HW3 question2

import pandas as pd
import matplotlib.pyplot as plt
from datetime import datetime, timedelta
import numpy as np

Part A: Function to calculate number of weekdays

def nweekdays(date):
    start_date = pd.Timestamp('2023-01-01')
    end_date = pd.Timestamp(date)
    
    dates = pd.date_range(start=start_date, end=end_date)
    weekday_count = 0
    
    for date in dates:
        # weekday() returns 0-6 (Monday-Sunday)
        if date.weekday() < 5:  # 0-4 are weekdays
            weekday_count += 1
            
    return weekday_count

# Verification function using pd.bdate_range()
def verify_weekdays(date):
    start_date = pd.Timestamp('2023-01-01')
    end_date = pd.Timestamp(date)
    return len(pd.bdate_range(start_date, end_date))

Part B: Import and process data

# Read the CSV file
df = pd.read_csv('vti.csv')

# Convert date column to datetime
df['date'] = pd.to_datetime(df['date'])

# Calculate weekdays for each date
df['cum_weekdays'] = df['date'].apply(nweekdays)

# Calculate number of weekdays in each month using diff()
df['weekdays_in_month'] = df['cum_weekdays'].diff()

# Fix first month manually
df.loc[0, 'weekdays_in_month'] = df.loc[0, 'cum_weekdays']

Part C: Calculate daily returns and create visualization

# Convert monthly returns to decimals
df['monthly_return'] = df['pct_return'] / 100

# Calculate daily returns using the compound formula
# R_m = (1 + R_d)^t - 1
# Solving for R_d: R_d = (1 + R_m)^(1/t) - 1
df['daily_return_pct'] = ((1 + df['monthly_return'])**(1/df['weekdays_in_month']) - 1) * 10000  # Convert to basis points

# Create bar plot
plt.figure(figsize=(12, 6))
plt.bar(df['date'], df['daily_return_pct'])
plt.title('Average Daily Returns by Month (in Basis Points)')
plt.xlabel('Date')
plt.ylabel('Average Daily Return (Basis Points)')
plt.xticks(rotation=45)
plt.grid(True, alpha=0.3)
plt.tight_layout()

# Display the results
print("\nFirst few rows of the processed data:")
print(df[['date', 'pct_return', 'weekdays_in_month', 'daily_return_pct']].head())

# Save the plot
plt.savefig('daily_returns.png')
plt.close()

First few rows of the processed data:
        date  pct_return  weekdays_in_month  daily_return_pct
0 2023-01-31        6.93               22.0         30.502895
1 2023-02-28       -2.40               20.0        -12.138973
2 2023-03-31        2.71               23.0         11.632542
3 2023-04-30        1.08               20.0          5.372491
4 2023-05-31        0.43               23.0          1.865731

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