[SOLVED] CS 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 financestocks <- 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) %>%
mutate(return = log(adjusted/lag(adjusted)) * 252 ) %>%
# select only columns symbol, date and return
select(symbol, date, return) %>%
# remove rows with NaNs
na.omit() %>%
# unstack the stocks as column variables
spread(symbol, return) %>%
# remove columns with too many NaNs
select(where(~ sum(!is.na(.x)) > 700 )) %>%
# remove rows with even one NaNs
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$xmu <- eigenPort$center# the first 5 components explain 50% of Sigmacumsum(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 themfor(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$date, pc_port, ylab = “”, xlab = “”, main = paste0(“PC”, ii), type = “l”)}# after we interpreted the components we are interested on as risk factors,# we can calculate the exposure to each one of them # for any given a portfolio allocation we want to invest into# Es.1: equally weighted portfoliow_eq <- rep(1/ncol(X), ncol(X))# Es.2: min-Var portfolio with target returnlibrary(PortfolioAnalytics)portf <- portfolio.spec(colnames(X))portf <- add.constraint(portf, type=”weight_sum”, min_sum=0.99, max_sum=1.01)portf <- add.constraint(portf, type=”long_only”)portf <- add.constraint(portf, type=”return”,return_target = 0.1)portf <- add.objective(portf, type=”risk”, name = “var”)portf_res <- optimize.portfolio(zoo(X, ret$date), portf, optimize_method = “ROI”,trace = F, message = F,verbose = F)w_minvar <- portf_res$weightsbarplot(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 portfoliost(eigenvectors) %*% cbind(w_eq, w_minvar)