Table of Contents

• 1  Introduction
• 2  Rate of Return
• 3  Month Over Month (MOM) Growth Rate
• 4  Compounding Monthly Growth Rate (CMGR)
  • 4.1  Simple CGR
  • 4.2  Windowed CMGR
• 5  Year over Year (YoY) Growth Rate
• 6  Compounding Annual Growth Rate (CAGR)
  • 6.1  Simple CAGR
• 7  Windowed CAGR
• 8  References

Introduction

This is the part 3 of our Python for Stock Market Analysis series and here, we will explore some of popular growth rates that can be used to see how well is our value is changing over the period of time. Lets take some of scenarios:

• If we want to know by what rate is our current month's closing price is changed compared to the previous, we could simply divide change of values by the values at base month.
• If we want to know the compounding change rate of our closing price compared to the base period.
• We want to predict how much will the growth rate be on the next month or to achieve the constant growth rate, what should be the value.

The scenarios can be many more but lets focus on some.

Again we will be using the data reading part's code from the previous blogs.

import pandas as pd
import numpy as np
import plotly.express as px
import cufflinks
import plotly.io as pio 
import yfinance as yf
import warnings 
warnings.filterwarnings("ignore")
cufflinks.go_offline()
cufflinks.set_config_file(world_readable=True, theme='pearl')
pio.renderers.default = "notebook"

pd.options.display.max_columns = None

symbols = ["AAPL"]

df = yf.download(tickers=symbols)
# convert column names into lowercase
df.columns = [c.lower() for c in df.columns]
df.rename(columns={"adj close":"adj_close"},inplace=True)

df.head()

NumExpr defaulting to 8 threads.

[*********************100%***********************]  1 of 1 completed

See Full Dataframe in Mito

	open	high	low	close	adj_close	volume
Date
1980-12-12	0.128348	0.128906	0.128348	0.128348	0.100323	469033600
1980-12-15	0.122210	0.122210	0.121652	0.121652	0.095089	175884800
1980-12-16	0.113281	0.113281	0.112723	0.112723	0.088110	105728000
1980-12-17	0.115513	0.116071	0.115513	0.115513	0.090291	86441600
1980-12-18	0.118862	0.119420	0.118862	0.118862	0.092908	73449600

Rate of Return

Lets suppose that we bought a stock 2 months ago and we want to find out how much profit we currently have then we might subtract the price at the time we bought from the current price. And it can be simply called return. The rate of return is simple measurement that tells us how much has been the price increase from the base period. It is calculated as:

$$ ror = \frac{V_{current}-V_{initial}}{V_{initial}} * 100 $$

RoR is the simplest growth rate and it does not take external factors like inflation into consideration.

Month Over Month (MOM) Growth Rate

This is the simple measurement of the growth rate where we simply calculate the rate of change from the previous month.

$$ rate = \frac{v_t - v_{t-1}}{v_{t-1}} * 100 $$

Where,

• v(t) is value at month t.
• v(t-1) is value at month t-1.

Lets calculate this in our python. But first, lets make a dataframe to store the closing price of the month only.

mdf = df.resample("1M").close.last().rename("Close").reset_index()
mdf["momgr"] = mdf.Close.pct_change()*100
mdf

See Full Dataframe in Mito

	Date	Close	momgr
0	1980-12-31	0.152344	NaN
1	1981-01-31	0.126116	-17.216307
2	1981-02-28	0.118304	-6.194292
3	1981-03-31	0.109375	-7.547504
4	1981-04-30	0.126674	15.816225
...	...	...	...
491	2021-11-30	165.300003	10.347129
492	2021-12-31	177.570007	7.422870
493	2022-01-31	174.779999	-1.571216
494	2022-02-28	165.119995	-5.526950
495	2022-03-31	173.041000	4.797121

import plotly.graph_objects as go
from plotly.subplots import make_subplots

fig=make_subplots(specs=[[{"secondary_y": True}]])


lastn = 100
ldf = mdf[-lastn:]

fig.add_trace(go.Line(x=ldf.Date, y=ldf.momgr, line=dict(
                color='rgb(104, 14, 24)',

            ), 
              name="MOM Growth Rate Closing Price"),secondary_y=True)
fig.add_trace(go.Line(x=ldf.Date, y=ldf.Close, line=dict(
                color='rgb(10, 104, 204)',), 
              name="MOM Closing Price"),secondary_y=False)


fig.update_layout(
    title= "AAPL Stock Data",
    yaxis_title="MOM Growth Rate Closing Price",
    xaxis_title="Date")               
fig.update_yaxes(title_text="MOM Closing Price", secondary_y=False)
fig.update_yaxes(title_text="MOM Growth Rate Closing Price", secondary_y=True)

fig.show()