In excel with formulas!

There are three assets:

A$,$ is the market portfolio

$B,$ is a risky assat

and $C,$ is the risk$-$free asset.

Assume that the CAPM holds. The expected return on the market portfolio is $12\%$ and the standard

deviation is $20\%.$ The return on Asset B has standard deviation $40\%$ and market beta $1.$ The risk$-$free

asset yields $4\%.$

a$)$ Compute the expected return of asset $B$ and its covariances with assets A and $C.$

b$)$ Compute the correlation between assets A and $B.$

c$)$ Consider a portfolio of assets A and $B,$ with weight $w$ on asset A and $(1-w)$ on asset $B.$ Compute the

expected retum and standard deviation of the portfolio in the three cases $w=0,w=\frac{1}{2}$ and $w=1.$

d$)$ Can you rank the three portfolios in the question above? Explain.

e$)$ Consider a portfolio of assets B and C$,$ with equal weight on each asset. Denote this portfolio as

asset D$.$ Compute the expected return and standard deviation of asset D$.$

f$)$ Consider a portfolio of assets A and $C.$ Find the weights such that the standard deviation of this

portfolio is the same as that of asset $D$ in the question above.

What is the expected return of this portfolio?

g$)$ What can you say about the mean$-$variance efficiency of assets A$,$ B and C $($i$.$e$.,$ are they efficient

portfolios$)?$ Explain.

h$)$ Construct an efficient portfolio from assets A$,$ B and C with an expected return of $10\%.$

i$)$ How would your answers to questions $g)$ and h$)$ change if asset $B$ has market beta $0$