R Notebook

#install.packages("tseries")
library("tseries")
#install.packages("quantmod")
library("quantmod")
#install.packages("Quandl")
library("Quandl")
#install.packages("PortfolioAnalytics")
library("PortfolioAnalytics")
#install.packages("DEoptim")
library("DEoptim")
library("xts")
#install.packages("knitr")
#library("knitr")

# Reading of Data
data <- read.csv("anupam.csv", header = T)
data <- xts(data[ ,2:5], order.by = as.Date.factor(data[,1]))  
View(data)

# Indian Stocks from BSE Index 
stocks <- data[,1]
mstocks <- monthlyReturn(stocks, type = "arithmetic")
colnames(mstocks) <- "mstocks"
table.AnnualizedReturns(mstocks)

charts.PerformanceSummary(mstocks)

# Indian Bonds - PGIM India Premier Bond Fund Growth (0P00005VBS.BO)

indian_bonds <- data[,2]
m_indian_bonds <- monthlyReturn(indian_bonds)
colnames(indian_bonds) <- "m_indian_bonds"
table.AnnualizedReturns(m_indian_bonds)

charts.PerformanceSummary(m_indian_bonds)

# International Stocks - From NASDAQ

int_stocks <- data[,3]
mint_stocks <- monthlyReturn(int_stocks)
colnames(mint_stocks) <- "mint_stocks"
table.AnnualizedReturns(mint_stocks)

charts.PerformanceSummary(mint_stocks)

# International Bonds - NASDAQ
intl_bonds <- data[,4]
mintl_bonds <- monthlyReturn(intl_bonds)
colnames(intl_bonds) <- "mintl_bonds"
table.AnnualizedReturns(mintl_bonds)

charts.PerformanceSummary(mintl_bonds)

# Comparing Indian & Intl Bonds
bondscomp <- cbind(m_indian_bonds,mintl_bonds)
table.AnnualizedReturns(bondscomp)

charts.PerformanceSummary(bondscomp)

# Comparing Indian BSE & Intl Stocks

stockcomp <- cbind(mstocks,mint_stocks)
table.AnnualizedReturns(stockcomp)

charts.PerformanceSummary(stockcomp)

# 4. Portfolio Optimization

# 4.2. Portfolio Benchmarks 

# 4.2.1. Portfolio Assets Returns Matrix
mport <- cbind(mstocks,mint_stocks,m_indian_bonds, mintl_bonds)

# 4.2.2. Naive Global Portfolio (Monthly Rebalancing)
mnaivew <- as.numeric(t(c(0.25,0.25,0.25,0.25)))
names(mnaivew) <- c("mstocks","mint_stocks","m_indian_bonds","mintl_bonds")
mnaive <- Return.portfolio(R=mport,weights=mnaivew,geometric=F,rebalance_on="months")
colnames(mnaive) <- "mnaive"

# 4.2.3. Roche Global Portfolio (Monthly Rebalancing)
mrochew <- as.numeric(t(c(0.24,0.18,0.33,0.25)))
names(mrochew) <- c("mstocks","mint_stocks","m_indian_bonds","mintl_bonds")
mroche <- Return.portfolio(R=mport,weights=mrochew,geometric=F,rebalance_on="months")
colnames(mroche) <- "mroche"

# 4.2.4. Bogle U.S. Portfolio (Monthly Rebalancing)
mboglew <- as.numeric(t(c(0.40,0.60,0.00,0.00)))
names(mboglew) <- c("mstocks","mint_stocks","m_indian_bonds","mintl_bonds")
mbogle <- Return.portfolio(R=mport,weights=mboglew,geometric=F,rebalance_on="months")
colnames(mbogle) <- "mbogle"

# 4.2.6. Benchmark Portfolios Returns Comparison
benchcomp <- cbind(mnaive,mroche,mbogle)
table.AnnualizedReturns(benchcomp)

charts.PerformanceSummary(benchcomp)

# 4.3. Portfolio Optimization 

# 4.3.1. Mean Maximization 

# Portfolio Specifications
mport1c <- portfolio.spec(assets = colnames(mport))

# Portfolio Constraints
mport1c <- add.constraint(mport1c,type="weight_sum",min_sum=0.99,max_sum=1.01)
mport1c <- add.constraint(mport1c,type="long_only")

# Portfolio Objectives
mport1c <- add.objective(mport1c,type="return",name="mean")

# Portfolio Optimization
mportopt1 <- optimize.portfolio(R=mport["::2021-12-31"],portfolio=mport1c,optimize_method="DEoptim",search_size=20000,trace=T )

