FinanceProject.Rmd

---
title: "R Notebook"
output:
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---

This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code. 

Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Ctrl+Shift+Enter*. 


```{r test, echo = FALSE}

#Loading packages
library("readxl")
library("lubridate") 
library("dplyr")
library("PerformanceAnalytics")
library("quantmod")
library("fPortfolio")
library('FinCovRegularization')
library("randomcoloR")
library("ggplot2")

#Loading currency data, converting to JPY, standardising currencies
data <- read_excel("ETFfxReturns.xlsx")
currencydata <- read_excel("ETFfxReturns.xlsx", sheet = 3)
data$`AGG US Equity` = (1+data$`AGG US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`SCHP US Equity` = (1+data$`SCHP US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`VCSH US Equity` = (1+data$`SCHP US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`BNDX US Equity` = (1+data$`BNDX US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`VWOB US Equity` = (1+data$`VWOB US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`VOO US Equity` = (1+data$`VOO US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`VO US Equity` = (1+data$`VO US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`VSS US Equity` = (1+data$`VSS US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`VGK US Equity` = (1+data$`VGK US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`VWO US Equity` = (1+data$`VWO US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`VNQ US Equity` = (1+data$`VNQ US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`VNQI US Equity` = (1+data$`VNQI US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`IAU US Equity` = (1+data$`IAU US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$`BCI US Equity` = (1+data$`BCI US Equity`)*(1+currencydata$USDJPY.Curncy) - 1
data$x = as.Date(data$x)
data$year = year(data$x)


#Data cleaning
TSdata2<- xts(data[,-1], order.by = data$x)
yearly <- apply.yearly(TSdata2, Return.cumulative)
monthly <- apply.monthly(TSdata2, Return.cumulative)
test <- yearly[1:18,3:18]
testfull <-yearly[1:18,]
actual <- yearly


#Setting of portfolio specifications and constraints
spec2 <- portfolioSpec()
setRiskFreeRate(spec2) <- colMeans(yearly[, 2])
#setTargetRisk(spec2) <- 0.15
setNFrontierPoints(spec2) <- 100
setTargetReturn(spec2) <- 0.11

tangency <- tangencyPortfolio(as.timeSeries(test), spec = spec2
    , constraints = c("maxW[colnames(yearly)[c(3:18)]]=0.25", "minW[colnames(yearly)[c(3:18)]]=0.01"))

minvar <- minvariancePortfolio(as.timeSeries(test), spec = spec2
    , constraints = c("maxW[colnames(yearly)[c(3:18)]]=0.25", "minW[colnames(yearly)[c(3:18)]]=0.01"))

maxreturn <- maxreturnPortfolio(as.timeSeries(test), spec = spec2
    , constraints = c("maxW[colnames(yearly)[c(3:18)]]=0.25", "minW[colnames(yearly)[c(3:18)]]=0.01"))

minvariance <- minvariancePortfolio(as.timeSeries(test), spec = spec2
    , constraints = c("maxW[colnames(yearly)[c(3:18)]]=0.25", "minW[colnames(yearly)[c(3:18)]]=0.01"))

tangencyfrontier <- portfolioFrontier(as.timeSeries(test), spec = spec2
    , constraints = c("maxW[colnames(yearly)[c(3:18)]]=0.25", "minW[colnames(yearly)[c(3:18)]]=0.01"))


#Weights charts (For visualisation only, not submitted)
plot(tangencyfrontier, c(1, 2, 4))
