Risk and Returns: The Sharpe Ratio

# Importing required modules import pandas as pd import numpy as np import matplotlib.pyplot as plt # Settings to produce nice plots in a Jupyter notebook plt.style.use('fivethirtyeight') %matplotlib inline # Reading in the data stock_data = pd.read_csv('/work/stock_data.csv', parse_dates = True, index_col = ['Date']).dropna() benchmark_data = pd.read_csv('/work/benchmark_data.csv', parse_dates = True, index_col = ['Date']).dropna()

# Display summary for stock_data print('Stocks\n') stock_data.info() print(stock_data.head()) # Display summary for benchmark_data print('\nBenchmarks\n') benchmark_data.info() print(benchmark_data.head())

Stocks

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 252 entries, 2016-01-04 to 2016-12-30
Data columns (total 2 columns):
 #   Column    Non-Null Count  Dtype  
---  ------    --------------  -----  
 0   Amazon    252 non-null    float64
 1   Facebook  252 non-null    float64
dtypes: float64(2)
memory usage: 5.9 KB
                Amazon    Facebook
Date                              
2016-01-04  636.989990  102.220001
2016-01-05  633.789978  102.730003
2016-01-06  632.650024  102.970001
2016-01-07  607.940002   97.919998
2016-01-08  607.049988   97.330002

Benchmarks

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 252 entries, 2016-01-04 to 2016-12-30
Data columns (total 1 columns):
 #   Column   Non-Null Count  Dtype  
---  ------   --------------  -----  
 0   S&P 500  252 non-null    float64
dtypes: float64(1)
memory usage: 3.9 KB
            S&P 500
Date               
2016-01-04  2012.66
2016-01-05  2016.71
2016-01-06  1990.26
2016-01-07  1943.09
2016-01-08  1922.03

# visualize the stock_data stock_data.plot(subplots = True, title = 'Stock Data') # summarize the stock_data stock_data.describe()

# plot the benchmark_data benchmark_data.plot(title = 'S&P 500') # summarize the benchmark_data benchmark_data.describe()

# calculate daily stock_data returns stock_returns = stock_data.pct_change() # plot the daily returns stock_returns.plot() # summarize the daily returns stock_returns.describe()

# calculate daily benchmark_data returns sp_returns = benchmark_data['S&P 500'].pct_change() # plot the daily returns sp_returns.plot() # summarize the daily returns sp_returns.describe()

# calculate the difference in daily returns excess_returns = stock_returns.sub(sp_returns, axis = 0) # plot the excess_returns excess_returns.plot(); # summarize the excess_returns excess_returns.describe()

# calculate the mean of excess_returns avg_excess_return = excess_returns.mean() # plot avg_excess_returns avg_excess_return.plot.bar(title = 'Mean of the Return Difference');

# calculate the standard deviations sd_excess_return = excess_returns.std() # plot the standard deviations sd_excess_return.plot.bar(title = 'Standard Deviation of the Return Difference')

# calculate the daily sharpe ratio daily_sharpe_ratio = avg_excess_return.div(sd_excess_return) # annualize the sharpe ratio annual_factor = np.sqrt(252) annual_sharpe_ratio = daily_sharpe_ratio.mul(annual_factor) # plot the annualized sharpe ratio annual_sharpe_ratio.plot.bar(title = 'Annualized Sharpe Ratio: Stocks vs S&P 500')

# Uncomment your choice. buy_amazon = True # buy_facebook = True