## 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)
ema_up = up.ewm(com=13, adjust=False).mean()
ema_down = down.ewm(com=13, adjust=False).mean()
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)
ema_up = up.ewm(com=13, adjust=False).mean()
ema_down = down.ewm(com=13, adjust=False).mean()
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)
ticker['Close'].plot(ax=ax1)
ax1.set_ylabel('Price (\$)')
ticker['RSI'].plot(ax=ax2)
ax2.set_ylim(0,100)
ax2.axhline(30, color='r', linestyle='--')
ax2.axhline(70, color='r', linestyle='--')
ax2.set_ylabel('RSI')
plt.show()
```

Also, we we remove the x-axis of the first graph (ax1). Adjust the y-axis of the second graph (ax2). Also, we have set two horizontal lines to indicate overbought and oversold at 70 and 30, respectively. Notice, that Yahoo! Finance use 80 and 20 as indicators by default.

## 12% Investment Solution

Would you like to get 12% in return of your investments?

D. A. Carter promises and shows how his simple investment strategy will deliver that in the book The 12% Solution. The book shows how to test this statement by using backtesting.

Did Carter find a strategy that will consistently beat the market?

Actually, it is not that hard to use Python to validate his calculations. But we can do better than that. If you want to work smarter than traditional investors then continue to read here.

## What is CACR and why not use AAGR?

Often when you see financial advisors have statements with awesome returns. These returns might be what is called Annual Average Growth Rates (AAGR). Why should you be skeptical with AAGR?

Simple example will show you.

• You start by investing 10.000\$.
• First year you get 100% in return, resulting in 20.000\$.
• The year after you have a fall of 50%, which makes your value back to 10.000\$

Using AAGR, your investor will tell you you have (100% – 50%)/2 = 25% AAGR or calls it average annual return.

But wait a minute? You have the same amount of money after two years, so how can that be 25%?

With Compound Annual Growth Rate the story is different as it only considers the start and end value. Here the difference is a big 0\$, resulting in a 0% CAGR.

The formula for calculating CAGR is.

((end value)/(start value))^(1/years) – 1

As the above example: (10.000/10.000)^(1/2) – 1 = 0

## Step 1: Getting access to financial sector data

In this tutorial we will use the Alpha Vantage. To connect to them you need to register to get a API_KEY.

To claim your key go to: https://www.alphavantage.co/support/#api-key

Where you will select Software Developer in the drop-down Which of the following best describes you? Write your organization of choice. Then write your email address and click that you are not a robot. Or are you?

Then it will give you hare API_KEY on the screen (not in a email). The key is probably a 16 upper case character and integer string.

## Step 2: Get the sector data to play with

Looking at Pandas-datareaders API you will see you can use the get_sector_performance_av() function.

```import pandas_datareader.data as web
API_KEY = "INSERT YOUR KEY HERE"
data = web.get_sector_performance_av(api_key=API_KEY)
print(data)
```

Remember to change API_KEY to the key you got from Step 1.

You should get an output similar to this one (not showing all columns).

```                            RT      1D      5D  ...       3Y       5Y      1
0Y
Communication Services   0.38%   0.38%  -0.20%  ...   24.04%   29.92%   74.7
8%
Information Technology   0.04%   0.04%  -1.36%  ...  104.45%  183.51%  487.3
3%
Consumer Discretionary  -0.06%  -0.06%   1.36%  ...   66.06%   92.37%  384.7
1%
Materials               -0.07%  -0.07%   1.75%  ...   17.50%   37.64%  106.9
0%
Health Care             -0.16%  -0.17%   0.90%  ...   37.21%   43.20%  268.5
8%
Consumer Staples        -0.19%  -0.19%   1.42%  ...   15.96%   27.65%  137.66%
Utilities               -0.38%  -0.38%   0.60%  ...   13.39%   34.79%   99.63%
Financials              -0.61%  -0.61%   3.23%  ...    1.67%   23.89%  119.46%
Industrials             -0.65%  -0.65%   4.45%  ...   12.57%   40.05%  155.56%
Real Estate             -1.23%  -1.23%  -0.63%  ...   12.51%      NaN      NaN
Energy                  -1.99%  -1.99%   1.38%  ...  -39.45%  -44.69%  -29.07%
```

The columns we are interested in are the 1Y, 3Y, 5Y, and 10Y.

## Step 3: Convert columns to floats

As you saw in the previous Step that the columns all contain in %-sign, which tells you that the entries are strings and not floats and need to be converted.

This can be done by some string magic. First we need to remove the %-sign before we convert it to a float.

```import pandas_datareader.data as web
API_KEY = "INSERT YOUR KEY HERE"
data = web.get_sector_performance_av(api_key=API_KEY)
for column in data.columns:
data[column] = data[column].str.rstrip('%').astype('float') / 100.0
print(data[['1Y', '3Y', '5Y' , '10Y']])
```

Where we convert all columns in the for-loop. Then we print only the columns we need.

