Table of Contents

Sharpe Ratio and Portfolio Values

Portfolio Values

Imports

In [1]:
import pandas as pd
import quandl

Create a Portfolio from Quandl

In [2]:
start = pd.to_datetime('2012-01-01')
end = pd.to_datetime('2017-01-01')
In [3]:
# Grabbing a bunch of tech stocks for our portfolio
# Adjusted Close column only (11)
aapl = quandl.get('WIKI/AAPL.11',start_date=start,end_date=end)
cisco = quandl.get('WIKI/CSCO.11',start_date=start,end_date=end)
ibm = quandl.get('WIKI/IBM.11',start_date=start,end_date=end)
amzn = quandl.get('WIKI/AMZN.11',start_date=start,end_date=end)

Alternative: from CSV file

In [4]:
# aapl = pd.read_csv('AAPL_CLOSE',index_col='Date',parse_dates=True)
# cisco = pd.read_csv('CISCO_CLOSE',index_col='Date',parse_dates=True)
# ibm = pd.read_csv('IBM_CLOSE',index_col='Date',parse_dates=True)
# amzn = pd.read_csv('AMZN_CLOSE',index_col='Date',parse_dates=True)
In [5]:
aapl.to_csv('AAPL_CLOSE')
cisco.to_csv('CISCO_CLOSE')
ibm.to_csv('IBM_CLOSE')
amzn.to_csv('AMZN_CLOSE')

Normalize Prices

This is the same as Cumulative Daily Returns

In [6]:
# Example
aapl.iloc[0]['Adj. Close']
Out[6]:
52.848786580038
In [7]:
for stock_df in (aapl,cisco,ibm,amzn):
    stock_df['Normed Return'] = stock_df['Adj. Close']/stock_df.iloc[0]['Adj. Close']
In [8]:
aapl.head()
Out[8]:
Adj. Close Normed Return
Date
2012-01-03 52.848787 1.000000
2012-01-04 53.132802 1.005374
2012-01-05 53.722681 1.016536
2012-01-06 54.284287 1.027162
2012-01-09 54.198183 1.025533
In [9]:
aapl.tail()
Out[9]:
Adj. Close Normed Return
Date
2016-12-23 115.080808 2.177549
2016-12-27 115.811668 2.191378
2016-12-28 115.317843 2.182034
2016-12-29 115.288214 2.181473
2016-12-30 114.389454 2.164467

Allocations

Let's pretend we had the following allocations for our total portfolio:

  • 30% in Apple
  • 20% in Cisco
  • 40% in Amazon
  • 10% in IBM

Let's have these values be reflected by multiplying our Norme Return by out Allocations

In [10]:
# zip([aapl,cisco,ibm,amzn],[.3,.2,.4,.1])
In [11]:
# Argument after in: can be a tuple or list
for stock_df, allo in zip([aapl,cisco,ibm,amzn],[.3,.2,.4,.1]):
    # tuple unpacking
    stock_df['Allocation'] = stock_df['Normed Return']*allo
In [12]:
aapl.head()
Out[12]:
Adj. Close Normed Return Allocation
Date
2012-01-03 52.848787 1.000000 0.300000
2012-01-04 53.132802 1.005374 0.301612
2012-01-05 53.722681 1.016536 0.304961
2012-01-06 54.284287 1.027162 0.308149
2012-01-09 54.198183 1.025533 0.307660

Investment

Let's pretend we invested a million dollars in this portfolio

In [13]:
for stock_df in [aapl,cisco,ibm,amzn]:
    stock_df['Position Values'] = stock_df['Allocation']*1000000

Total Portfolio Value

Use concat() to add up portfolio values

In [14]:
portfolio_val = pd.concat([aapl['Position Values'],cisco['Position Values'],ibm['Position Values'],amzn['Position Values']], axis=1)
In [15]:
portfolio_val.head()
Out[15]:
Position Values Position Values Position Values Position Values
Date
2012-01-03 300000.000000 200000.000000 400000.000000 100000.000000
2012-01-04 301612.236461 203864.734300 398368.223296 99150.980283
2012-01-05 304960.727573 203113.258186 396478.797638 99206.836843
2012-01-06 308148.724558 202361.782072 391926.999463 101999.664861
2012-01-09 307659.946988 203650.026838 389887.278583 99737.474166

Change the column names by using member variable columns

In [16]:
portfolio_val.columns = ['AAPL Pos','CISCO Pos','IBM Pos','AMZN Pos']
In [17]:
portfolio_val.head()
Out[17]:
AAPL Pos CISCO Pos IBM Pos AMZN Pos
Date
2012-01-03 300000.000000 200000.000000 400000.000000 100000.000000
2012-01-04 301612.236461 203864.734300 398368.223296 99150.980283
2012-01-05 304960.727573 203113.258186 396478.797638 99206.836843
2012-01-06 308148.724558 202361.782072 391926.999463 101999.664861
2012-01-09 307659.946988 203650.026838 389887.278583 99737.474166

