#---------------------------#
#   Loesungen UeBlatt 11    #
#---------------------------#


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#  Aufgabe 1  #
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# we can use the code from week11.txt:

ExpWeightedVol = function( d , ret )
{
  n = length(ret)
  vol = rep(0,n)
  volsq = rep(0,n)     # vol^2
  vol0sq = sd(ret)^2   # we put start vol to bsvol
  w = 1 - 1/d

  # the first step is special:
  volsq[1] = w * vol0sq + (1-w)*ret[1]^2
  for(k in 2:n)
  {
    volsq[k] = w * volsq[k-1] + (1-w)*ret[k]^2 
  }
  vol = sqrt( volsq )
  return(vol)
}

EquallyWeightedVol = function( d , ret )
{
  n = length(ret)
  vol = rep(0,n)

  # we use vectorized calculation logic:
  cumsum_retsquared = cumsum(ret^2)
  
  # remove last d elements:
  cumsum_retsquared_shifted = cumsum_retsquared[-((n-d+1):n)]

  # fill in d zeros at the first d places:
  cumsum_retsquared_shifted = c(rep(0,d),cumsum_retsquared_shifted)

  sum_dretsquared = cumsum_retsquared - cumsum_retsquared_shifted
  
  # now we have to divide this sum by d, but the first d elements 
  # are special:
  divisor1 = 1:d
  divisor2 = rep(d,n-d)
  divisor = c(divisor1,divisor2)

  sum_dretsquared = sum_dretsquared/divisor
  
  # equally weighted vol:
  vol = sqrt( sum_dretsquared )
  return(vol)
}


spx = read.table("C:/Users/detlef/OneDrive/hochschule/Vorlesungen/WS2223/Datenanalyse-mit-R/SPX.txt",header=TRUE,sep=";")
spx = na.omit(spx)
S = spx[,2]
n=length(S)
ret = rep(0,n)       
for(i in 2:n)
{
  ret[i] = (S[i]-S[i-1])/S[i-1]
}
plot(ret,type="l",main="SPX-returns")

# since the time series is quite long, we compare the following
# values of d: d = 120, d = 250 and d = 500

d = 120
ewvol = ExpWeightedVol( d , ret )
vol = EquallyWeightedVol( d , ret )
info = "exp weighted (in red) vs. equally weighted vol for SPX, d = " 
info = paste(info,d)
plot(vol,type="l",main=info,ylim=c(0,4/100))
lines(ewvol,col="red")

d = 250
ewvol = ExpWeightedVol( d , ret )
vol = EquallyWeightedVol( d , ret )
info = "exp weighted (in red) vs. equally weighted vol for SPX, d = " 
info = paste(info,d)
plot(vol,type="l",main=info,ylim=c(0,4/100))
lines(ewvol,col="red")

d = 500
ewvol = ExpWeightedVol( d , ret )
vol = EquallyWeightedVol( d , ret )
info = "exp weighted (in red) vs. equally weighted vol for SPX, d = " 
info = paste(info,d)
plot(vol,type="l",main=info,ylim=c(0,4/100))
lines(ewvol,col="red")


# same for GE-series:
ge = read.table("C:/Users/detlef/OneDrive/hochschule/Vorlesungen/WS2223/Datenanalyse-mit-R/GE.txt",header=TRUE,sep=";")
ge = na.omit(ge)
S = ge[,2]
n=length(S)
ret = rep(0,n)       
for(i in 2:n)
{
  ret[i] = (S[i]-S[i-1])/S[i-1]
}
plot(ret,type="l",main="GE-returns")

# since the time series is quite long, we compare the following
# values of d: d = 120, d = 250 and d = 500

d = 120
ewvol = ExpWeightedVol( d , ret )
vol = EquallyWeightedVol( d , ret )
info = "exp weighted (in red) vs. equally weighted vol for GE, d = " 
info = paste(info,d)
plot(vol,type="l",main=info,ylim=c(0,6/100))
lines(ewvol,col="red")

d = 250
ewvol = ExpWeightedVol( d , ret )
vol = EquallyWeightedVol( d , ret )
info = "exp weighted (in red) vs. equally weighted vol for GE, d = " 
info = paste(info,d)
plot(vol,type="l",main=info,ylim=c(0,6/100))
lines(ewvol,col="red")

d = 500
ewvol = ExpWeightedVol( d , ret )
vol = EquallyWeightedVol( d , ret )
info = "exp weighted (in red) vs. equally weighted vol for GE, d = " 
info = paste(info,d)
plot(vol,type="l",main=info,ylim=c(0,6/100))
lines(ewvol,col="red")