent analysis.