Examination Question $-$ Sections $7$ and $8$

$($Parts $a,b$ and $c$ are independent. No information from one should be assumed for the

other.$)$

$($a$)$ Suppose there are three types of people in an economy, type A$\text{'}$s$,$ B$\text{'}$s and C$\text{'}$s$.$ There are

also three assets $x,Y$ and $Z.$ Assets $x$ and $Y$ are risky but asset $Z$ is risk free. Type A$\text{'}$s

hold $45$ percent of their portfolios in $x,30$ percent in $Y$ and $25$ percent in $Z.$ Type B$\text{'}$s

hold $30$ percent of their portfolios in $x,20$ percent in $Y$ and $50$ percent in $Z.$ Type C$\text{'}$s

hold $15$ percent in X$,10$ percent in $Y$ and $75$ percent in $Z.$ Are these holdings consistent

with the Capital Asset Pricing Model being satisfied? Explain briefly why or why not.

$($b$)$ Suppose that the Capital Asset Pricing Model holds. The market portfolio has an

expected return of $0\mathrm{.}14$ and a standard deviation of $0\mathrm{.}35.$ The risk free rate is $0\mathrm{.}05.$ How

could you construct a portfolio having an expected return of $0\mathrm{.}20?$ What are the beta and

standard deviation of this portfolio?

$($c$)$ You have discovered three portfolios with the following characteristics.

Plot expected returns against betas for these three portfolios.

$($i$)$ Do they all lie on the security market line and is there an arbitrage opportunity

available?

$($ii$)$ Give a zero$-$investment, zero$-$risk portfolio with positive expected payoff that has

either $+$$$1$ or $-$$$1$ invested in $C.$

$($iii$)$ What is the expected payoff on the portfolio in $($ii$)?$