Project 5

Apple daily prices

getSymbols("AAPL",from = "2008-01-01",to = "2019-12-31")

## 'getSymbols' currently uses auto.assign=TRUE by default, but will
## use auto.assign=FALSE in 0.5-0. You will still be able to use
## 'loadSymbols' to automatically load data. getOption("getSymbols.env")
## and getOption("getSymbols.auto.assign") will still be checked for
## alternate defaults.
## 
## This message is shown once per session and may be disabled by setting 
## options("getSymbols.warning4.0"=FALSE). See ?getSymbols for details.

## [1] "AAPL"

chartSeries(AAPL)

Daily returns

return <- CalculateReturns(AAPL$AAPL.Close)
return <- return[-1]
hist(return)

chart.Histogram(return,
                methods = c('add.density', 'add.normal'),
                colorset = c('blue', 'green', 'red'))

chartSeries(return)

Annualized volatility

chart.RollingPerformance(R = return["2008::2019"],
                         width = 252,
                         FUN = "sd.annualized",
                         scale = 252,
                         main = "Apple's yearly rolling volatility")

sGARCH model with contant mean

s <- ugarchspec(mean.model = list(armaOrder = c(0,0)),
                variance.model = list(model = "sGARCH"),
                distribution.model = 'norm')
m <- ugarchfit(data = return, spec = s)
plot(m, which = 'all')

## 
## please wait...calculating quantiles...

f <- ugarchforecast(fitORspec = m, n.ahead = 20)
plot(fitted(f))

plot(sigma(f))

Application example - portfolio allocation

v <- sqrt(252) * sigma(m)
w <- 0.1/v
plot(merge(v, w), multi.panel = T)

GARCH with sstd

s <- ugarchspec(mean.model = list(armaOrder = c(0,0)),
                variance.model = list(model = "sGARCH"),
                distribution.model = 'sstd')
m <- ugarchfit(data = return, spec = s)
plot(m, which = 'all')

## 
## please wait...calculating quantiles...

GJR-GARCH

s <- ugarchspec(mean.model = list(armaOrder = c(0,0)),
                variance.model = list(model = "gjrGARCH"),
                distribution.model = 'sstd')
m <- ugarchfit(data = return, spec = s)
plot(m, which = 'all')

## 
## please wait...calculating quantiles...

AR(1) GJR-GARCH

s <- ugarchspec(mean.model = list(armaOrder = c(1,0)),
                variance.model = list(model = "gjrGARCH"),
                distribution.model = 'sstd')
m <- ugarchfit(data = return, spec = s)
plot(m, which = 'all')

## 
## please wait...calculating quantiles...

GJR-GARCH in mean

s <- ugarchspec(mean.model = list(armaOrder = c(0,0),
                                  archm =T,
                                  archpow = 2),
                variance.model = list(model = "gjrGARCH"),
                distribution.model = 'sstd')
m <- ugarchfit(data = return, spec = s)
plot(m, which = 'all')

## 
## please wait...calculating quantiles...

Simulation

s <- ugarchspec(mean.model = list(armaOrder = c(0,0)),
                variance.model = list(model = "gjrGARCH"),
                distribution.model = 'sstd')
m <- ugarchfit(data = return, spec = s)
sfinal <- s
setfixed(sfinal) <- as.list(coef(m))

f2008 <- ugarchforecast(data = return["/2008-12"],
                        fitORspec = sfinal,
                        n.ahead = 252)
f2019 <- ugarchforecast(data = return["/2019-12"],
                        fitORspec = sfinal,
                        n.ahead = 252)

Plots

par(mfrow = c(1,1))
plot(sigma(f2008))

plot(sigma(f2019))

sim <- ugarchpath(spec = sfinal,
                  m.sim = 3,
                  n.sim = 1*252,
                  rseed = 123)
plot.zoo(fitted(sim))

plot.zoo(sigma(sim))

p <- 291.52*apply(fitted(sim), 2, 'cumsum') + 291.52
matplot(p, type = "l", lwd = 3)