91Ó°ÊÓ

Assume that the value of \(\sigma^{2}\) for the \(A R(2)\) process in Example 10.7 is actually equal to .0002 a) Find \(\operatorname{var}\left[\delta_{(t)}\right]\). b) Find \(\operatorname{cov}\left[\delta_{[t]}, \delta_{[t+2]}\right]\)

It is known that \(\delta_{(l)}\) is normally distributed and follows as AR(1) process. The following values are given: $$\begin{array}{ccc} Z & \text {Actual } \delta_{[z]} & \text {Estimated } \delta_{[z]} \\ \hline 1 & .100 & .104 \\ 2 & .105 & .096 \\ 3 & .095 & .100 \end{array}$$ a) Find \(\delta_{[4]}^{E}\). b) If \(\operatorname{var}\left[\delta_{[t]}\right]=.0001,\) find \(\operatorname{cov}\left[\delta_{[3]}, \delta_{[6]}\right]\).

A business firm decides to use the Capital Asset Pricing Model to evaluate two projects \(A\) and \(B\). Project \(A\) has normal risk with \(\beta=1,\) while Project \(B\) has high risk with \(\beta=2 .\) Each project is expected to return the same dollar amount at the end of one year and nothing thereafter. The risk free rate of interest is \(5 \%\) and the market risk premium is \(7 \% .\) If the two projects are combined into one project. find \(\beta\) for the combined project.

An investment is projected to return \(\$ 110\) at the end of one year and \(\$ 121\) at the end of two years. The risk-free rate of interest is \(5 \%,\) the market risk premium is \(10 \%\) and \(\beta\) for this investment is .5 a) Find the present value of the investment at the risk adjusted rate. b) Find the certainty-equivalent dollar returns at the end of each year.