I use R to calculate Tangency portfolio for all the equities in SP500.
The list of equity is load via python script
import urllib2
import pytz
import pandas as pd
import numpy as np
from bs4 import BeautifulSoup
from datetime import datetime
from pandas.io.data import DataReader
SITE = "http://en.wikipedia.org/wiki/List_of_S%26P_500_companies"
START = datetime(1900, 1, 1, 0, 0, 0, 0, pytz.utc)
END = datetime.today().utcnow()
def scrape_list(site):
hdr = {'User-Agent': 'Mozilla/5.0'}
req = urllib2.Request(site, headers=hdr)
page = urllib2.urlopen(req)
soup = BeautifulSoup(page)
table = soup.find('table', {'class': 'wikitable sortable'})
sector_tickers = dict()
for row in table.findAll('tr'):
col = row.findAll('td')
if len(col) > 0:
sector = str(col[3].string.strip()).lower().replace(' ', '_')
ticker = str(col[0].string.strip())
if sector not in sector_tickers:
sector_tickers[sector] = list()
sector_tickers[sector].append(ticker)
return sector_tickers
# export sp500 in a list
def get_sp500_all():
sector_tickers = scrape_list(SITE)
a = sector_tickers.values()
b = a[0]
for i in range(1, len(a)):
b.extend(a[i])
return b
if __name__ == '__main__':
all_symbols = get_sp500_all()
all_symbols.sort()
print len(all_symbols)
np.savetxt('all_symbols.csv',all_symbols, delimiter=',',fmt="%s")
Then load the csv which contains all the equities into R, in R to calculate the Tangency portfolio
library(PerformanceAnalytics)
library(zoo)
library(tseries)
#load all the equities in SP500,
#file generate from python
# need transpose with t()
equity_list = t(read.csv("all_symbols.csv", header = FALSE, sep=","))
# start_date & end_date
start_date = "2012-10-30"
end_date = "2014-10-30"
# create a blank zoo type var
all_prices = zoo()
# download equity data from yahoo
for (i in 1:length(equity_list)){
a = get.hist.quote(instrument = equity_list[i], start = start_date, end = end_date,
quote = "AdjClose", provider = "yahoo", origin = "1970-01-01",
compression = "m", retclass = "zoo")
index(a) = as.yearmon(index(a))
if (i == 1){all_prices = a} else {all_prices = merge(all_prices, a)
all_prices}
}
colnames(all_prices) = equity_list
# Calculate cc returns as difference in log prices
returns_df = diff(log(all_prices))
# remove the column which begining with NA
for (i in equity_list){
if(is.na(returns_df[1, i])){returns_df = returns_df[, colnames(returns_df)!=i]}
}
# first forward fill the NA, then back foward fill the NA,
#if there has long time NA, should delete the symbol, fix it in future
returns_df = na.locf(returns_df)
returns_df = na.locf(returns_df, fromLast = TRUE)
####################################################################################
# Parameters CER model
mu_hat_month = apply(returns_df, 2, mean)
sigma2_month = apply(returns_df, 2, var)
sigma_month = apply(returns_df, 2, sd)
cov_mat_month = var(returns_df)
cor_mat_month = cor(returns_df)
####################################################################################
#tangency portfolio
rf = 0.00001
mu2 = mu_hat_month - fr
tangency_portfolio = solve(cov_mat_month, mu2)
But there always has error
Error in solve.default(cov(returns_df), mu2) :
system is computationally singular: reciprocal condition number = 1.59968e-21
I can also use function tangency.portfolio.r
##Tangency portfolio
# download tangency.portfolio.r
# https://r-forge.r-project.org/scm/viewvc.php/pkg/IntroCompFinR/R/tangency.portfolio.R?view=markup&root=introcompfinr
source("D:\\MOOC\\compfinance\\excise\\tangency.portfolio.r")
#The tangency portfolio
# risk free rate
t_bill_rate = 0.00001
# Tangency portfolio short sales allowed
tangency_portfolio_short = tangency.portfolio(mu_hat_month, cov_mat_month, risk.free=t_bill_rate, shorts=TRUE)
There has error
Error in chol.default(cov.mat) :
the leading minor of order 25 is not positive definite
Seems data in returns_df has problem, but don't know where is wrong. Anyone can help?
