pca2.R

# What is PCA?
# - PCA is a form of multi-dimensional scaling. 
# - It transforms the data into a lower dimensional space while keeping the maxiumum of information. 
# Book: Multi-Dimensional Diversification

# get data https://www.msci.com/end-of-day-data-search

library(tidyverse)
library(tidyquant)
library(readxl)

msci <- read_excel("historyIndex_msci.xls", skip = 6, col_names = T)

msci <- msci %>% mutate(Date = as.Date(Date))

msci <- msci %>% gather(Index, Value, -Date)

msci %>% group_by(Index) %>% filter(!is.na(Value)) %>% summarise(start = min(Date)) %>% 
  arrange(desc(start))

msci <- msci %>% filter(Date >= "1997-01-01")

msci %>% ggplot(aes(x = Date, y = Value, color = Index)) + geom_line() +
  theme_tq()

returns <- msci %>% group_by(Index) %>% tq_transmute(select = Value, 
                                          mutate_fun = periodReturn,
                                          period = "monthly",
                                          type = "arithmetic")

returns %>% filter(Date >= "2018-01-01") %>% ggplot(aes(x = Date, y = monthly.returns, fill = Index)) +
  geom_bar(stat = "identity") +
  facet_wrap(~Index) +
  theme_tq()

correlations <- returns %>% spread(Index, monthly.returns) %>% select(-Date) %>% cor()

returns %>% spread(Index, monthly.returns) %>% select(-Date) %>% chart.Correlation()

## PCA

pca <- returns %>% spread(Index, monthly.returns) %>% select(-Date) %>% as.matrix() %>% 
  prcomp(scale. = T, center = T)

pca %>% summary()

library(factoextra)

pca %>% fviz_eig()
pca %>% fviz_pca_ind()

pca$rotation

eigenvectors <- returns %>% spread(Index, monthly.returns) %>% select(-Date) %>% as.matrix() %>% 
  cor() %>% eigen()

eigenvectors$vectors
pca$sdev^2
eigenvectors$values

t(pca$rotation[,1])%*%pca$rotation[,4]

pca %>% fviz_pca_var(repel = T)

# Varimax rotation

pca$rotation[,1:3] %>% varimax()

returns %>% tq_portfolio(assets_col = Index, weights = rep(1/6,6), returns_col = monthly.returns) %>% 
  tq_performance(Ra =  portfolio.returns, performance_fun = table.AnnualizedReturns) * 100

returns %>% tq_portfolio(assets_col = Index, weights = c(1, 1, 0, 1, 1, 0)/4, returns_col = monthly.returns) %>% 
  tq_performance(Ra =  portfolio.returns, performance_fun = table.AnnualizedReturns) * 100