#    Read stock price time series from .csv files
#    Estimate yield mean and covariance
#    Use mean/variance analysis to calculate the efficient frontier

#    For the class
#  https://www.math.nyu.edu/faculty/goodman/teaching/MathFin2019/MathFinance.html
#    For use with Assignment 7, posted there

#    The "tickers" for assets you want to invest in.
#    There must be a .csv file for each of at least the required length

tickerList = c( "T",                #   ATT (phone company)
                "F",                #   Ford (cars)
                "IBM",              #   IBM (computers, mostly software)
                "MSFT",             #   Microsoft (software)
                "BA",               #   Boeing (planes, aerospace)
                "GM",               #   General Motors (cars)
                "AAPL",             #   Apple (computers, phones, software)
                "GE",               #   General Electric (jet engines, other things)
                "AMD",              #   AMD (chips)
                "JPM",              #   J P Morgan Chase (bank)
                "NVDA",             #   Nvidia (chips)
                "SPY")              #   S & P index ETF

#        Read historical time series from .csv files in this directory

T = 250                   # number of days of historical data to use
n = length(tickerList)    # number of assets

#  prices[t,k] = closing price on day t (counting back from today) of asset k

prices = matrix( nrow = T, ncol = n)     # allocate memory for the matrix

for ( k in 1:n){                    #  iterate over k, not the ticker name
    ticker = tickerList[k]          #  get the corresponding ticker name

    fileName = paste( c( "StockPriceTimeSeries_",  # Every series starts like this
                          ticker,                  #
                         ".csv"),                  # a .csv file
                         collapse = "")            # no blanks between the parts
  
    CSVfile = read.csv( fileName )
    closingPriceSeries = CSVfile[["close"]]        # The column under "close"...
                                                   # ... holds the closing prices
    for ( t in 1:T){                               # Copy from the "data frame"...
        prices[ t, k] = closingPriceSeries[t]      # ... to the matrix
     }
  }

#     Calculate the daily returns, the mean return, and the empirical covariance

returns = matrix( nrow = (T-1), ncol = n)
for ( t in 1:(T-1)){
    for ( k in 1:n){
        returns[ t, k] = ( prices[ t+1, k] - prices[ t,k ])/prices[ t, k]
      }
  }

mu = matrix( 0, ncol = 1, nrow = n)         # Column vector of expected returns
                                            # initialized to zero so this works:
for ( k in 1:n){                            # For asset k ...
    for ( t in 1:(T-1)){                    # ... add the returns over time
        mu[k] = mu[k] + returns[t,k]
      }
    mu[k] = mu[k]/(T-1)                     # Divide by the number of samples ...
 }                                          # ... to get the empirical mean

C = matrix( 0, ncol = n, nrow = n)