## What is the Relative Strength Index?

The Relative Strength Index (RSI) on a stock is a technical indicator.

The relative strength index (RSI) is a momentum indicator used in technical analysis that measures the magnitude of recent price changes to evaluate overbought or oversold conditions in the price of a stock or other asset.

https://www.investopedia.com/terms/r/rsi.asp

A technical indicator is a mathematical calculation based on past prices and volumes of a stock. The RSI has a value between 0 and 100. It is said to be overbought if above 70, and oversold if below 30.

## Step 1: How to calculate the RSI

To be quite honest, I found the description on investopedia.org a bit confusing. Therefore I went for the Wikipedia description of it. It is done is a couple of steps, so let us do the same.

1. If previous price is lower than current price, then set the values.
• U = close_now – close_previous
• D = 0
2. While if the previous price is higher than current price, then set the values
• U = 0
• D = close_previous – close_now
3. Calculate the Smoothed or modified moving average (SMMA) or the exponential moving average (EMA) of D and U. To be aligned with the Yahoo! Finance, I have chosen to use the (EMA).
4. Calculate the relative strength (RS)
• RS = EMA(U)/EMA(D)
5. Then we end with the final calculation of the Relative Strength Index (RSI).
• RSI = 100 – (100 / (1 + RSI))

Notice that the U are the price difference if positive otherwise 0, while D is the absolute value of the the price difference if negative.

## Step 2: Get a stock and calculate the RSI

We will use the Pandas-datareader to get some time series data of a stock. If you are new to using Pandas-datareader we advice you to read this tutorial.

In this tutorial we will use Twitter as an examples, which has the TWTR ticker. It you want to do it on some other stock, then you can look up the ticker on Yahoo! Finance here.

Then below we have the following calculations.

```import pandas_datareader as pdr
from datetime import datetime

ticker = pdr.get_data_yahoo("TWTR", datetime(2020, 1, 1))

delta = ticker['Close'].diff()
up = delta.clip(lower=0)
down = -1*delta.clip(upper=0)
rs = ema_up/ema_down

print(ticker)
```

To have a naming that is close to the definition and also aligned with Python, we use up for U and down for D.

This results in the following output.

```                 High        Low       Open      Close    Volume  Adj Close
Date
2020-01-02  32.500000  31.959999  32.310001  32.299999  10721100  32.299999
2020-01-03  32.099998  31.260000  31.709999  31.520000  14429500  31.520000
2020-01-06  31.709999  31.160000  31.230000  31.639999  12582500  31.639999
2020-01-07  32.700001  31.719999  31.799999  32.540001  13712900  32.540001
2020-01-08  33.400002  32.349998  32.349998  33.049999  14632400  33.049999
...               ...        ...        ...        ...       ...        ...
2021-10-08  64.339996  63.310001  64.250000  63.680000   8094900  63.680000
2021-10-11  63.509998  62.070000  62.990002  62.099998   9020400  62.099998
2021-10-12  62.799999  60.790001  61.680000  61.450001   9952100  61.450001
2021-10-13  62.740002  61.509998  61.959999  62.200001   9423500  62.200001
2021-10-14  63.779999  62.759998  63.009998  63.130001   3455733  63.130001
```

This tutorial was written 2020-08-18 (updated in 2021-10-14), and comparing with the RSI for twitter on Yahoo! Finance.

As you can see in the lower left corner, the RSI for the same ending day was 51.56 (it was measured in trading hours, so the end-of-day number is different), which fits the calculated value. Further checks reveal that they also fit the values of Yahoo.

## Step 3: Visualize the RSI with the daily stock price

We will use the matplotlib library to visualize the RSI with the stock price. In this tutorial we will have two rows of graphs by using the subplots function. The function returns an array of axis (along with a figure, which we will not use).

The axis can be parsed to the Pandas DataFrame plot function.

```import pandas_datareader as pdr
from datetime import datetime
import matplotlib.pyplot as plt

ticker = pdr.get_data_yahoo("TWTR", datetime(2020, 1, 1))

delta = ticker['Close'].diff()
up = delta.clip(lower=0)
down = -1*delta.clip(upper=0)
rs = ema_up/ema_down

ticker['RSI'] = 100 - (100/(1 + rs))

# Skip first 14 days to have real values
ticker = ticker.iloc[14:]

print(ticker)
fig, (ax1, ax2) = plt.subplots(2)
ax1.get_xaxis().set_visible(False)