You have $$100,000$ to invest and decide to invest in a combination of a riskless asset $($f$),$ a

stock index fund $($S$)$ and a long$-$term bond fund $($B$),$ with the following properties:

E$($r$)\backslash$sigma

Riskless Asset $($f$)0\mathrm{.}05(2\%)0\mathrm{.}00$

Stock index fund $($S$)0\mathrm{.}120\mathrm{.}19$

Long$-$term bond fund $($B$)0\mathrm{.}0550\mathrm{.}10$

The correlation of the returns on the long$-$term bond fund and the stock index fund is equal

to $0\mathrm{.}3.$

$10.$ From the portfolios below which one do you think is the closest to the tangency portfolio:

A$.60\%$ on S and $40\%$ on B $($Assume that the $\backslash$sigma of this portfolio is $13\mathrm{.}17\%)$

B$.30\%$ on S and $70\%$ on B $($Assume that the $\backslash$sigma of this portfolio is $10\mathrm{.}27\%)$

C$.90\%$ on S and $10\%$ on B $($Assume that the $\backslash$sigma of this portfolio is $17\mathrm{.}43\%)$

D$.20\%$ on S and $80\%$ on B $($Assume that the $\backslash$sigma of this portfolio is $9\mathrm{.}83\%)$

$11.$ Assume that the tangency portfolio return is equal to $9\mathrm{.}8\%.$ What dollar amounts should be

invested in each of the three asset classes f$,$ S$,$ and B if you would like to achieve $($for the

year $2008)$ standard deviation of $8\mathrm{.}75\%$ with the highest possible expected return?

A$.$ $$44,250$ in S$,$ $$17,250$ in B$,$ and $$38,500$ in f$.$

B$.$ $$37,250$ in S$,$ $$25,250$ in B$,$ and $$37,500$ in f$.$

C$.$ $$41,250$ in S$,$ $$21,250$ in B$,$ and $$37,500$ in f$.$

D$.$ $$34,250$ in S$,$ $$24,250$ in B$,$ and $$41,500$ in f$.$

E$.$ $$31,250$ in S$,$ $$11,250$ in B$,$ and $$57,500$ in f$.$

$12.$ Assume that the tangency portfolio return is equal to $9\mathrm{.}8\%.$ In this market, what is the

diversifiable risk $($in standard deviation units$)$ of a portfolio that has a standard deviation of

$30\%$ and return of $15\%?$ Assume that CAPM holds.

A$.4\%$

B$.7\%$

C$.11\%$

D$.0\%$

E$.14\%$