Choose $3$ domestic indexes from the Data tab on the template. Include one stock and one bond

index. Compute the following for each index and the $3-$month US TBill Index from $2003-2022$:

a$.$ mean, wealth index, annualized return $(4$ each$)$

b$.$ variance, standard deviation, Sharpe ratio, semi$-$deviation $(4$ each$)$

c$.$ correlation matrix $($also not for the $3-$mo Bill $$ correlation of anything with a constant $=$

$0)(12)$

d$.$ Graph the Growth of $$1$ for all four indices from $2003-2022.$ Label axes, legend, last point

$($ending wealth per $$1).$ You must include proper labelling for full credit. $(8)$

$2.$ Choose $1$ stock index and $1$ bond index from your $3$ indexes $($NOTE: Not recommended: S&P$500$

and Russell $2000$ as a portfolio$).$ Enter the expected return, standard deviation, Sharpe,

correlation, and covariance for them in the space provided. Compute the portfolio expected

return, standard deviation, and reward$-$to$-$risk ratio for the listed weights on the template. $(14)$

a$.$ Graph the efficient frontier of the combinations from Part $2.$ Label axes and data points.

You must include proper labelling for full credit. $(8)$

b$.$ Explain why you chose your $2$ indices for the portfolio.

$3.$ For a portfolio containing your two indexes, calculate:

a$.$ Weights, expected return, and standard deviation for the Minimum Variance Portfolio $(4)$

$($NOTE: You may get a negative weight on one of the indexes. This is not realistic, but OK for

our purposes$)$

b$.$ Weights, expected return, standard deviation, and Reward$-$to$-$Risk ratio for the Optimal

Risky Portfolio $(6)($NOTE: You may get a negative weight on one of the indexes. This is not

realistic, but OK for our purposes$)$

c$.$ Explain why $($conceptually$,$ in general$)$ the optimal risky portfolio had the weights it did

$($ie$,$ How do the weights relate to the returns of and correlation between the indices?$).(2)$

d$.$ Standard deviation for a portfolio with a target expected return equal to the expected

return of the $50/50$ weighted portfolio $($assuming the risk$-$free asset is not available$)(6)$

e$.$ Weights and standard deviation for a Complete Portfolio with the same target expected

return as in the Part $3$c $50/50$ portfolio $($assume the risk$-$free asset is available for lending

and borrowing$)(6)$

f$.$ Explain why $($conceptually$,$ in general$)$ the complete portfolio had a different standard

deviation then the $50/50$ portfolio without the risk$-$free asset available. $(2)$

You can either use a formula to get the weights for $3$a$,$ b$,$ and d$,$ or use the Excel Add$-$in Solver to do

optimization $($see the link in Canvas if you don$$t know how to use Solver $$ I will check the setup to see if

you set it up correctly$).$

Historical Index Returns Source: Factset EX$1$ S$18$ T

S&P $500$ Russell $2000$ Russell $2000$ Growth Russell $2000$ Value BC US Long Tsy BC US Inv Grade Corp Barclays Capital US Aggregate

$12/31/200410\mathrm{.}88\%18\mathrm{.}33\%14\mathrm{.}31\%22\mathrm{.}25\%7\mathrm{.}70\%5\mathrm{.}39\%4\mathrm{.}34\%$

$12/31/20054\mathrm{.}91\%4\mathrm{.}55\%4\mathrm{.}15\%4\mathrm{.}71\%6\mathrm{.}50\%1\mathrm{.}68\%2\mathrm{.}43\%$

$12/31/200615\mathrm{.}79\%18\mathrm{.}37\%13\mathrm{.}35\%23\mathrm{.}48\%1\mathrm{.}85\%4\mathrm{.}30\%4\mathrm{.}33\%$

$12/31/20075\mathrm{.}49\%-1\mathrm{.}57\%7\mathrm{.}05\%-9\mathrm{.}78\%9\mathrm{.}81\%4\mathrm{.}56\%6\mathrm{.}97\%$

