First, here are the tickers for stocks in the S&P; 500.

stocks = ['MMM', 'ABT', 'ABBV', 'ACN', 'ATVI', 'AYI', 'ADBE', 'AMD', 'AAP', 'AES', 'AET', 'AMG', 'AFL', 'A', 'APD', 'AKAM', 'ALK', 'ALB', 'ARE', 'ALXN', 'ALLE', 'AGN', 'ADS', 'LNT', 'ALL', 'GOOGL', 'GOOG', 'MO', 'AMZN', 'AEE', 'AAL', 'AEP', 'AXP', 'AIG', 'AMT', 'AWK', 'AMP', 'ABC', 'AME', 'AMGN', 'APH', 'APC', 'ADI', 'ANTM', 'AON', 'APA', 'AIV', 'AAPL', 'AMAT', 'ADM', 'ARNC', 'AJG', 'AIZ', 'T', 'ADSK', 'ADP', 'AN', 'AZO', 'AVB', 'AVY', 'BHI', 'BLL', 'BAC', 'BK', 'BCR', 'BAX', 'BBT', 'BDX', 'BBBY', 'BRK.B', 'BBY', 'BIIB', 'BLK', 'HRB', 'BA', 'BWA', 'BXP', 'BSX', 'BMY', 'AVGO', 'BF.B', 'CHRW', 'CA', 'COG', 'CPB', 'COF', 'CAH', 'CBOE', 'KMX', 'CCL', 'CAT', 'CBG', 'CBS', 'CELG', 'CNC', 'CNP', 'CTL', 'CERN', 'CF', 'SCHW', 'CHTR', 'CHK', 'CVX', 'CMG', 'CB', 'CHD', 'CI', 'XEC', 'CINF', 'CTAS', 'CSCO', 'C', 'CFG', 'CTXS', 'CLX', 'CME', 'CMS', 'COH', 'KO', 'CTSH', 'CL', 'CMCSA', 'CMA', 'CAG', 'CXO', 'COP', 'ED', 'STZ', 'COO', 'GLW', 'COST', 'COTY', 'CCI', 'CSRA', 'CSX', 'CMI', 'CVS', 'DHI', 'DHR', 'DRI', 'DVA', 'DE', 'DLPH', 'DAL', 'XRAY', 'DVN', 'DLR', 'DFS', 'DISCA', 'DISCK', 'DISH', 'DG', 'DLTR', 'D', 'DOV', 'DOW', 'DPS', 'DTE', 'DD', 'DUK', 'DXC', 'ETFC', 'EMN', 'ETN', 'EBAY', 'ECL', 'EIX', 'EW', 'EA', 'EMR', 'ETR', 'EVHC', 'EOG', 'EQT', 'EFX', 'EQIX', 'EQR', 'ESS', 'EL', 'ES', 'EXC', 'EXPE', 'EXPD', 'ESRX', 'EXR', 'XOM', 'FFIV', 'FB', 'FAST', 'FRT', 'FDX', 'FIS', 'FITB', 'FE', 'FISV', 'FLIR', 'FLS', 'FLR', 'FMC', 'FL', 'F', 'FTV', 'FBHS', 'BEN', 'FCX', 'GPS', 'GRMN', 'IT', 'GD', 'GE', 'GGP', 'GIS', 'GM', 'GPC', 'GILD', 'GPN', 'GS', 'GT', 'GWW', 'HAL', 'HBI', 'HOG', 'HRS', 'HIG', 'HAS', 'HCA', 'HCP', 'HP', 'HSIC', 'HSY', 'HES', 'HPE', 'HOLX', 'HD', 'HON', 'HRL', 'HST', 'HPQ', 'HUM', 'HBAN', 'IDXX', 'INFO', 'ITW', 'ILMN', 'IR', 'INTC', 'ICE', 'IBM', 'INCY', 'IP', 'IPG', 'IFF', 'INTU', 'ISRG', 'IVZ', 'IRM', 'JEC', 'JBHT', 'SJM', 'JNJ', 'JCI', 'JPM', 'JNPR', 'KSU', 'K', 'KEY', 'KMB', 'KIM', 'KMI', 'KLAC', 'KSS', 'KHC', 'KR', 'LB', 'LLL', 'LH', 'LRCX', 'LEG', 'LEN', 'LVLT', 'LUK', 'LLY', 'LNC', 'LKQ', 'LMT', 'L', 'LOW', 'LYB', 'MTB', 'MAC', 'M', 'MNK', 'MRO', 'MPC', 'MAR', 'MMC', 'MLM', 'MAS', 'MA', 'MAT', 'MKC', 'MCD', 'MCK', 'MJN', 'MDT', 'MRK', 'MET', 'MTD', 'KORS', 'MCHP', 'MU', 'MSFT', 'MAA', 'MHK', 'TAP', 'MDLZ', 'MON', 'MNST', 'MCO', 'MS', 'MOS', 'MSI', 'MUR', 