Use aggregate function sum() to get the Total Portfolio Value

In [18]:
portfolio_val['Total Pos'] = portfolio_val.sum(axis=1)
In [19]:
portfolio_val.head()
Out[19]:
AAPL Pos CISCO Pos IBM Pos AMZN Pos Total Pos
Date
2012-01-03 300000.000000 200000.000000 400000.000000 100000.000000 1.000000e+06
2012-01-04 301612.236461 203864.734300 398368.223296 99150.980283 1.002996e+06
2012-01-05 304960.727573 203113.258186 396478.797638 99206.836843 1.003760e+06
2012-01-06 308148.724558 202361.782072 391926.999463 101999.664861 1.004437e+06
2012-01-09 307659.946988 203650.026838 389887.278583 99737.474166 1.000935e+06

Plot Portfolio

In [20]:
import matplotlib.pyplot as plt
%matplotlib inline
In [21]:
portfolio_val['Total Pos'].plot(figsize=(10,8))
plt.title('Total Portfolio Value')
Out[21]:
Text(0.5,1,'Total Portfolio Value')

Note the use of drop() when plotting indvidual portfolio

In [22]:
portfolio_val.drop('Total Pos',axis=1).plot(kind='line', figsize=(10,8))
Out[22]:
<matplotlib.axes._subplots.AxesSubplot at 0x9650610>
In [23]:
portfolio_val.tail()
Out[23]:
AAPL Pos CISCO Pos IBM Pos AMZN Pos Total Pos
Date
2016-12-23 653264.617079 377469.015679 407359.955612 424839.412389 1.862933e+06
2016-12-27 657413.396830 379323.596496 408410.671112 430877.506563 1.876025e+06
2016-12-28 654610.167268 376108.989746 406089.322915 431285.259454 1.868094e+06
2016-12-29 654441.973495 376603.544631 407091.167926 427386.471541 1.865523e+06
2016-12-30 649340.095692 373636.215323 405600.618032 418851.589119 1.847429e+06

Portfolio Statistics

Daily Returns

In [24]:
portfolio_val['Daily Return'] = portfolio_val['Total Pos'].pct_change(1)

Cumulative Return

In [25]:
cum_ret = 100 * (portfolio_val['Total Pos'][-1]/portfolio_val['Total Pos'][0] -1 )
total_pos = portfolio_val['Total Pos'][-1]
print('Our cumulative return {} was percent! Our portfolio grew to ${}'.format(cum_ret, total_pos))

Our cumulative return 84.74285181665545 was percent! Our portfolio grew to $1847428.5181665544

Avg Daily Return

In [26]:
portfolio_val['Daily Return'].mean()
Out[26]:
0.0005442330716215244

Standard Deviation of Daily Return

In [27]:
portfolio_val['Daily Return'].std()
Out[27]:
0.010568287769161718

Plot: Histogram, KDE

In [28]:
portfolio_val['Daily Return'].plot(kind='hist', bins=100, figsize=(8,5))
Out[28]:
<matplotlib.axes._subplots.AxesSubplot at 0xcb96270>
In [29]:
portfolio_val['Daily Return'].plot(kind='kde', figsize=(8,5))
Out[29]:
<matplotlib.axes._subplots.AxesSubplot at 0xd5a4930>
In [30]:
aapl['Adj. Close'].pct_change(1).plot('kde', figsize=(8,5), label='AAPL')
ibm['Adj. Close'].pct_change(1).plot('kde', label='IBM')
amzn['Adj. Close'].pct_change(1).plot('kde', label='AMZN')
cisco['Adj. Close'].pct_change(1).plot('kde', label='CISCO')
plt.legend()
Out[30]:
<matplotlib.legend.Legend at 0xf295230>

Sharpe Ratio

The Sharpe Ratio is a measure for calculating risk-adjusted return, and this ratio has become the industry standard for such calculations.

$SR = \frac{R_p - R_f}{\sigma_p}$

Sharpe ratio = (Mean portfolio return − Risk-free rate)/Standard deviation of portfolio return

The original Sharpe Ratio

Annualized Sharpe Ratio = K-value * SR

K-values for various sampling rates:

  • Daily = sqrt(252)
  • Weekly = sqrt(52)
  • Monthly = sqrt(12)

Since I'm based in the USA, I will use a very low risk-free rate (the rate you would get if you just put your money in a bank, its currently very low in the USA, let's just say its ~0% return). If you are in a different country with higher rates for your trading currency, you can use this trick to convert a yearly rate with a daily rate:

daily_rate = ((1.0 + yearly_rate)**(1/252))-1

Other values people use are things like the 3-month treasury bill or LIBOR.

Read more: Sharpe Ratio http://www.investopedia.com/terms/s/sharperatio

In [31]:
import numpy as np
np.sqrt(252)* (np.mean(.001-0.0002)/.001)
Out[31]:
12.699606293110037

Sharpe Ratio (SR): risk-free rate of zero is used

In [32]:
SR = portfolio_val['Daily Return'].mean()/portfolio_val['Daily Return'].std()
SR
Out[32]:
0.05149680662648092

Annualized Sharpe Ratio (ASR):

In [33]:
ASR = (252**0.5)*SR
ASR
Out[33]:
0.8174864618859096

Generally speaking, a Sharpe Ratio greater than 1 is considered acceptable. A ratio greater than 2 is considered very good.