[SOLVED] R statistic #Practical Assignment #4

#Practical Assignment #4
# This assignment is worth 150 points.

# Useful hints: Utilize book examples and make sure to download and library
# appropriate packages (FRAPO, timeSeries, QRM, fGarch,copula)
# Under each of the items provide the relevant R code and answer the questions.

# 1) Set your working directory to RStudio folder
#that you have created inside the ANLY 515 forlder

# 2) Download the followin data set, and lable it fcur
#This data sets reperesnets daily exchange rates between US dollar
#and 21 foreign currencies. Moreove, it has an Nominal Broad Dollar Index
#that captures the performance of USD against a equal weight basket
#of all the currencies. The exchange rates are expressed as price 1 USD
#in the foreign currency. Make sure to set first column in the date format
#and the remaining columns are in the numerical format.
#Hint: May have to set the format of each column manually.

# 3) Upload all of the following packages:
#FRAPO, timeSeries, QRM, fGarch, copula

# 4) Create a data set fcurcc that is a sub set of
#fcur and consists of all complete cases.

# 5) By using the Time Period column of the fcurcc create
#a date variable and save it as.character.

# 6) Create a new data set fcurccd, that excludes
#the first column of the fcurcc data set(Time Period).
#Should have 22 columns

# 7) By using sapply function modify all exchnge rates including the Broad Index
#to represent the prices of 1 foreign currency in terms of USD.
#Save these exchange rates as fcprice
#Hint: The price of 1 foreign currency in terms of USD, is a reciprocal
#of the price 1 USD in terms of foreign currency.

# 8) By using fcprice and date variables create time series object,
#and label it fcpricets.

# 9) By using first 3250 observations of the fcpricets create two objects
#called: RM and RA. The RM should represent, daily returns
#of Nominal Broad Dollar Index while the RA should represent
#daily returns on each foreign currency.If the percentage change
#is positive it means that the foreign currency is getting stronger,
#and more dollars are need to buy 1 unit of foreign currency.
#Hint: Use returnseries function and specify trim=TRUE
#to get rid of the missing values.

# 10) By using apply function compute the value of Beta for each currency.
# The beta (?? or beta coefficient) of an investment indicates whether
# the investment is more or less volatile than the market as a whole.
# Beta can be found by dividing cov(Foreign, Index)/Var(Index)
# Which currency has the lowest Beta?

# 11) By using apply function compute the value of Tau for each currency.
# Tau is a Kendall rank correlation coefficient, between
# two measured quantities(one of a foreign currency and one of Broad Index).

# 12) By using Kendal rank correlation coeffients Tau, estimate the
# value of Clayton (Archimedean family) copula parameter Theta

# 13) Use Theta to extact lower tail dependence coefficients Lambda.
# Lambda represents the interdependence between each foreign currency
# and Broad Index at the lower tail of the distributions

# 14) Select foreign currencies which Betas are below the median value of Beta,
# and save the results as IdxBeta.
# Which currencies would you select?

# 15) Create a variable WBeta which represents inverse log-weighted
# and scaled portfolio weights of each selected currency.

# 16) Select foreign currencies with Lambdas below
# the median value of Lambda, and save the results as IdxTD
# Which currencies would you select?

# 17) Create a variable WTD which represents inverse log-weighted
# and scaled portfolio weights of each selected currency based on
# low tale dependency selction criteria.

# 18) Create a variable Intersection that represnts in percentage terms
# how similar are the portfolios currency selections based
# on Low Tau vs Low Lambda criteria.

# Out-of-Sample Performance
# 19) By using last 44 observations of the fcpricets create two objects
# called: RMo and RAo. The RMo should represent, daily returns
# of Nominal Broad Dollar Index, while the RAo should represent
# the daily returns on each foreign currency.
# Hint: use returnseries function, express returns as decimals
# and DO NOT trim.

# 20) Set the value of the first observation of the RMo object to 100.

# 21) Generate a new variable called RMEquity that calculates cumulative
# product of the RMo object. By doing so you will find cumulative perfomance
# of the Broad Index.

# 22) Create a new variable called LBEquite, that is subset of the RAo object
# and includes only columns that represent currencies that were selected
# to be a part of the portfolio under the low beta selection criteria.

# 23) Assign the values of the first row of the LBEquite object to be equal to
# WBeta verctor.

# 24) Apply rowSums(apply()) function to calculate weighted cumulative
# product of the LBEquity object. By doing so you will find cumulative
# perfomance of the low beta portfolio over the out-of-sample period.
# Save the results as LBEquity.

# 25) Create a new variable called TDEquite, that is subset of the RAo
# object and includes only columns that represent currencies that were
# selected to be a part of the portfolio under the low tail dependence
# selection criteria.

# 26) Assign the values of the first row of the TDEquity object to be equal to
# WTD verctor.

# 27) Apply rowSums(apply()) function to calculate weighted cumulative product
# of the TDEquity object. By doing so you will find cumulative perfomance
# of the low tail dependency portfolio over the out-of-sample period.
# Save the results as TDEquity.

# 28) Collect results of the out-of-sample performance by binding together
# RMEquity, LBEquity, TDEquity, and compute summary statistics for each
# element. Which investment strategy yeilds the best average equity?

# 29) Create a time series plots of equity curves for the Out-of-Sample Periods.

# 30) Create a Bar plot of relative performance of the Broad Currency Index,
# Low Beta Portfolio, and Low Tail Dependency Portfolio
# Which portfolio would you choose?