R Notebook

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

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

# Indian Stocks from Bse Index
indian_stocks <- data[,1]
m_indian_stocks <- monthlyReturn(indian_stocks, type = "arithmetic")
colnames(indian_stocks) <- "m_indian_stocks"
table.AnnualizedReturns(m_indian_stocks)

charts.PerformanceSummary(m_indian_stocks)

# Indian Bonds

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

international_stock <- data[,3]
m_international_stock <- monthlyReturn(international_stock)
colnames(international_stock) <- "m_international_stock"
table.AnnualizedReturns(m_international_stock)

charts.PerformanceSummary(m_international_stock)

# International Bonds
international_bonds <- data[,4]
m_international_bond <- monthlyReturn(international_bonds)
colnames(international_bonds) <- "m_international_bond"
table.AnnualizedReturns(m_international_bond)

charts.PerformanceSummary(m_international_bond)

# Bonds Compare
bondscomp <- cbind(m_indian_bonds,m_international_bond)
table.AnnualizedReturns(bondscomp)

charts.PerformanceSummary(bondscomp)

# stocks Compare

stockcomp <- cbind(m_indian_stocks,m_international_stock)
table.AnnualizedReturns(stockcomp)

charts.PerformanceSummary(stockcomp)

# 4. Portfolio Optimization

# 4.1. Portfolio Performance Metrics

# 4.1.1. Sharpe Ratio 
#msharpe <- SharpeRatio(mlstocks,Rf=mean(mcash))
#msharpe

# 4.1.2. Treynor Ratio
#mtreynor <- TreynorRatio(Ra=mlstocks,Rb=mstocks,Rf=mean(mcash))
#mtreynor

# 4.2. Portfolio Benchmarks 

# 4.2.1. Portfolio Assets Returns Matrix
mport <- cbind(m_indian_stocks,m_international_stock,m_indian_bonds, m_international_stock)

# 4.2.2. Naive Global Portfolio (Monthly Rebalancing)
mnaivew <- as.numeric(t(c(0.25,0.25,0.25,0.25)))
names(mnaivew) <- c("m_indian_stocks","m_international_stock","m_indian_bonds","m_international_stock")
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("m_indian_stocks","m_international_stock","m_indian_bonds","m_international_stock")
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("m_indian_stocks","m_international_stock","m_indian_bonds","m_international_stock")
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: -0.012355 bestmemit:    0.002000    0.688000    0.010000    0.308000
Iteration: 2 bestvalit: -0.012412 bestmemit:    0.012000    0.038000    0.000000    0.960000
Iteration: 3 bestvalit: -0.012412 bestmemit:    0.012000    0.038000    0.000000    0.960000
Iteration: 4 bestvalit: -0.012412 bestmemit:    0.012000    0.038000    0.000000    0.960000
Iteration: 5 bestvalit: -0.012412 bestmemit:    0.012000    0.038000    0.000000    0.960000
Iteration: 6 bestvalit: -0.012412 bestmemit:    0.012000    0.038000    0.000000    0.960000
Iteration: 7 bestvalit: -0.012412 bestmemit:    0.012000    0.038000    0.000000    0.960000
Iteration: 8 bestvalit: -0.012412 bestmemit:    0.012000    0.038000    0.000000    0.960000
Iteration: 9 bestvalit: -0.012412 bestmemit:    0.012000    0.038000    0.000000    0.960000
[1] 0.012 0.038 0.000 0.960

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: 0.000913 bestmemit:    0.010000    0.000000    0.978000    0.006000
Iteration: 2 bestvalit: 0.000875 bestmemit:    0.010000    0.000000    0.978000    0.004279
Iteration: 3 bestvalit: 0.000875 bestmemit:    0.010000    0.000000    0.978000    0.004279
Iteration: 4 bestvalit: 0.000875 bestmemit:    0.010000    0.000000    0.978000    0.004279
Iteration: 5 bestvalit: 0.000875 bestmemit:    0.010000    0.000000    0.978000    0.004279
Iteration: 6 bestvalit: 0.000875 bestmemit:    0.010000    0.000000    0.978000    0.004279
Iteration: 7 bestvalit: 0.000875 bestmemit:    0.010000    0.000000    0.978000    0.004279
Iteration: 8 bestvalit: 0.000875 bestmemit:    0.010000    0.000000    0.978000    0.004279
Iteration: 9 bestvalit: 0.000875 bestmemit:    0.010000    0.000000    0.978000    0.004279
[1] 0.010000000 0.000000000 0.978000000
[4] 0.004278807