Iteration: 1 bestvalit: -0.013132 bestmemit:    0.004000    0.994000    0.000000    0.012000
Iteration: 2 bestvalit: -0.013132 bestmemit:    0.004000    0.994000    0.000000    0.012000
Iteration: 3 bestvalit: -0.013132 bestmemit:    0.004000    0.994000    0.000000    0.012000
Iteration: 4 bestvalit: -0.013132 bestmemit:    0.004000    0.994000    0.000000    0.012000
Iteration: 5 bestvalit: -0.013132 bestmemit:    0.004000    0.994000    0.000000    0.012000
Iteration: 6 bestvalit: -0.013132 bestmemit:    0.004000    0.994000    0.000000    0.012000
Iteration: 7 bestvalit: -0.013132 bestmemit:    0.004000    0.994000    0.000000    0.012000
[1] 0.004 0.994 0.000 0.012

chart.Weights(mportopt1)

# 4.3.2. Standard deviation minimization

# Portfolio Specifications
mport2c <- portfolio.spec(assets=colnames(mport))

# Portfolio Constraints
mport2c <- add.constraint(mport2c,type="weight_sum",min_sum=0.99,max_sum=1.01)
mport2c <- add.constraint(mport2c,type="long_only")

# Portfolio Objectives
mport2c <- add.objective(mport2c,type="risk",name="StdDev")

# Portfolio Optimization
mportopt2 <- optimize.portfolio(R=mport["::2021-12-31"],portfolio=mport2c,optimize_method="DEoptim",search_size=20000,trace=T)

Iteration: 1 bestvalit: 0.001255 bestmemit:    0.004000    0.026000    0.974000    0.000000
Iteration: 2 bestvalit: 0.001255 bestmemit:    0.004000    0.026000    0.974000    0.000000
Iteration: 3 bestvalit: 0.001255 bestmemit:    0.004000    0.026000    0.974000    0.000000
Iteration: 4 bestvalit: 0.001255 bestmemit:    0.004000    0.026000    0.974000    0.000000
Iteration: 5 bestvalit: 0.001255 bestmemit:    0.004000    0.026000    0.974000    0.000000
Iteration: 6 bestvalit: 0.001255 bestmemit:    0.004000    0.026000    0.974000    0.000000
Iteration: 7 bestvalit: 0.001058 bestmemit:    0.014000    0.000000    0.964000    0.014000
Iteration: 8 bestvalit: 0.000691 bestmemit:    0.000000    0.000000    0.996000    0.014000
Iteration: 9 bestvalit: 0.000691 bestmemit:    0.000000    0.000000    0.996000    0.014000
Iteration: 10 bestvalit: 0.000628 bestmemit:    0.002000    0.006000    0.990000    0.000000
Iteration: 11 bestvalit: 0.000628 bestmemit:    0.002000    0.006000    0.990000    0.000000
Iteration: 12 bestvalit: 0.000628 bestmemit:    0.002000    0.006000    0.990000    0.000000
Iteration: 13 bestvalit: 0.000628 bestmemit:    0.002000    0.006000    0.990000    0.000000
Iteration: 14 bestvalit: 0.000628 bestmemit:    0.002000    0.006000    0.990000    0.000000
Iteration: 15 bestvalit: 0.000628 bestmemit:    0.002000    0.006000    0.990000    0.000000
Iteration: 16 bestvalit: 0.000628 bestmemit:    0.002000    0.006000    0.990000    0.000000
Iteration: 17 bestvalit: 0.000628 bestmemit:    0.002000    0.006000    0.990000    0.000000
[1] 0.002 0.006 0.990 0.000

chart.Weights(mportopt2)

# 4.3.3. Mean Maximization and Standard Deviation Minimization Portfolio

# Portfolio Specifications
mport3c <- portfolio.spec(assets=colnames(mport))

# Portfolio Constraints
mport3c <- add.constraint(mport3c,type="weight_sum",min_sum=0.99,max_sum=1.01)
mport3c <- add.constraint(mport3c,type="long_only")

# Portfolio Objectives
mport3c <- add.objective(mport3c,type="return",name="mean")
mport3c <- add.objective(mport3c,type="risk",name="StdDev")

# Portfolio Optimization
mportopt3 <- optimize.portfolio(R=mport["::2021-12-31"],portfolio=mport3c,optimize_method="DEoptim",search_size=20000,trace=T)