$12/31/2008-37\mathrm{.}00\%-33\mathrm{.}79\%-38\mathrm{.}54\%-28\mathrm{.}92\%24\mathrm{.}03\%-4\mathrm{.}94\%5\mathrm{.}24\%$

$12/31/200926\mathrm{.}46\%27\mathrm{.}17\%34\mathrm{.}47\%20\mathrm{.}58\%-12\mathrm{.}92\%18\mathrm{.}68\%5\mathrm{.}93\%$

$12/31/201015\mathrm{.}06\%26\mathrm{.}85\%29\mathrm{.}09\%24\mathrm{.}50\%9\mathrm{.}38\%9\mathrm{.}00\%6\mathrm{.}54\%$

$12/31/20112\mathrm{.}11\%-4\mathrm{.}18\%-2\mathrm{.}91\%-5\mathrm{.}50\%29\mathrm{.}93\%8\mathrm{.}15\%7\mathrm{.}84\%$

$12/31/201216\mathrm{.}00\%16\mathrm{.}35\%14\mathrm{.}59\%18\mathrm{.}05\%3\mathrm{.}56\%9\mathrm{.}82\%4\mathrm{.}21\%$

$12/31/201332\mathrm{.}39\%38\mathrm{.}82\%43\mathrm{.}30\%34\mathrm{.}52\%-12\mathrm{.}66\%-1\mathrm{.}53\%-2\mathrm{.}02\%$

$12/31/201413\mathrm{.}69\%4\mathrm{.}89\%5\mathrm{.}60\%4\mathrm{.}22\%25\mathrm{.}07\%7\mathrm{.}46\%5\mathrm{.}97\%$

$12/31/20151\mathrm{.}38\%-4\mathrm{.}41\%-1\mathrm{.}38\%-7\mathrm{.}47\%-1\mathrm{.}21\%-0\mathrm{.}68\%0\mathrm{.}55\%$

$12/31/201611\mathrm{.}96\%21\mathrm{.}31\%11\mathrm{.}32\%31\mathrm{.}74\%1\mathrm{.}33\%6\mathrm{.}11\%2\mathrm{.}65\%$

$12/31/201721\mathrm{.}83\%14\mathrm{.}65\%22\mathrm{.}17\%7\mathrm{.}84\%8\mathrm{.}53\%6\mathrm{.}42\%3\mathrm{.}54\%$

$12/31/2018-4\mathrm{.}38\%-11\mathrm{.}01\%-9\mathrm{.}31\%-12\mathrm{.}86\%-1\mathrm{.}84\%-2\mathrm{.}51\%0\mathrm{.}01\%$

$12/31/201931\mathrm{.}49\%25\mathrm{.}52\%28\mathrm{.}48\%22\mathrm{.}39\%14\mathrm{.}83\%14\mathrm{.}54\%8\mathrm{.}72\%$

$12/31/202018\mathrm{.}40\%19\mathrm{.}96\%34\mathrm{.}63\%4\mathrm{.}63\%17\mathrm{.}70\%9\mathrm{.}89\%7\mathrm{.}51\%$

$12/31/202128\mathrm{.}71\%14\mathrm{.}82\%2\mathrm{.}83\%28\mathrm{.}27\%-6\mathrm{.}42\%-1\mathrm{.}04\%-3\mathrm{.}39\%$

$12/31/2022-18\mathrm{.}11\%-20\mathrm{.}45\%-26\mathrm{.}35\%-14\mathrm{.}48\%-29\mathrm{.}32\%-15\mathrm{.}76\%-12\mathrm{.}87\%$

$12/31/202326\mathrm{.}29\%16\mathrm{.}93\%18\mathrm{.}66\%14\mathrm{.}65\%2\mathrm{.}65\%8\mathrm{.}52\%5\mathrm{.}52\%$