Assignment3-SukhmanKaur-1.docx

Assignment 3
Sukhman Kaur
2021-06-09
“Part A – Risks
1. Using two securities from your portfolio (from different sectors)”
## [1] “Part A – Risksn1. Using two securities from your portfolio (from different sectors)”
“a) Construct a variance-covariance matrix:”
## [1] “a) Construct a variance-covariance matrix:”
r = getOption(“repos”)
r[“CRAN”] = “http://cran.us.r-project.org”

options(repos = r)
library(quantmod)
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: ‘zoo’
## The following objects are masked from ‘package:base’:
##
## as.Date, as.Date.numeric
## Loading required package: TTR
## Registered S3 method overwritten by ‘quantmod’:
## method from
## as.zoo.data.frame zoo
library(xts)

getwd() # verify your working directory
## [1] “/Users/sukhmankaur/Downloads”
# Importing Amazon data from Yahoo Finance

data.AMZN.2 = read.csv(“~/Downloads/AMZN-2.csv”, stringsAsFactors=TRUE)
# Check data
head(data.AMZN.2)
## Date Open High Low Close Adj.Close Volume
## 1 2010-06-09 120.31 121.47 117.36 117.91 117.91 7369200
## 2 2010-06-10 120.00 123.50 119.20 123.21 123.21 6061800
## 3 2010-06-11 121.39 123.53 120.29 123.03 123.03 4204600
## 4 2010-06-14 124.24 125.70 123.50 123.83 123.83 3923000
## 5 2010-06-15 123.20 126.92 122.50 126.84 126.84 4541000
## 6 2010-06-16 125.39 127.98 125.36 126.90 126.90 3964300
# Variable Date
date = as.Date(data.AMZN.2$Date,format=”%M-%D-%Y”)
# Replace date variable with the date
data.AMZN.2 = cbind(date,data.AMZN.2[,-1])
# Sort data in chronological
data.AMZN.2 = data.AMZN.2[ (data.AMZN.2$date),]
class(data.AMZN.2)
## [1] “data.frame”
# Renaming the columns
names(data.AMZN.2) = paste(c(“AMZN.2.Open”, “AMZN.2.High”, “AMZN.2.Low”,
“AMZN.2.Close”, “AMZN.2.Adjusted”, “AMZN.2.Volume”))

data.AMZN.2[c(2:5,nrow(data.AMZN.2)),]
## AMZN.2.Open AMZN.2.High AMZN.2.Low AMZN.2.Close AMZN.2.Adjusted
## 2 120.00 123.50 119.20 123.21
## 3 121.39 123.53 120.29 123.03
## 4 124.24 125.70 123.50 123.83
## 5 123.20 126.92 122.50 126.84
## 2517 2500.20 2530.00 2487.34 2524.06
## AMZN.2.Volume NA
## 2 123.21 6061800
## 3 123.03 4204600
## 4 123.83 3923000
## 5 126.84 4541000
## 2517 2524.06 3970700
“Since we want forth-year data, in my case it’s the year 2009.”
## [1] “Since we want forth-year data, in my case it’s the year 2009.”
BTC.USD <- read.csv("~/Downloads/BTC-USD.csv") # create variable date date = as.Date(BTC.USD$Date,format="%Y-%m-%d") # Replace date variable with the date data.BTC.USD = cbind(date,BTC.USD[,-1]) # Sort data in chronological data.BTC.USD = data.BTC.USD[ (data.BTC.USD$date),] class(data.BTC.USD) ## [1] "data.frame" # Renaming the columns names(data.BTC.USD) <- paste(c("BTC.USD.Open", "BTC.USD.High", "BTC.USD.Low", "BTC.USD.Close", "BTC.USD.Adjusted", "BTC.USD.Volume")) data.BTC.USD[c(1:5,nrow(data.BTC.USD)),] ## BTC.USD.Open BTC.USD.High BTC.USD.Low BTC.USD.Close BTC.USD.Adjusted ## 1 2015-06-09 228.537994 230.953995 227.929001 229.048004 ## 2 2015-06-10 228.994995 229.781998 228.009995 228.802994 ## 3 2015-06-11 228.854996 230.287003 228.766998 229.705002 ## 4 2015-06-12 229.705002 231.057007 229.313004 229.981995 ## 5 2015-06-13 229.919998 232.651993 229.210007 232.401993 ## 1828 2020-06-09 9774.360352 9836.369141 9664.719727 9795.700195 ## BTC.USD.Volume NA ## 1 229.048004 28353100 ## 2 228.802994 15904800 ## 3 229.705002 14416000 ## 4 229.981995 14017700 ## 5 232.401993 13305300 ## 1828 9795.700195 23717842783 # Using the subset command for getting data. test.BTC.USD <-subset(BTC.USD, + index(BTC.USD) >= “2015-07-01” &+ index(BTC.USD) <= "2016-07-31") test.BTC.USD[c(1:3,nrow(test.BTC.USD))] ## [1] Date Open High ## <0 rows> (or 0-length row.names)
##BTC.USD.ret = Delt(BTC.USD$BTC.USD.Adjusted)
##BTC.USD.ret[c(1:3,nrow(BTC.USD.ret)),]

