## read in data (which were saved from Excel
## through "save as> Text (tab delimited)"
dj <- read.table(file="DJ.txt", h=T, sep="\t", na="")

## have a look
#fix(dj)

## inspect object structure (to see if everything ok)
str(dj)

## dj*_open are the opening prices for the given indices, where
## * can be "c"=Composite, "i"=Industrial, "t"=Transportation,
## "u"=Utilities
## DGS10 is the return on 10y US Treasury bonds

## model: log(P_t/P_(t-1)) - Rf = beta * [log(M_t/M_(t-1)) - Rf] + u



## make model formula for Industrials
## (notice we take out the first observation from the Treasuries series
## to match its length with the log returns, where the first data point
## is lost in taking first differences)
fm.i <- I(diff(log(dji_open))-DGS10[-1]/100) ~ I(diff(log(djc_open))-DGS10[-1]/100)

## estimate CAPM for Industrials
mod.i <- lm(fm.i, data=dj)

## inspect it
summary(mod.i)

## alternatively: all in one line
## (Notice: no model object remains in the workspace, results ## are only printed out!)
summary(lm(fm.i, data=dj))

## comments: beta is very close to one, alpha not significant at the
## 5 percent level (see Jensen!)

## test hypothesis beta = 1
beta.hat <- coef(mod.i)[2]
se.beta.hat <- sqrt(diag(vcov(mod.i)))[2] # by the functional nature of R,
                                          # this is solved as h(g(f(x)))

## a look at how it worked:
vcov(mod.i)
diag(vcov(mod.i))
sqrt(diag(vcov(mod.i)))
sqrt(diag(vcov(mod.i)))[2]

## another way to retrieve it:
summary(mod.i)$coef[2, 2]

## actual test:
t.stat <- (beta.hat - 1)/se.beta.hat

## get critical value
t.bar.05 <- qt(0.025, df=169)  # notice that we are looking at the left tail!

## compare them:
t.stat < t.bar.05

## or: calculate p.value
pt(t.stat, df=169, lower.tail=TRUE)*2


## Utilities:

#fm.u <- diff(log(dju_open)) ~ diff(log(djc_open))
fm.u <- I(diff(log(dju_open))-DGS10[-1]/100) ~ I(diff(log(djc_open))-DGS10[-1]/100)

## estimate CAPM for Utilities
mod.u <- lm(fm.u, data=dj)

## inspect it
summary(mod.u)

## comments on the different beta? And on the significance of alpha?


## Transportation:

fm.t <- I(diff(log(djt_open))-DGS10[-1]/100) ~ I(diff(log(djc_open))-DGS10[-1]/100)

summary(lm(fm.t, dj))