TVP_CAPM.R

########################################
# Time-varying parameter CAPM
########################################

library(ggplot2)
library(BatchGetSymbols)
library(dplyr)
library(tidyr)
library(dlm)

ticker_symbols <- c('AMZN','NFLX','^GSPC')
start_date <- '2015-01-01'

# Getting data from APIs
data = yfR::yf_get(ticker_symbols,
                   first_date = start_date,
                   last_date = Sys.Date(),
                   bench_ticker = "^GSPC",
                   type_return = "log")
# data = BatchGetSymbols(ticker_symbols,
#                        first.date = start_date,
#                        last.date = Sys.Date(),
#                        bench.ticker = "^GSPC",
#                        type.return = "log",
#                        freq.data = "daily",
#                        do.complete.data = TRUE,
#                        do.fill.missing.prices = TRUE)

df.tickers <- data %>%
  filter(volume!=0)

p <- ggplot(df.tickers, aes(x=ref_date, y=price_close, group=ticker)) +
  geom_line(aes(color=ticker))+
  geom_point(aes(color=ticker))+
  theme(legend.position="top")+
  xlab('Data')+ylab('$')
p

r <- ggplot(df.tickers, aes(x=ref_date, y=ret_closing_prices, group=ticker)) +
  geom_line(aes(color=ticker))+
  geom_point(aes(color=ticker))+
  theme(legend.position="top")+
  xlab('Data')+ylab('$')
r

# Static CAPM

ret_amazon <- df.tickers %>%
  dplyr::select(ticker,ret_closing_prices) %>%
  dplyr::filter(ticker == 'AMZN') %>%
  drop_na(ret_closing_prices)

ret_netflix <- df.tickers %>%
  dplyr::select(ticker,ret_closing_prices) %>%
  dplyr::filter(ticker == 'NFLX') %>%
  drop_na(ret_closing_prices)

ret_sp500 <- df.tickers %>%
  dplyr::select(ticker,ret_closing_prices) %>%
  dplyr::filter(ticker == '^GSPC') %>%
  drop_na(ret_closing_prices)

capm_amazon = lm(ret_amazon$ret_closing_prices~ret_sp500$ret_closing_prices)
capm_netflix = lm(ret_netflix$ret_closing_prices~ret_sp500$ret_closing_prices)
summary(capm_amazon)
summary(capm_netflix)

par(mfrow=c(1,1))
rang = range(ret_sp500$ret_closing_prices,ret_amazon$ret_closing_prices)
plot(ret_sp500$ret_closing_prices,ret_amazon$ret_closing_prices,xlab="Market return (S&P500)",ylab="Amazon",xlim=rang,ylim=rang)
abline(capm_amazon$coef,col=2,lwd=3)
title(paste("Amazon = ",round(capm_amazon$coef[1],4)," + ",round(capm_amazon$coef[2],4),"*SP500",sep=""))

par(mfrow=c(1,1))
rang = range(ret_sp500$ret_closing_prices,ret_netflix$ret_closing_prices)
plot(ret_sp500$ret_closing_prices,ret_netflix$ret_closing_prices,xlab="Market return (S&P500)",ylab="Netflix",xlim=rang,ylim=rang)
abline(capm_netflix$coef,col=2,lwd=3)
title(paste("Netflix = ",round(capm_netflix$coef[1],4)," + ",round(capm_netflix$coef[2],4),"*SP500",sep=""))

# set up DLM
dlm2 = function(parm,x.mat){
  parm = exp(parm)
  return( dlmModReg(X=x.mat, dV=parm[1], dW=c(parm[2],parm[3])) )
}
# estimate parameters
fit2 = dlmMLE(y=ret_amazon$ret_closing_prices,parm=c(1,1,1),x.mat=ret_sp500$ret_closing_prices,build=dlm2,hessian=T)

# get estimates
se =  sqrt(exp(fit2$par))
se

# get parameter estimates over time
# these are the smoothed state values
mod2  = dlm2(fit2$par,ret_sp500$ret_closing_prices)
mod2f = dlmFilter(ret_amazon$ret_closing_prices,mod2)
mod2s = dlmSmooth(mod2f)

# plot filtered and smoothed states
date = df.tickers$ref_date[df.tickers$ticker == 'AMZN'][-1]
plot(date,mod2f$m[,1][-1],xlab="day",ylab=expression(alpha[t]),type="l",main="")
lines(date,mod2s$s[,1][-1],col=2)
abline(h=capm_amazon$coef[1],col=3)
abline(h=1,lty=2)

date = df.tickers$ref_date[df.tickers$ticker == 'AMZN'][-1]
plot(date,mod2f$m[,2][-1],xlab="day",ylab=expression(beta[t]),type="l",main="")
lines(date,mod2s$s[,2][-1],col=2)
abline(h=capm_amazon$coef[2],col=3)
abline(h=1,lty=2)