pie(getWeights(tangency))
pie(getWeights(minvar))
pie(getWeights(maxreturn))


#Plotting pretty weights charts (Used for submission)
tangencyweights <- getWeights(tangency)
minvarweights <- getWeights(minvar)
maxreturnweights <- getWeights(maxreturn)
colours <- randomColor(count = 16, luminosity = "light")

plot3 <- barplot(maxreturnweights * 100, horiz = FALSE, las = 3, cex.names = 0.6, col = colours, ylab = "Percentage of Portfolio (%)", main = "Portfolio for High Risk")
text(plot3, y = 0, round(maxreturnweights * 100, 1), pos = 3, cex = 0.8)

plot1 <- barplot(tangencyweights * 100, horiz = FALSE, las = 3, cex.names = 0.6, col = colours, ylab = "Percentage of Portfolio (%)", main = "Portfolio for Medium Risk")
text(plot1, y = 0, round(tangencyweights * 100, 1), pos = 3, cex = 0.8)

plot2 <- barplot(minvarweights * 100, horiz = FALSE, las = 3, cex.names = 0.6, col = colours, ylab = "Percentage of Portfolio (%)", main = "Portfolio for Low Risk")
text(plot2, y = 0, round(minvarweights * 100, 1), pos = 3, cex = 0.8)


#calculate returns and related statistics
returns <- as.matrix(test)
tangencyweights <- as.matrix(getWeights(tangency))
minvarweights <- as.matrix(getWeights(minvar))
maxreturnweights <- as.matrix(getWeights(maxreturn))
tangencyreturns <- returns %*% tangencyweights
minvarreturns <- returns %*% minvarweights
maxreturnreturns <- as.timeSeries(returns %*% maxreturnweights)
yearlyreturns <- cumprod(testfull$mkt +1) - 1
minvarcum <- cumprod(minvarreturns[, 1] + 1) - 1
maxreturncum <- cumprod(maxreturnreturns[, 1] + 1) - 1
tangencycum <- cumprod(tangencyreturns[, 1] + 1) - 1
ggplot(data = yearlyreturns, aes(x = as.Date(index(testfull)), y = mkt, color = "Market Benchmark")) +
  geom_line() +
geom_line(aes(x = as.Date(index(test)), y = maxreturncum, color = "High Risk")) +
geom_line(aes(x = as.Date(index(test)), y = tangencycum, color = "Medium Risk")) +
geom_line(aes(x = as.Date(index(test)), y = minvarcum, color = "Low Risk")) +
labs(x = 'Date',
       y = 'Cumulative Returns',
       color = "Legend",
       title = 'Portfolio Cumulative Returns')

#BETA
highbeta <- cov(testfull$mkt, maxreturnreturns)/sd(testfull$mkt)**2
midbeta <- cov(testfull$mkt, tangencyreturns)/sd(testfull$mkt)**2
lowbeta <- cov(testfull$mkt, minvarreturns)/sd(testfull$mkt)**2

cat("The beta of the high risk portfolio is", highbeta)
cat("\nThe beta of the medium risk portfolio is", midbeta)
cat("\nThe beta of the low risk portfolio is", lowbeta)

##Expected Yearly Returns
highavg <- mean(maxreturnreturns)
midavg <- mean(tangencyreturns)
lowavg <- mean(minvarreturns)
marketavg <- mean(testfull$mkt)
cat("\nThe expected returns of the high risk portfolio is", highavg)
cat("\nThe expected returns of the medium risk portfolio is", midavg)
cat("\nThe expected returns of the low risk portfolio is", lowavg)
cat("\nThe expected returns of the market portfolio is", marketavg)

#Yearly volatility
highsd <- sd(maxreturnreturns)
midsd <- sd(tangencyreturns)
lowsd <- sd(minvarreturns)
marketsd <- sd(testfull$mkt)
cat("\nThe annual volatility of the high risk portfolio is", highsd)
cat("\nThe annual volatility of the medium risk portfolio is", midsd)
cat("\nThe annual volatility of the low risk portfolio is", lowsd)
cat("\nThe annual volatility of the market portfolio is", marketsd)

#Sharpe Ratio
