##extra credit number 2

kat<-read.csv("katherine.csv",main=TRUE)
attach(kat)
large_real <- large[2:1087]-(cpi[2:1087]/cpi[1:1086]-1)
rf_real <- rf[2:1087]-(cpi[2:1087]/cpi[1:1086]-1)
Y<-5000*1.005^(0:480)

simulation <- function(N,s,w){
sampl <- c()
for (j in 1:N) {

R <- sample(480,1086,replace=TRUE)
W <- c(0)
for (i in 1:480) {
r <- R[i]
W[i+1]<-(W[i]+s*Y[i])*(w*large_real[r]+(1-w)*rf_real[r]+1)
}

sampl[j] <- W[481]
}
return(sampl)
}
par(mfrow=c(3,2))
s<-c(.1,.1,.15,.5,.2)
w<-c(.5,1,.5,1,0)
sapply(1:5, function(i) {hist(simulation(1000,s[i],w[i]),main=noquote(paste("(N,s,w) = (",1000,", ",s[i],", ",w[i],")",sep="")),xlab="Terminal Wealth")})

par(mfrow=c(3,2))
sapply(1:5, function(i) {hist(simulation(5000,s[i],w[i]),main=noquote(paste("(N,s,w) = (",5000,", ",s[i],", ",w[i],")",sep="")),xlab="Terminal Wealth")})

par(mfrow=c(3,2))
sapply(1:5, function(i) {hist(simulation(10000,s[i],w[i]),main=noquote(paste("(N,s,w) = (",10000,", ",s[i],", ",w[i],")",sep="")),xlab="Terminal Wealth")})

###6

small_real <- small[2:1087]-(cpi[2:1087]/cpi[1:1086]-1)

9. For the Mt defined in (4.28), prove that E[Mt] = 0. (Hint: Use...