Assignment $5$: Based on Index Fund Example

ABC has a substantial number of clients who wish to own a mutual fund portfolio that closely matches the performance of the S&P $500$ stock index. A manager at ABC has selected five mutual funds $($shown in the table below$)$ that will be considered for inclusion in the portfolio. The manager must decide what percentage of the portfolio should be invested in each mutual fund. Based on the given information, please create your spreadsheet model and find the optimal portfolio. Please submit your business model and solution.

Table: Five Mutual Funds and Annual Returns

$\backslash$table$[[$Mutual Fund,Year $1,$Year $2,$Year $3,$Year $4],[$International Stock,$$15\mathrm{.}64,$$$17\mathrm{.}62,$$$5\mathrm{.}80,$$$3\mathrm{.}13],[$Large$-$Cap Blend,$$15\mathrm{.}31,$$$18\mathrm{.}77,-$$$5\mathrm{.}06,$$$1\mathrm{.}75],[$Mid$-$Cap Blend,$$18\mathrm{.}74,$$$18\mathrm{.}43,$$$6\mathrm{.}28,-$$$1\mathrm{.}04],[$Small$-$Cap Blend,$$14\mathrm{.}19,$$$12\mathrm{.}37,$$$1\mathrm{.}92,$$$7\mathrm{.}32],[$Intermediate Bond,$$7\mathrm{.}88,$$$9\mathrm{.}45,-$$$1\mathrm{.}56,$$$3\mathrm{.}31],[$S&P $500,$$$13\mathrm{.}00,$$$12\mathrm{.}00,$$$7\mathrm{.}00,$$$1\mathrm{.}50]]$