CS计算机代考程序代写 finance # Tutorial Week 7

# Tutorial Week 7
# Davide Benedetti
# 27/02/2021

library(tidyverse)
library(tidyquant)

tickers <- read.csv("AMS Yahoo Ticker Symbols 2017.csv") # load the list of tickers from Yahoo finance stocks <- tq_get(tickers\$Ticker, from = "2018-01-01") ## alternatively you can run # load("stocks.RData") ret <- stocks %>%
# remove stocks “GROHA.AS” and “HUNDP.AS”
filter(symbol != “GROHA.AS” & symbol != “HUNDP.AS”) %>%
# caluclate log annualized returns
group_by(symbol) %>%
# select only columns ‘symbol’, ‘date’ and ‘return’
select(symbol, date, return) %>%
# remove rows with NaN’s
na.omit() %>%
# unstack the stocks as column variables
# remove columns with too many NaN’s
select(where(~ sum(!is.na(.x)) > 700 )) %>%
# remove rows with even one NaN’s
na.omit()

# check the data
library(stargazer)
ret %>% as.data.frame() %>%
stargazer(type = “text”)

# There are a lot of stocks which are not very liquid,
# and their returns are zero for long periods as they are
# not often traded, so their price does not change

# We are going to remove stocks which are not traded at least 50% of the times
X <- data.frame(ret[,-1]) X <- X[, colSums(X == 0) < 300] %>%
as.matrix()

# now we can apply PCA on X
eigenPort <- prcomp(X, center = T, scale = F) eigenvalues <- as.matrix(eigenPort\$sdev^2) eigenvectors <- as.matrix(eigenPort\$rotation) princomp <- eigenPort\$x mu <- eigenPort\$center # the first 5 components explain 50% of Sigma cumsum(eigenvalues) / sum(eigenvalues) * 100 # eigenvectors can be interpreted as portfolio weights # applying them to the stocks will generate new portfolios # that are incorrelated with one another # These portfolios can also be intepreted as latent (unobservable) risk factors # and we can plot their weights (eigenvectors) to interpret them for(ii in 1:5){ barplot(eigenvectors[,ii], ylab = "", xlab = "", main = paste0("PC", ii)) } # PC1 can be intepreted as the market portfolio # PC2 is a portfolio that goes long on stock "ESP.AS" # we can find similar interpretation for the others # and we can use more components # we can also plot the PC portfolios (latent risk factors) for(ii in 1:5){ pc_port <- X %*% eigenvectors[,ii]/sum(eigenvectors[,ii]) plot(ret\$date, pc_port, ylab = "", xlab = "", main = paste0("PC", ii), type = "l") } # after we interpreted the components we are interested on as risk factors, # we can calculate the exposure to each one of them # for any given a portfolio allocation we want to invest into # Es.1: equally weighted portfolio w_eq <- rep(1/ncol(X), ncol(X)) # Es.2: min-Var portfolio with target return library(PortfolioAnalytics) portf <- portfolio.spec(colnames(X)) portf <- add.constraint(portf, type="weight_sum", min_sum=0.99, max_sum=1.01) portf <- add.constraint(portf, type="long_only") portf <- add.constraint(portf, type="return", return_target = 0.1) portf <- add.objective(portf, type="risk", name = "var") portf_res <- optimize.portfolio(zoo(X, ret\$date), portf, optimize_method = "ROI", trace = F, message = F, verbose = F) w_minvar <- portf_res\$weights barplot(w_eq, ylab = "", xlab = "", main = "Weights Equally-Weighted Portfolio") barplot(w_minvar, ylab = "", xlab = "", main = "Weights Min-Var Portfolio") # exposure to PCA risk factors for the two portfolios t(eigenvectors) %*% cbind(w_eq, w_minvar)