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: -0.004148 bestmemit:    0.018000    0.068000    0.904000    0.000000
Iteration: 2 bestvalit: -0.004148 bestmemit:    0.018000    0.068000    0.904000    0.000000
Iteration: 3 bestvalit: -0.006212 bestmemit:    0.006000    0.012000    0.986000    0.006000
Iteration: 4 bestvalit: -0.006212 bestmemit:    0.006000    0.012000    0.986000    0.006000
Iteration: 5 bestvalit: -0.006212 bestmemit:    0.006000    0.012000    0.986000    0.006000
Iteration: 6 bestvalit: -0.006212 bestmemit:    0.006000    0.012000    0.986000    0.006000
Iteration: 7 bestvalit: -0.006212 bestmemit:    0.006000    0.012000    0.986000    0.006000
Iteration: 8 bestvalit: -0.006212 bestmemit:    0.006000    0.012000    0.986000    0.006000
Iteration: 9 bestvalit: -0.006212 bestmemit:    0.006000    0.012000    0.986000    0.006000
Iteration: 10 bestvalit: -0.006212 bestmemit:    0.006000    0.012000    0.986000    0.006000
[1] 0.006 0.012 0.986 0.006

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: 0.002548 bestmemit:    0.094000    0.008000    0.898000    0.006000
Iteration: 2 bestvalit: 0.002548 bestmemit:    0.094000    0.008000    0.898000    0.006000
Iteration: 3 bestvalit: -0.003647 bestmemit:    0.030000    0.058000    0.920000    0.002000
Iteration: 4 bestvalit: -0.003647 bestmemit:    0.030000    0.058000    0.920000    0.002000
Iteration: 5 bestvalit: -0.005864 bestmemit:    0.000000    0.030000    0.926000    0.052000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.00157553045118132
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.00800.9580.024

Iteration: 6 bestvalit: -0.005864 bestmemit:    0.000000    0.030000    0.926000    0.052000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -6.90829274658297e-05
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.03800.9540.002

Iteration: 7 bestvalit: -0.005864 bestmemit:    0.000000    0.030000    0.926000    0.052000
Iteration: 8 bestvalit: -0.006120 bestmemit:    0.028000    0.012000    0.946000    0.024000
Iteration: 9 bestvalit: -0.006754 bestmemit:    0.020000    0.010000    0.934000    0.030000
Iteration: 10 bestvalit: -0.006754 bestmemit:    0.020000    0.010000    0.934000    0.030000
Iteration: 11 bestvalit: -0.007049 bestmemit:    0.002000    0.054000    0.936000    0.012000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.0014757113543874
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.020.0020.9680.002

Iteration: 12 bestvalit: -0.007049 bestmemit:    0.002000    0.054000    0.936000    0.012000
Iteration: 13 bestvalit: -0.007049 bestmemit:    0.002000    0.054000    0.936000    0.012000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.000776293722815273
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.0120.0060.950.03

Iteration: 14 bestvalit: -0.007049 bestmemit:    0.002000    0.054000    0.936000    0.012000
Iteration: 15 bestvalit: -0.007224 bestmemit:    0.000000    0.032000    0.934000    0.034000
Iteration: 16 bestvalit: -0.007224 bestmemit:    0.000000    0.032000    0.934000    0.034000
Iteration: 17 bestvalit: -0.007224 bestmemit:    0.000000    0.032000    0.934000    0.034000
Iteration: 18 bestvalit: -0.007224 bestmemit:    0.000000    0.032000    0.934000    0.034000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.000147798621543293
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.0040.0480.9380.00816507252357672

Iteration: 19 bestvalit: -0.007224 bestmemit:    0.000000    0.032000    0.934000    0.034000
Iteration: 20 bestvalit: -0.007224 bestmemit:    0.000000    0.032000    0.934000    0.034000
Iteration: 21 bestvalit: -0.007224 bestmemit:    0.000000    0.032000    0.934000    0.034000

VaR calculation produces unreliable result (inverse risk) for column: 1 : -1.53409120965025e-05
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.001999999999999990.0603482989168770.9362294183330390
VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.00130191054928627
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.0080.0320.9560.002
VaR calculation produces unreliable result (inverse risk) for column: 1 : -0.00175569663332701
Warning in FUN(newX[, i], ...) :
  NA or NaN produced in objective function for weights 0.0020.010.970.02

Iteration: 22 bestvalit: -0.007224 bestmemit:    0.000000    0.032000    0.934000    0.034000
[1] 0.000 0.032 0.934 0.034

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,mportopt4)
#mportcomp = cbind(mnaive["2015-01-31::"],mport1c,mport2c,mport3c,mport4c)
table.AnnualizedReturns(mportcomp)

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