Consider the following risk and return profiles for each hypothetical portfolio and the risk$-$free asset:

$\backslash$table$[[$Portfolio$,\backslash$table$[[$Expected returns$],[($in $\%)]],$Beta$],[$Risk$-$free,$2,0],[$A$,5,0\mathrm{.}6],[$Market$,7,1]]$

a$.$ Based on the risk$-$free rate and the market returns, write the securities market line $($SML$)$ for all securities assuming the simple CAPM holds. Draw the SML for all three portfolios and plot portfolio $A$ on the SML$.$

b$.$ Based on the SML$,$ calculate the expected return for a portfolio B with Beta $=1\mathrm{.}2.$

c$.$ Suppose there exists another portfolio C where Beta is $1\mathrm{.}5$ but the expected return is $15\%.$ Is it possible to observe this portfolio under the simple CAPM? Why or why not?

d$.$ Continue from $c,$ calculate the implied alpha of portfolio $C.$

e$.$ If you could choose from portfolio A and portfolio $C,$ which one would you choose, and why?

$2.$ For the following questions, assume the risk$-$free$]$rate is $4\%$ and the returns to market index is $14\%.$ Also assume that the simple CAPM holds.

a$.$ If you buy a stock today for $$100$ and will pay $$5$ in dividends throughout the year, what is the price you should expect to sell it one year from now? Hint: calculate the expected returns as capital gains yield $+$ dividend yield.

b$.$ Suppose you found a zero$-$coupon bond $($a bond that does not pay any interest$)$ whose beta is equal to zero. What does it mean if the bond has a beta of zero? What is the expected return as suggested by the SML$?$

c$.$ Continuing from $b,$ if you can receive $$104$ on this bond a year from now, what is the price you should pay for this bond today?

d$.$ Continuing from $c,$ what should the price today be if the beta of the bond is actually $1?$ Did you overpay or underpay for the bond?