“Combine the two return series”
## [1] “Combine the two return series”
##”Create a vector of weights AMZN: 25%

##WGT.2asset <- c(0.25,0.75) ##WGT.2asset <- matrix(WGT.2asset,1) ##WGT.2asset “Part B – Suitable distributions for returns” “1. Fit the data using GHD, HYP and NIG” #plot the density function - BITCOIN library(fBasics) ## Loading required package: timeDate ## Loading required package: timeSeries ## ## Attaching package: 'timeSeries' ## The following object is masked from 'package:zoo': ## ## time<- ## ## Attaching package: 'fBasics' ## The following object is masked from 'package:TTR': ## ## volatility library(timeSeries) ##Port.ret<-0.25*AMZN.2.ret +0.75*BTC.USD.ret ##Port.ret<-Port.ret[-1,] ##ef = density(Port.ret, na.rm = TRUE) ##par(mfrow = c(1,1)) ##plot(ef) #Fit the Generalized Hyperbolic Distribution library(ghyp) ## Loading required package: numDeriv ## Loading required package: MASS #Fit the Hyperbolic Distribution hypfit<- fit.hypuv(Port.ret, symmetric = FALSE, control = list(maxit = 1000), na.rm = TRUE) #Fit the Normal Inverse Gaussian Distribution nigfit <- fit.NIGuv(Port.ret, symmetric =FALSE, control = list(maxit = 1000), na.rm= TRUE) “2. Plot the combined density functions” ghddens <- dghyp(efx, hypfit) nigdens <- dghyp(efx, mean = mean(Port.ret, na.rm=TRUE), sd = sd(c(Port.ret[, 1]), na.rm=TRUE)) col.def <- c(“black”, “red”, “blue”, “green”, “orange”) plot(ef, xlab = "“, ylab = expression(f(x)), ylim = c(0, 30)) lines(ef$x, ghddens, col = "red") lines(ef$x, hypdens, col =”blue“) lines(ef$x, nigdens, col = "green") lines(ef$x, nordens, col =”orange“) legend(”topleft“, legend = c(”empirical“,”GHD“,”HYP“,”NIG“,”NORM"), col = col.def, lty = 1) “3. Create a Q-Q plot” qqghyp(ghdfit, line = TRUE, ghyp.col = “red”, plot.legend = FALSE, gaussian = FALSE, main = "“, cex = 0.8) qqghyp(hypfit, add = TRUE, ghyp.pch = 2, ghyp.col =”blue“, gaussian = FALSE, line = FALSE, cex = 0.8) qqghyp(nigfit, add = TRUE, ghyp.pch = 3, ghyp.col =”green“, gaussian = FALSE, line = FALSE, cex = 0.8) legend(”topleft“, legend = c(”GHD“,”HYP“,”NIG"), col = col.def[-c(1,5)], pch = 1:3) “4. Make a model recommendation using lik.ratio.test” AIC <- stepAIC.ghyp(Port.ret,control = list(maxit = 1000)) head(AIC$fit.table) “Use the function “lik.ratio.test” to perform a likelihood-ratio test on fitted generalized hyperbolic distribution objects of class