Is there a weakness in the analysis of the most efficient risk$-$return portfolios below? Which risk$($s$)$ would you consider? Are you ignoring any risks? How could you correct any shortcomings in your analysis? $2$a$.$ Risk$-$free rate $($rf$)=3\%$

Portfolio $1$: $100\%$ allocation to Acme Company

expected return: E$($rp$)=$w$1$ x E$($r$1)+$ Wrfx Rrf$=$ E$($rp$)=1$x$6\mathrm{.}0\%+0$x $0\mathrm{.}03=6\%$

Portfolio beta:

Beta$=$w$1$x B$1=1$x$0\mathrm{.}85=0\mathrm{.}85$

Portfolio $2$: $100\%$ allocation to Smith Corp

Expected return: $1$ x $8\mathrm{.}5\%+0$ x $3\%=8\mathrm{.}5\%$

Portfolio beta: beta$=1$ x $1\mathrm{.}05=1\mathrm{.}05$

Portfolio $3$: $100\%$ allocation to Jones Inc

Expected return: $1$x$12\mathrm{.}0\%+0$ x $3\%=12\mathrm{.}0\%$

Portfolio beta: beta$=1$x $1\mathrm{.}80=1\mathrm{.}80$

Portfolio $4$: $100\%$ allocation to risk free asset

Expected return: $1$x$3\%=3\mathrm{.}0\%$

Portfolio beta: beta$=0$

$2$b$).$ Portfolio $5$: equal allocation to each stock and risk$-$free asset

$$ x$(6\mathrm{.}0\%+8\mathrm{.}5\%+12\mathrm{.}0\%)+1/4$ x $3\%=26\mathrm{.}5\%/4+0\mathrm{.}75\%=6\mathrm{.}6875\%$

Portfolio beta: beta $1/4$x $(0\mathrm{.}85+1\mathrm{.}05+1\mathrm{.}80)=3\mathrm{.}7/4=0\mathrm{.}925$

$2$c$)$ Portfolio $6$: equal allocation to the three identified stocks

$1/3$ x $(6\mathrm{.}0\%+8\mathrm{.}5\%+12\mathrm{.}0\%)=26\mathrm{.}5\%/3=8\mathrm{.}833\%$

Portfolio beta: beta$=1/3$ x$(0\mathrm{.}85+1\mathrm{.}05+1\mathrm{.}80=3\mathrm{.}7/3=1\mathrm{.}2333$

$2$d$)$ Portfolio $750\%$ invested in Smith Corp and $50\%$ invested in risk free asset

$0\mathrm{.}5$x $8\mathrm{.}5\%+0\mathrm{.}5$ x $3\%=5\mathrm{.}75\%$

portfolio beta$=0\mathrm{.}5$x $1\mathrm{.}05=0\mathrm{.}525$

portfolio $1$: $6\mathrm{.}0\%$ return and $0\mathrm{.}85$ beta

portfolio $2$: $8\mathrm{.}5\%$ return and $1\mathrm{.}05$ beta

portfolio $3$: $12\mathrm{.}0\%$ return and $1\mathrm{.}80$ beta

portfolio $4$: $3\mathrm{.}0\%$ return and $0$ beta

portfolio $5$: $6\mathrm{.}6875\%$ return and $0\mathrm{.}925$ beta

portfolio $68\mathrm{.}8333\%$ return and $1\mathrm{.}233$ beta

portfolio $75\mathrm{.}75\%$ return and $0\mathrm{.}525$ beta