```                            1Y      3Y      5Y     10Y
Communication Services  0.1999  0.2404  0.2992  0.7478
Information Technology  0.4757  1.0445  1.8351  4.8733
Consumer Discretionary  0.2904  0.6606  0.9237  3.8471
Materials               0.1051  0.1750  0.3764  1.0690
Health Care             0.1908  0.3721  0.4320  2.6858
Consumer Staples        0.0858  0.1596  0.2765  1.3766
Utilities               0.0034  0.1339  0.3479  0.9963
Financials             -0.0566  0.0167  0.2389  1.1946
Industrials             0.0413  0.1257  0.4005  1.5556
Real Estate            -0.0658  0.1251     NaN     NaN
Energy                 -0.3383 -0.3945 -0.4469 -0.2907
```

All looking nice. Also, notice that we converted them to float values and not in %-values by dividing by 100.

## Step 4: Calculate the CAGR

Now we need to use the formula on the columns.

```import pandas_datareader.data as web
API_KEY = "INSERT YOUR KEY HERE"
data = web.get_sector_performance_av(api_key=API_KEY)
for column in data.columns:
data[column] = data[column].str.rstrip('%').astype('float') / 100.0
data['1Y-CAGR'] = data['1Y']*100
data['3Y-CAGR'] = ((1 + data['3Y']) ** (1/3) - 1) * 100
data['5Y-CAGR'] = ((1 + data['5Y']) ** (1/5) - 1) * 100
data['10Y-CAGR'] = ((1 + data['10Y']) ** (1/10) - 1) * 100
cols = ['1Y-CAGR','3Y-CAGR', '5Y-CAGR', '10Y-CAGR']
print(data[cols])
```

This should result in something similar.

```                        1Y-CAGR    3Y-CAGR    5Y-CAGR   10Y-CAGR
Communication Services    19.99   7.445258   5.374421   5.742403
Information Technology    47.57  26.919700  23.172477  19.368083
Consumer Discretionary    29.04  18.419079  13.979689  17.097655
Materials                 10.51   5.522715   6.597970   7.541490
Health Care               19.08  11.120773   7.445592  13.933956
Consumer Staples           8.58   5.059679   5.003594   9.042452
Utilities                  0.34   4.277734   6.152820   7.157502
Financials                -5.66   0.553596   4.377587   8.177151
Industrials                4.13   4.025758   6.968677   9.837158
Real Estate               -6.58   4.007273        NaN        NaN
Energy                   -33.83 -15.399801 -11.169781  -3.376449
```

Looks like the Information Technology sector is very lucrative.

But to make it more digestible we should visualize it.

## Step 5: Create a heatmap

We will use the seaborn library to create it, which is a statistical data visualizing library.

The heatmap endpoint is defined to simply take the DataFrame to visualize. It could not be easier.

```import pandas_datareader.data as web
import seaborn as sns
import matplotlib.pyplot as plt
API_KEY = "INSERT YOUR KEY HERE"
data = web.get_sector_performance_av(api_key=API_KEY)
for column in data.columns:
data[column] = data[column].str.rstrip('%').astype('float') / 100.0
data['1Y-CAGR'] = data['1Y']*100
data['3Y-CAGR'] = ((1 + data['3Y']) ** (1/3) - 1) * 100
data['5Y-CAGR'] = ((1 + data['5Y']) ** (1/5) - 1) * 100
data['10Y-CAGR'] = ((1 + data['10Y']) ** (1/10) - 1) * 100
cols = ['1Y-CAGR','3Y-CAGR', '5Y-CAGR', '10Y-CAGR']
sns.heatmap(data[cols], annot=True, cmap="YlGnBu")
plt.show()
```

Resulting in the following output.

## What is the Bollinger Bands?

A Bollinger Band® is a technical analysis tool defined by a set of trendlines plotted two standard deviations (positively and negatively) away from a simple moving average (SMA) of a security’s price, but which can be adjusted to user preferences.

https://www.investopedia.com/terms/b/bollingerbands.asp

The Bollinger Bands are used to discover if a stock is oversold or overbought. It is called a mean reversion indicator, which measures how far a price swing will stretch before a counter impulse triggers a retracement.

It is a lagging indicator, which is looking at historical background of the current price. Opposed to a leading indicator, which tries to where the price is heading.

## Step 1: Get some time series data on a stock

In this tutorial we will use the Apple stock as example, which has ticker AAPL. You can change to any other stock of your interest by changing the ticker below. To find the ticker of your favorite company/stock you can use Yahoo! Finance ticker lookup.

To get some time series of stock data we will use the Pandas-datareader library to collect it from Yahoo! Finance.

```import pandas_datareader as pdr
import datetime as dt

ticker = pdr.get_data_yahoo("AAPL", dt.datetime(2020, 1, 1), dt.datetime.now())[['Close', 'High', 'Low']]
print(ticker)
```

We will use the Close, High and Low columns to do the further calculations.