mle.ghyp." “The likelihood-ratio test can be used to check whether a special case of the generalized hyperbolic distribution is the “true” underlying distribution." “statistic: the value of the L-statistic.” “p.value: the p-value for the test (the p-value is less than 0.05, then there is evidence against the null hypothesis)” “df: the degrees of freedom for the L-statistic” “H0: a boolean stating whether the null hypothesis is TRUE or FALSE (if TRUE there is no relationship between the data sets)” LRghdnig <- lik.ratio.test(ghdfit, nigfit) LRghdnig LRghdhyp <- lik.ratio.test(ghdfit, hypfit) LRghdhyp “5. Calculate and plot the VaR (using all models)” p <- seq(0.001, 0.05, 0.001) ghd.VaR <- abs(qghyp(p,ghdfit)) hyp.VaR <- abs(qghyp(p, hypfit)) nig.VaR <- abs(qghyp(p, nigfit)) nor.VaR <- abs(qnorm(p, mean = mean(Port.ret, na.rm=TRUE), sd = sd(c(Port.ret[, 1]), na.rm = TRUE))) emp.VaR <- abs(quantile(x = Port.ret,probs= p, na.rm = TRUE)) plot(emp.VaR, type = “l”, xlab = "“, ylab =”VaR“, axes = FALSE, ylim = range(c(hyp.VaR, nig.VaR, ghd.VaR, nor.VaR, emp.VaR))) box() axis(1, at = seq(along = p), labels = names(emp.VaR), tick = FALSE) axis(2, at = pretty(range(emp.VaR, ghd.VaR, hyp.VaR, nig.VaR, nor.VaR))) lines(seq(along = p), ghd.VaR, col =”red“) lines(seq(along = p), hyp.VaR, col =”blue“) lines(seq(along = p), nig.VaR, col =”green“) lines(seq(along = p), nor.VaR, col =”orange“) legend(”topright“, legend = c(”Empirical“,”GHD“,”HYP“,”NIG“,”Normal"), col = col.def, lty = 1) “6. Calculate and plot the ES (using all models)” ghd.ES <- abs(ESghyp(p,ghdfit)) hyp.ES <- abs(ESghyp(p, hypfit)) nig.ES <- abs(ESghyp(p, nigfit)) nor.ES <- abs(mean(Port.ret, na.rm=TRUE) - sd(c(Port.ret[, 1]), na.rm = TRUE) dnorm(qnorm(1 - p)) / p) obs.p <- ceiling(plength(Port.ret)) emp.ES <- sapply(obs.p, function(x) abs(mean(sort(c(Port.ret)) [1:x]))) plot(emp.ES, type = “l”, xlab = "“, ylab =”ES“, axes = FALSE, ylim = range(c(hyp.ES, nig.ES, ghd.ES, nor.ES, emp.ES), na.rm = TRUE)) box() axis(1, at = 1:length(p), labels = names(emp.VaR), tick = FALSE) axis(2, at = pretty(range(emp.ES, ghd.ES, hyp.ES, nig.ES, nor.ES))) lines(1:length(p), ghd.ES, col =”red“) lines(1:length(p), hyp.ES, col =”blue“) lines(1:length(p), nig.ES, col =”green“) lines(1:length(p), nor.ES, col =”orange“) legend(”topright“, legend = c(”Empirical“,”GHD“,”HYP“,”NIG“,”Normal"), col = col.def, lty = 1,cex = 0.7)