Question $5.$

You estimated the single index $($market$)$ model for stocks $P$ and $Q$ with the following results:

Return $on$ Stock $P$: $R_P=0\mathrm{.}04+0\mathrm{.}6R_M+e_P$

Return $on$ Stock $Q$: $R_Q=0\mathrm{.}04+1\mathrm{.}4R_M+e_Q$

Where $R_M$ is return on the single index and $e_P$ and $e_Q$ are error terms which are not correlated

with anything and have zero means.

In addition, the following statistics are known for $R_M$ and the error terms:

a$.$ Based on the information above, calculate the smallest possible portfolio return

standard deviation one can get by forming a two$-$asset portfolio of Stock P and Q$.$

Hint: Recall the formula for the weight of the minimum variance portfolio.

$(6$ marks$)$

b$.$ Suppose you intend to hold a combined portfolio by allocating $50\%$ in the risk$-$free

asset and the remaining in the minimum variance portfolio $($i$.$e$.,$ the risky portfolio you

constructed in part a$).$ What is the expected return of your combined portfolio?

$(4$ marks$)$

c$.($Unrelated to parts a and b$).$ Consider the stock trading game you participated in earlier

during the semester. Do you think the market was efficient in the stock trading game

you participated in$?$ Why or why not? Explain. $($There is no right or wrong answer for

the question and marks will be awarded for sound reasoning.$)$

$(6$ marks$)$