rfavg <- mean(testfull$rf)
highsharpe <- (highavg-rfavg)/sd(maxreturnreturns)
midsharpe <- (midavg-rfavg)/sd(tangencyreturns)
lowsharpe <- (lowavg-rfavg)/sd(minvarreturns)
marketsharpe <- (marketavg - rfavg)/sd(testfull$mkt)
cat("\nThe sharpe ratio of the high risk portfolio is", highsharpe)
cat("\nThe sharpe ratio of the medium risk portfolio is", midsharpe)
cat("\nThe sharpe ratio of the low risk portfolio is", lowsharpe)
cat("\nThe sharpe ratio of the market portfolio is", marketsharpe)


#Backtesting high return high risk portfolio
actualreturns <- as.matrix(actual)
v1 <- c(0.11)
v2 <- c(0.11)
v3 <- c(0.11)
highreturns <- rbind(as.matrix(maxreturnreturns), v1)
highreturns <- rbind(highreturns, v2)
highreturns <- rbind(highreturns, v3)
rownames(highreturns)[19:21] = c("2019-12-31", "2020-12-31", "2021-12-31")
highreturnscum <- cumprod(highreturns + 1) - 1
actualhighreturns <- as.timeSeries(actualreturns[,3:18] %*% maxreturnweights)
actualhighreturnscum <- cumprod(actualhighreturns+1)-1
ggplot(data = data.frame(actualhighreturnscum[1:21]), aes(x = as.Date(index(yearly[1:21,])), y = actualhighreturnscum[1:21], color = "Actual")) +
geom_line() + 
geom_line(aes(x = as.Date(index(yearly[1:21,])), y = highreturnscum, color = "Predicted"))+ 
labs(x = 'Date',
       y = 'Cumulative Returns',
       color = "Legend",
       title = 'High Risk Portfolio Cumulative Returns')



#Backtesting mid return mid risk portfolio
v1 <- c(0.0807987)
v2 <- c(0.0807987)
v3 <- c(0.0807987)
midreturns <- rbind(tangencyreturns, v1)
midreturns <- rbind(midreturns, v2)
midreturns <- rbind(midreturns, v3)
rownames(midreturns)[19:21] = c("2019-12-31", "2020-12-31", "2021-12-31")
midreturnscum <- cumprod(midreturns + 1) - 1
actualmidreturns <- as.timeSeries(actualreturns[,3:18] %*% tangencyweights)
actualmidreturnscum <- cumprod(actualmidreturns+1)-1
ggplot(data = data.frame(actualmidreturnscum[1:21]), aes(x = as.Date(index(yearly[1:21,])), y = actualmidreturnscum[1:21], color = "Actual")) +
geom_line() + 
geom_line(aes(x = as.Date(index(yearly[1:21,])), y = midreturnscum, color = "Predicted"))+ 
labs(x = 'Date',
       y = 'Cumulative Returns',
       color = "Legend",
       title = 'Medium Risk Portfolio Cumulative Returns')


#Backtesting low return low risk portfolio
v1 <- c(0.05751864)
v2 <- c(0.05751864)
v3 <- c(0.05751864)
lowreturns <- rbind(as.matrix(minvarreturns), v1)
lowreturns <- rbind(lowreturns, v2)
lowreturns <- rbind(lowreturns, v3)
rownames(lowreturns)[19:21] = c("2019-12-31", "2020-12-31", "2021-12-31")
lowreturnscum <- cumprod(lowreturns + 1) - 1
actuallowreturns <- as.timeSeries(actualreturns[,3:18] %*% minvarweights)
actuallowreturnscum <- cumprod(actuallowreturns+1)-1
ggplot(data = data.frame(actuallowreturnscum[1:21]), aes(x = as.Date(index(yearly[1:21,])), y = actuallowreturnscum[1:21], color = "Actual")) +
geom_line() + 
geom_line(aes(x = as.Date(index(yearly[1:21,])), y = lowreturnscum, color = "Predicted"))+ 
labs(x = 'Date',
       y = 'Cumulative Returns',
       color = "Legend",
       title = 'Low Risk Portfolio Cumulative Returns')


#Beta OLS, use actual data ??
lm2 = lm(formula = tangencyreturns ~ testfull$mkt)
lm = lm(formula = maxreturnreturns ~ testfull$mkt)
lm3 = lm(formula = minvarreturns ~ testfull$mkt)
summary(lm)
summary(lm2)
summary(lm3)

```