```                 Close        High         Low
Date
2020-01-02  300.350006  300.600006  295.190002
2020-01-03  297.429993  300.579987  296.500000
2020-01-06  299.799988  299.959991  292.750000
2020-01-07  298.390015  300.899994  297.480011
2020-01-08  303.190002  304.440002  297.160004
...                ...         ...         ...
2020-08-06  455.609985  457.649994  439.190002
2020-08-07  444.450012  454.700012  441.170013
2020-08-10  450.910004  455.100006  440.000000
2020-08-11  437.500000  449.929993  436.429993
2020-08-12  452.040009  453.100006  441.190002
```

## Step 2: How are the Bollinger Bands calculated

Luckily, we can refer to Investopedia.org to get the answer, which states that the Bollinger Bands are calculated as follows.

BOLU=MA(TP,n)+mσ[TP,n]

BOLD=MA(TP,n)−mσ[TP,n]

Where BOLU is the Upper Bollinger Band and BOLD is Lower Bollinger Band. The MA is the Moving Average. The TP and σ are calculated as follows.

TP (typical price)=(High+Low+Close)÷3

σ[TP,n] = Standard Deviation over last n periods of TP​

Where n is the number of days in smoothing period (typically 20), and m is the number of standard deviations (typically 2).

## Step 3: Calculate the Bollinger Bands

This is straight forward. We start by calculating the typical price TP and then the standard deviation over the last 20 days (the typical value). Then we calculate the simple moving average of rolling over the last 20 days (the typical value). Then we have the values to calculate the upper and lower values of the Bolling Bands (BOLU and BOLD).

```ticker['TP'] = (ticker['Close'] + ticker['Low'] + ticker['High'])/3
ticker['std'] = ticker['TP'].rolling(20).std(ddof=0)
ticker['MA-TP'] = ticker['TP'].rolling(20).mean()
ticker['BOLU'] = ticker['MA-TP'] + 2*ticker['std']
ticker['BOLD'] = ticker['MA-TP'] - 2*ticker['std']
print(ticker)
```

Resulting in the following output.

```Date
Close        High  ...        BOLU        BOLD
Date                                ...
2020-01-02  300.350006  300.600006  ...         NaN         NaN
2020-01-03  297.429993  300.579987  ...         NaN         NaN
2020-01-06  299.799988  299.959991  ...         NaN         NaN
2020-01-07  298.390015  300.899994  ...         NaN         NaN
2020-01-08  303.190002  304.440002  ...         NaN         NaN
...                ...         ...  ...         ...         ...
2020-08-06  455.609985  457.649994  ...  445.784036  346.919631
2020-08-07  444.450012  454.700012  ...  453.154374  346.012626
2020-08-10  450.910004  455.100006  ...  459.958160  345.317173
2020-08-11  437.500000  449.929993  ...  464.516981  346.461685
2020-08-12  452.040009  453.100006  ...  469.891271  346.836730
```

Note, that if you compare you results with Yahoo! Finance for Apple, there will be some small difference. The reason is, that they by default use TP to be closing price and not the average of the Close, Low and High. If you change TP to equal Close only, you will get the same figures as they do.

## Step 4: Plotting it on a graph

Plotting the three lines is straight forward by using plot() on the DataFrame. Making an filled area with color between BOLU and BOLD can be achieved by using fill_between().

This results in the full program to be.

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

ticker = pdr.get_data_yahoo("AAPL", dt.datetime(2020, 1, 1), dt.datetime.now())[['Close', 'High', 'Low']]
# Boillinger band calculations
ticker['TP'] = (ticker['Close'] + ticker['Low'] + ticker['High'])/3
ticker['std'] = ticker['TP'].rolling(20).std(ddof=0)
ticker['MA-TP'] = ticker['TP'].rolling(20).mean()
ticker['BOLU'] = ticker['MA-TP'] + 2*ticker['std']
ticker['BOLD'] = ticker['MA-TP'] - 2*ticker['std']
ticker = ticker.dropna()
print(ticker)
# Plotting it all together
ax = ticker[['Close', 'BOLU', 'BOLD']].plot(color=['blue', 'orange', 'yellow'])
ax.fill_between(ticker.index, ticker['BOLD'], ticker['BOLU'], facecolor='orange', alpha=0.1)
plt.show()
```

Giving the following graph. Apple Stock Closing price with Bollinger Band indicators

## Step 5: How to use the Bollinger Band Indicator?

If the stock price are continuously touching the upper Bollinger Band (BOLU) the market is thought to be overbought. While if the price continuously touches the lower Bollinger Band (BOLD) the market is thought to be oversold.

The more volatile the market is, the wider the upper and lower band will be. Hence, it also indicates how volatile the market is at a given period.

The volatility measured by the Bollinger Band is referred to as a squeeze when the upper and lower band are close. This is considered to be a sign that there will be more volatility in the coming future, which opens up for possible trading opportunities.

A common misconception of the bands are that when the price outbreaks the the bounds of the upper and lower band, it is a trading signal. This is not the case.

As with all trading indicators, it should not be used alone to make trading decisions.

## 12% Investment Solution

Would you like to get 12% in return of your investments?

D. A. Carter promises and shows how his simple investment strategy will deliver that in the book The 12% Solution. The book shows how to test this statement by using backtesting.

Did Carter find a strategy that will consistently beat the market?

Actually, it is not that hard to use Python to validate his calculations. But we can do better than that. If you want to work smarter than traditional investors then continue to read here.