'MYL', 'NDAQ', 'NOV', 'NAVI', 'NTAP', 'NFLX', 'NWL', 'NFX', 'NEM', 'NWSA', 'NWS', 'NEE', 'NLSN', 'NKE', 'NI', 'NBL', 'JWN', 'NSC', 'NTRS', 'NOC', 'NRG', 'NUE', 'NVDA', 'ORLY', 'OXY', 'OMC', 'OKE', 'ORCL', 'PCAR', 'PH', 'PDCO', 'PAYX', 'PYPL', 'PNR', 'PBCT', 'PEP', 'PKI', 'PRGO', 'PFE', 'PCG', 'PM', 'PSX', 'PNW', 'PXD', 'PNC', 'RL', 'PPG', 'PPL', 'PX', 'PCLN', 'PFG', 'PG', 'PGR', 'PLD', 'PRU', 'PEG', 'PSA', 'PHM', 'PVH', 'QRVO', 'PWR', 'QCOM', 'DGX', 'RRC', 'RJF', 'RTN', 'O', 'RHT', 'REG', 'REGN', 'RF', 'RSG', 'RAI', 'RHI', 'ROK', 'COL', 'ROP', 'ROST', 'RCL', 'R', 'CRM', 'SCG', 'SLB', 'SNI', 'STX', 'SEE', 'SRE', 'SHW', 'SIG', 'SPG', 'SWKS', 'SLG', 'SNA', 'SO', 'LUV', 'SPGI', 'SWK', 'SPLS', 'SBUX', 'STT', 'SRCL', 'SYK', 'STI', 'SYMC', 'SYF', 'SNPS', 'SYY', 'TROW', 'TGT', 'TEL', 'FTI', 'TDC', 'TSO', 'TXN', 'TXT', 'TMO', 'TIF', 'TWX', 'TJX', 'TMK', 'TSS', 'TSCO', 'TDG', 'RIG', 'TRV', 'TRIP', 'FOXA', 'FOX', 'TSN', 'UDR', 'ULTA', 'USB', 'UA', 'UAA', 'UNP', 'UAL', 'UNH', 'UPS', 'URI', 'UTX', 'UHS', 'UNM', 'VFC', 'VLO', 'VAR', 'VTR', 'VRSN', 'VRSK', 'VZ', 'VRTX', 'VIAB', 'V', 'VNO', 'VMC', 'WMT', 'WBA', 'DIS', 'WM', 'WAT', 'WEC', 'WFC', 'HCN', 'WDC', 'WU', 'WRK', 'WY', 'WHR', 'WFM', 'WMB', 'WLTW', 'WYN', 'WYNN', 'XEL', 'XRX', 'XLNX', 'XL', 'XYL', 'YHOO', 'YUM', 'ZBH', 'ZION', 'ZTS']

And let’s get a little bit of stock data.

import pandas_datareader as pdr
import datetime
start = datetime.datetime(2016, 1, 1)
end = datetime.datetime(2017, 1, 1)
df = pdr.get_data_yahoo(stocks[:3], start, end)["Adj Close"]
df = df.pct_change().dropna()
print(df)

Let’s see what our covariance matrix looks like.

print(df.cov())

We are going to make a function to find the portfolio variance. To find the total variance we would need to add up all the variances adjusted for weight and then all the different covariance terms also adjusted for weight. An easy way to speed up this process is to use some quick linear algebra. We need a matrix of the covariances, and a matrix of the weights (it will be one dimensional). The supporting equation will be:

Before we jump into the function, I want you to see what x and x

^t

will look like. We use np.mat() to create matrices. When we have a matrix, we can get it’s transpose with the transpose() function.

import numpy as np
weights = np.mat([.6,.2,.2])
print(weights)
print("")
print(weights.transpose())