CS计算机代考程序代写 finance # Lecture 5 Analysis

# Lecture 5 Analysis
# Author: Chris Hansman
# Email: chansman@imperial.ac.uk
# Date : 06/02/21

# Libraries
library(tidyverse)
library(broom)

# Loading Returns
all_returns <- read_csv("returns.csv") #--------------------------------------------------- # CAPM Beta: Two Ways #--------------------------------------------------- # Calculating Beta #The Hard Way #The time series for asset 1 (SPY) returns_SPY <- all_returns %>%
filter(asset==”SPY”)
#Beta for SPY
beta_spy <- lm(returns ~ mkt_returns, data=returns_SPY) summary(beta_spy) #The time series for asset 2 (EFA) returns_efa <- all_returns %>%
filter(asset==”EFA”)
#Beta for EFY
beta_efa <- lm(returns ~ mkt_returns, data=returns_efa) summary(beta_efa) tidy(beta_efa) # And so on... # A trick from the tidyverse: returns_forbeta <- all_returns %>%
nest(-asset)

#Calculating all the betas
beta_assets <-map(returns_forbeta$data, ~ lm(returns ~ mkt_returns, data =.)) beta_assets #Using the Nest Approach to Make Nice Looking Output beta_assets <- all_returns %>%
nest(-asset) %>%
mutate(model = map(data, ~ lm(returns ~ mkt_returns, data = .))) %>%
unnest(model%>% map(tidy)) %>%
filter(term == “mkt_returns”) %>%
select(-term)

#A similar approach to recover Residual SD by Group
residual_sd <- all_returns %>%
nest(-asset) %>%
mutate(fit = map(data, ~ lm(returns ~ mkt_returns, data = .)), results = map(fit, augment)) %>%
unnest(results) %>%
select(asset, returns, mkt_returns, .resid) %>%
group_by(asset)%>%
summarize(sd_r = sd(.resid), sd_m=sd(mkt_returns)) %>%
mutate(sd_r=sd_r*sqrt(59/58))

# Combining the Two
beta_assets <- beta_assets %>%
left_join(residual_sd, by=”asset”)

#—————————————————
# Creating Covariance Matrix
#—————————————————
#Extracting Elements
betas <- as.matrix(beta_assets$estimate) var_r <- diag(as.vector(beta_assets$sd_r)^2) var_m <- as.matrix(beta_assets$sd_m[1])^2 #Variance Covariance Matrix sigma=betas%*%var_m%*%t(betas)+var_r #--------------------------------------------------- # FF Betas: #--------------------------------------------------- ###....Your work here... #--------------------------------------------------- # BARRA Industry Model #--------------------------------------------------- X<-read.table("m-barra-9003.txt", header=TRUE) # Demeaning Data xbar = colMeans(X) X<- X - rep(xbar, rep.int(nrow(X), ncol(X))) #Creating Dummies: Finance, Tech and Other fin = c(rep(1,4),rep(0,6)) tech = c(rep(0,4),rep(1,3),rep(0,3)) oth = c(rep(0,7),rep(1,3)) #The Actual B matrix B=cbind(fin, tech,oth) #Raw Covariance Matrix: cov_return <- var(X) corr_return <- cor(X) #OLS By Hand: F_hat<-solve(t(B)%*%B)%*%t(B)%*%t(X) #Residuals R_hat<-t(X)-B%*%F_hat # Estimating Variance of Residuals Psi <- apply(R_hat,1,var) Psi_inv <- diag(Psi^(-1)) # GLS by Hand F_hat_gls<-solve(t(B)%*%Psi_inv%*%B)%*%t(B)%*%Psi_inv%*%t(X) #Residuals e_hat_gls<-t(X)-B%*%F_hat_gls # Estimating Variance of Residuals Psi_hat <- apply(e_hat_gls,1,var) # Estimating Covariance Matrix cov_barra <- B%*%var(t(F_hat_gls))%*%t(B)+diag(Psi_hat) #Correlation Matrix corr_barra <- cov2cor(cov_barra) # Porfolio Weights omega<-solve(t(B)%*%Psi_inv%*%B)%*%t(B)%*%Psi_inv #--------------------------------------------------# #A bit of Plotting #--------------------------------------------------# #Converting to Tibble for ggplot Factors <- as_tibble(t(F_hat_gls)) %>%
mutate(t=1)%>%
mutate(t=cumsum(t))

# Plotting
ggplot(data = Factors ) +
geom_line(aes(x = t, y = fin))