#    R program to read prices of stocks from Yahoo Finance and estimate the vector
#    of expected returns and the covariance matrix
#    Use the daily closing prices.
#    The list of stocks is "tickerList".  You have to update this by hand.


baseURL = "http://ichart.finance.yahoo.com/table.csv?s="   #    The base URL is yahoo finance

tickerList = c("T",                                        #    Tickers of the stocks you want to analyse
               "BA",
               "CSCO"  )
n = length( tickerList)
cat( n, " tickers\n")

#-----------------------------------------------------------------------------------

#   Read price time series from Yahoo!

#-----------------------------------------------------------------------------------


PriceTimeSeries = list()      #   An R "list" of time series, one series for each ticker
                              #   Create an empty list, add the series info as they come.

SeriesLengths   = c()         #   A vector to hold the lengths of the series

for ( ticker in tickerList){

#  Make the string to send to Yahoo! that asks for the prices for the given ticker.
#  Do this by adding the ticker symbol to complete the generic price request.
#  The second line, with "sep" and "collapse" keeps R from putting a space between the two strings

   fullURL = paste( baseURL , ticker,
                    sep = "", collapse = NULL)
                    
#   Send the request to Yahoo! and put the reply into the file PRices.csv

   download.file( fullURL, "Prices.csv",  "auto", quiet = TRUE, mode = "w")
   
#   The R function "read.csv" reads a csv file (simple spreadsheet format) and
#   puts the result into an R "data frame".  This is called "Prices"
   
   Prices = read.csv("Prices.csv")

#     The fifth column of the Prices data frame, which is the fifth column of
#     the csv file from Yahoo! has the daily closing prices for that ticker

   ClosingPrices = Prices[[5]]
   L             = length( ClosingPrices)
   cat("ticker ", ticker, " has L = ", L, "\n")
   cat("   most recent prices are ", ClosingPrices[1:5], "\n")
   
#    The R command "append( list, item)" returns the list with the item appended to the end
#    The "list( ClosingPrices)" says to append the list as a list.  Don't add the numbers
#    to the end of the previous list.

   PriceTimeSeries = append( PriceTimeSeries, list( ClosingPrices))
   SeriesLengths   = append( SeriesLengths, L)
   
  }


#-----------------------------------------------------------------------------------

#   Compute the returns, expected returns, and covariance matrix

#-----------------------------------------------------------------------------------

ReturnSeries = list()          #  An R list that will contain the return sequences
mu           = numeric(n)      #  An R vector that will have the means of the return sequences

for (i in 1:n){

   L = SeriesLengths[i]          # the length of this series
   R = numeric( L - 1)           # allocate the vector for the returns of this ticker
   S = PriceTimeSeries[[i]]         # the time series of daily close prices for this stock
   
   for ( t in 1:(L-1)) {
   
      R[t] = (S[t] - S[t+1])/S[t+1]        # S[t] is the price t days ago.
                                           # This is the return from the previous day, which is S[t+1]
    }
   ReturnSeries = append( ReturnSeries, list(R))
   mu[i]        = mean(R)
 }

for (i in 1:n){
    cat("Ticker ", tickerList[i], " has mean daily return ", mu[i], "\n")
  }

C = matrix( numeric(n^2), nrow=n, ncol=n)

R1 = ReturnSeries[[1]]         # Use double square brackets to retrieve a time series from the list
R2 = ReturnSeries[[2]]

C[1,1] = var(R1)               # var() computes the variance of a list of numbers
C[2,2] = var(R2)

L1 = length(R1)
L2 = length(R2)
L  = min( L1, L2)                 #  Find the length of the shorter time series

cov( R1[1:L], R2[1:L])            #  cov() calculates the covariance of two lists of the same length
C[1,2] = cov( R1[1:L], R2[1:L])
C[2,1] = C[1,2]                   #  cov( R2[1:L], R1[1:L]) does unnecessary extra calculation

cat("C_11 = var(", tickerList[1], ") is ", C[1,1], "\n")
cat("C_12 = cov(", tickerList[1], ",", tickerList[2], ") is ", C[1,2], "\n")
rho_12 = C[1,2]/sqrt(C[1,1]*C[2,2])
cat("The correlation coefficient is ",rho_12, "\n")


#-----------------------------------------------------------------------------------

#   Compute some efficient portfolios

#-----------------------------------------------------------------------------------