Consider the table below which lists a set of portfolios with each of their expected return $E(R)$ and

risk measured by the standard deviation:

Assume that the portfolio is composed of $5$ different types of assets, and the risk free rate $(r_f)$ is $1\mathrm{.}5\%.$

Answer the following set of questions.

$($a$)$ Plot the set of portfolios from the table above, and create the efficient frontier. Fully label the

plot, including the global minimum variance portfolio. What do the two end points of the efficient

frontier represent?

$($b$)$ Consider a portfolio that provides an expected return of $13\%$ and risk of $16\mathrm{.}8\%.$ Is this portfolio

efficient? Explain.

$($c$)$ Draw the capital market line and label the optimal portfolio. How do we determine the optimal

portfolio?

$($d$)$ A fund manager is considering a few other securities to add into the construction of portfolios.

Below are the $3$ securities the manager is considering:

Consider the Fama$-$French $3$ factor model. Discuss in details the differences in these securities$,$ and

what the Fama$-$French model suggests regarding each of these securities relative to the optimal

portfolio you found in c$.).$