Financial Analysis: The Sharpe Ratio¶
The Sharpe Ratio measures the performance of an investment compared to a risk-free asset, after adjusting for its risk. It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment. In this project I will use the S&P 500 index as the risk-free benchmark and Apple, Facebook, and Amazon as the stocks of interest.
Import Data¶
In [11]:
import yfinance as yf
import pandas as pd
#Import Apple, Facebook, and Amazon from Yahoo Finance. Use adjusted close for computation.
ticker_list=['AAPL','FB','AMZN']
stock_data = yf.download(ticker_list,'2018-01-01','2019-08-01')['Adj Close']
#Import S&P 500 index
index_data = yf.download('SPY','2018-01-01','2019-08-01')['Adj Close']
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Exploratory Data Analysis¶
In [17]:
stock_data
Out[17]:
| AAPL | AMZN | FB | |
|---|---|---|---|
| Date | |||
| 2018-01-02 | 41.442081 | 1189.010010 | 181.419998 |
| 2018-01-03 | 41.434864 | 1204.199951 | 184.669998 |
| 2018-01-04 | 41.627323 | 1209.589966 | 184.330002 |
| 2018-01-05 | 42.101261 | 1229.140015 | 186.850006 |
| 2018-01-08 | 41.944889 | 1246.869995 | 188.279999 |
| ... | ... | ... | ... |
| 2019-07-25 | 50.964642 | 1973.819946 | 200.710007 |
| 2019-07-26 | 51.141891 | 1943.050049 | 199.750000 |
| 2019-07-29 | 51.619480 | 1912.449951 | 195.940002 |
| 2019-07-30 | 51.397919 | 1898.530029 | 197.039993 |
| 2019-07-31 | 52.446659 | 1866.780029 | 194.229996 |
397 rows × 3 columns
In [15]:
index_data
Out[15]:
Date
2018-01-02 254.112717
2018-01-03 255.719986
2018-01-04 256.797821
2018-01-05 258.509186
2018-01-08 258.981873
...
2019-07-25 291.712341
2019-07-26 293.666748
2019-07-29 293.131927
2019-07-30 292.412415
2019-07-31 289.213287
Name: Adj Close, Length: 397, dtype: float64
In [18]:
stock_data.describe()
Out[18]:
| AAPL | AMZN | FB | |
|---|---|---|---|
| count | 397.000000 | 397.000000 | 397.000000 |
| mean | 45.774501 | 1698.278414 | 172.927103 |
| std | 4.863853 | 190.309536 | 19.136734 |
| min | 34.721451 | 1189.010010 | 124.059998 |
| 25% | 42.065174 | 1580.949951 | 161.449997 |
| 50% | 45.564064 | 1692.689941 | 175.039993 |
| 75% | 49.758747 | 1863.040039 | 186.639999 |
| max | 56.472256 | 2039.510010 | 217.500000 |
In [19]:
index_data.describe()
Out[19]:
count 397.000000 mean 265.744161 std 12.387822 min 225.768829 25% 257.190338 50% 264.744415 75% 275.591797 max 293.666748 Name: Adj Close, dtype: float64
In [24]:
stock_data.plot(subplots=True,title='Stock Data Adj Close', figsize=(15,10));
In [25]:
index_data.plot(title='S&P 500 Adj Close', figsize=(15,5));
Calculation¶
In [26]:
stock_returns=stock_data.pct_change()
stock_returns.plot(subplots=True,title='Stock Returns', figsize=(15,10));
In [27]:
index_returns=index_data.pct_change()
index_returns.plot(title='Index Returns', figsize=(15,5));
In [29]:
excess_returns = stock_returns.sub(index_returns,axis=0)
excess_returns.plot(subplots=True,title='Excess Returns',figsize=(15,10));
The Sharpe Ratio is annualized by multiplying it by the square root of the number of periods. Number or trading days in a year is 252
In [38]:
import numpy as np
daily_sharpe_ratio = excess_returns.mean() / excess_returns.std()
annual_sharpe_ratio = daily_sharpe_ratio * np.sqrt(252)
annual_sharpe_ratio.plot(kind='bar' ,title='Annual Sharpe Ratio', figsize=(15,5));
Conclusion¶
Investors consider a ratio greater than 1 to be good, greater than 2 to be very good, and greater than 3 to be excellent. Looks like we will recommend Amazon.