Sharpe Ratio

Beta

Jensen's Alpha

Unit Root

Augumented Dickey-Fuller (ADF) Test

Weiner Process

The Random Walk of Stock Market

Beta is a coefficient is a measure of its volatility over time compared to a market benchmark. Market benchmark has a beta of 1. Shortly, if volatility is 1.5 it means it is 50% more volatile than the market.

- A stock that swings more than the market over time has a beta greater than 1.0.
- If a stock moves less than the market, the stock’s beta is less than 1.0.

- Get the Historical Price of the Stock or Index.
- Get the Historical Price of the other Stock or Index against which You are trying to benchmark.
- Calculate the Percentage Change for the same period for both the stock/index and the benchmark.
- Calculate the covariance of the stock/index to the benchmark.
- Calculate the Variance of the benchmark.

Now,

**Beta = Covariance/Variance**

In simple terms,

- Covariance is the measure of a stock/index’s return relative to the market.
- Variance is the measure of how the market moves relative to its mean.

This python code patch is written for NSEPython Library first time. We shall use `Daily`

as period and `NIFTY 50`

as default benchmark.

We are using the `equity_history()`

function. We are building Pandas Dataframe over last `10`

days’ data of `SBIN`

.

` ````
```symbol = "SBIN"
days = 10
end_date = datetime.datetime.now().strftime("%d-%m-%Y")
end_date = str(end_date)
start_date = (datetime.datetime.now()- datetime.timedelta(days=days)).strftime("%d-%m-%Y")
start_date = str(start_date)
df = equity_history(symbol,"EQ",start_date,end_date)
df["daily_change"]=df["CH_CLOSING_PRICE"].pct_change()
df=df[['CH_TIMESTAMP','daily_change']]
df = df.iloc[1: , :] #thispointer.com/drop-first-row-of-pandas-dataframe-3-ways/
print(df)

We are using the `index_history()`

function. We are building Pandas Dataframe over the last `10`

days’ data of `NIFTY 50`

similarly as We did for `SBIN`

.

` ````
```symbol = "NIFTY 50"
days = 10
end_date = datetime.datetime.now().strftime("%d-%b-%Y")
end_date = str(end_date)
start_date = (datetime.datetime.now()- datetime.timedelta(days=days)).strftime("%d-%b-%Y")
start_date = str(start_date)
df2=index_history("NIFTY 50",start_date,end_date)
df2["daily_change"]=df2["CLOSE"].astype(float).pct_change()
df2=df2[['HistoricalDate','daily_change']]
df2 = df2.iloc[1: , :]
print(df2)

` ````
``` CH_TIMESTAMP daily_change
1 2021-06-11 -0.001743
2 2021-06-10 0.006169
3 2021-06-09 -0.024986
4 2021-06-08 0.013643
5 2021-06-07 0.011821

` ````
``` HistoricalDate daily_change
1 11 Jun 2021 -0.000791
2 10 Jun 2021 -0.003899
3 09 Jun 2021 -0.006507
4 08 Jun 2021 0.006700
5 07 Jun 2021 0.000734

There is no need for ** Part 3** as We have already calculated the Percentage Change using

`pct_change()`

function of `Pandas`

.First We shall convert the `daily_change`

column of both the Pandas Dataframe to `List`

for our ease of Calculation. Even When in our first article, `CoVariance`

applied on Google Sheets was done Series only. You can revisit clicking here.

` ````
```x=df["daily_change"].tolist()
y=df2["daily_change"].tolist()
print("List of x:")
print(x)
print("List of y:")
print(y)
#stackoverflow.com/questions/42670055/is-there-any-better-way-to-calculate-the-covariance-of-two-lists-than-this
mean_x = sum(x) / len(x)
mean_y = sum(y) / len(y)
covariance = sum((a - mean_x) * (b - mean_y) for (a,b) in zip(x,y)) / len(x)
print(covariance)

` ````
```List of x:
[-0.0017427675148135036, 0.006168528864059608, -0.02498554077501447, 0.013643374065725578, 0.011821161048689133]
List of y:
[-0.0007905463307582572, -0.003898894574776879, -0.0065066480278311856, 0.006699562209992127, 0.0007337945756380471]
4.873388157877867e-05

` ````
```mean = sum(y) / len(y)
variance = sum((i - mean) ** 2 for i in y) / len(y)
print(variance)

` ````
```2.0150753721209677e-05

` ````
```beta = covariance/variance
print(beta)

` ````
```2.418464453142704

So, That’s How You calculate the Beta of stock in the Indian Share Market in Python.

Here goes the final version of the `get_beta()`

function. It has more brevity and it also fixes the mess of various types of timestamps across the `equity_history()`

and `index_history()`

function.

` ````
```def get_beta_df_maker(symbol,days):
if("NIFTY" in symbol):
end_date = datetime.datetime.now().strftime("%d-%b-%Y")
end_date = str(end_date)
start_date = (datetime.datetime.now()- datetime.timedelta(days=days)).strftime("%d-%b-%Y")
start_date = str(start_date)
df2=index_history(symbol,start_date,end_date)
df2["daily_change"]=df2["CLOSE"].astype(float).pct_change()
df2=df2[['HistoricalDate','daily_change']]
df2 = df2.iloc[1: , :]
return df2
else:
end_date = datetime.datetime.now().strftime("%d-%m-%Y")
end_date = str(end_date)
start_date = (datetime.datetime.now()- datetime.timedelta(days=days)).strftime("%d-%m-%Y")
start_date = str(start_date)
df = equity_history(symbol,"EQ",start_date,end_date)
df["daily_change"]=df["CH_CLOSING_PRICE"].pct_change()
df=df[['CH_TIMESTAMP','daily_change']]
df = df.iloc[1: , :] #thispointer.com/drop-first-row-of-pandas-dataframe-3-ways/
return df
def get_beta(symbol,days,symbol2="NIFTY 50"):
df = get_beta_df_maker(symbol,days)
df2 = get_beta_df_maker(symbol2,days)
x=df["daily_change"].tolist()
y=df2["daily_change"].tolist()
#stackoverflow.com/questions/42670055/is-there-any-better-way-to-calculate-the-covariance-of-two-lists-than-this
mean_x = sum(x) / len(x)
mean_y = sum(y) / len(y)
covariance = sum((a - mean_x) * (b - mean_y) for (a,b) in zip(x,y)) / len(x)
mean = sum(y) / len(y)
variance = sum((i - mean) ** 2 for i in y) / len(y)
beta = covariance/variance
return round(beta,3)
for x in fnolist():
try:
print(x+" : "+str(get_beta(x,255)))
break
except:
pass
#NIFTY Against NIFTY Bank
x = "NIFTY 50"
print(x+" : "+str(get_beta(x,255,"NIFTY BANK")))
#NIFTY Bank Against NIFTY
x = "NIFTY BANK"
print(x+" : "+str(get_beta(x,255)))

` ````
```TORNTPHARM : -0.168
NIFTY 50 : 0.55
NIFTY BANK : 1.395

If You remove the `break`

command in the `Line 49`

as highlighted here, You will get the list of entire stocks of `FNO`

and their `Beta`

s.

Note – We used `255`

as `Number of Days`

because it is globally assumed that, there are `255`

trading days. For near-term correlation, feel free to change the values.

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