Iteration: 1 bestvalit: -0.005359 bestmemit:    0.006000    0.004000    0.990000    0.000000
Iteration: 2 bestvalit: -0.005359 bestmemit:    0.006000    0.004000    0.990000    0.000000
Iteration: 3 bestvalit: -0.005359 bestmemit:    0.006000    0.004000    0.990000    0.000000
Iteration: 4 bestvalit: -0.005359 bestmemit:    0.006000    0.004000    0.990000    0.000000
Iteration: 5 bestvalit: -0.005359 bestmemit:    0.006000    0.004000    0.990000    0.000000
Iteration: 6 bestvalit: -0.005359 bestmemit:    0.006000    0.004000    0.990000    0.000000
Iteration: 7 bestvalit: -0.005359 bestmemit:    0.006000    0.004000    0.990000    0.000000
Iteration: 8 bestvalit: -0.005359 bestmemit:    0.006000    0.004000    0.990000    0.000000
[1] 0.006 0.004 0.990 0.000

chart.Weights(mportopt3)

chart.EfficientFrontier(mportopt3,match.col="StdDev")

# 4.3.4. Mean Maximization Value at Risk (VaR) Minimization Portfolio

# Portfolio Specifications
mport4c <- portfolio.spec(assets=colnames(mport))

# Portfolio Constraints
mport4c <- add.constraint(mport4c,type="weight_sum",min_sum=0.99,max_sum=1.01)
mport4c <- add.constraint(mport4c,type="long_only")

# Portfolio Objectives
mport4c <- add.objective(mport4c,type="return",name="mean")
mport4c <- add.objective(mport4c,type="risk",name="VaR",arguments=list(p = 0.99,method="modified"))

# Portfolio Optimization
mportopt4 <- optimize.portfolio(R=mport["::2021-12-31"],portfolio=mport4c,optimize_method="DEoptim",search_size=20000,trace=T)

Iteration: 1 bestvalit: -0.003747 bestmemit:    0.000000    0.008000    0.912000    0.084000
Iteration: 2 bestvalit: -0.003747 bestmemit:    0.000000    0.008000    0.912000    0.084000
Iteration: 3 bestvalit: -0.003747 bestmemit:    0.000000    0.008000    0.912000    0.084000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -1.29607669646214e-05
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.0160.0020.960.028

Iteration: 4 bestvalit: -0.003747 bestmemit:    0.000000    0.008000    0.912000    0.084000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.000792700838880535
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.0040.0180.9580.0190368894291137

Iteration: 5 bestvalit: -0.003747 bestmemit:    0.000000    0.008000    0.912000    0.084000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.00128555619418081
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 00.0040.9720.034

Iteration: 6 bestvalit: -0.003747 bestmemit:    0.000000    0.008000    0.912000    0.084000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.000459446799292463
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.004708329857731880.020.9505835071134060.022

Iteration: 7 bestvalit: -0.005319 bestmemit:    0.002376    0.034867    0.935243    0.031624
Iteration: 8 bestvalit: -0.005319 bestmemit:    0.002376    0.034867    0.935243    0.031624
Iteration: 9 bestvalit: -0.005319 bestmemit:    0.002376    0.034867    0.935243    0.031624

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.00116990908081472
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.00800.9720.024

Iteration: 10 bestvalit: -0.005319 bestmemit:    0.002376    0.034867    0.935243    0.031624
Iteration: 11 bestvalit: -0.005319 bestmemit:    0.002376    0.034867    0.935243    0.031624

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.000612935601496843
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.0100.950.034

Iteration: 12 bestvalit: -0.005319 bestmemit:    0.002376    0.034867    0.935243    0.031624
Iteration: 13 bestvalit: -0.005319 bestmemit:    0.002376    0.034867    0.935243    0.031624

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.00105573779958479
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.0060.010.9740.016

Iteration: 14 bestvalit: -0.005319 bestmemit:    0.002376    0.034867    0.935243    0.031624
[1] 0.002376075 0.034867119 0.935243386
[4] 0.031623732

chart.Weights(mportopt4)

# 4.3.5. Optimized Portfolios Backtesting Comparison

#mportcomp <- cbind(mnaive["2015-01-31::"],mportopt1,mportopt2,mportopt3,mportopt4)

mportcomp <- cbind(mportopt1,mportopt2,mportopt3,mport4c)

table.AnnualizedReturns(mportcomp)

Error in if (class(x) == "numeric") { : the condition has length > 1