Consider a scenario where the market risk premium is $8\%$ and the risk$-$free rate is $4\%.$ You believe that the previous month's Unearned Revenue is a good predictor of the current month's stock returns. The following table provides information on Unearned Revenue, Stock Returns, and Market Capitalisation for six stocks over three months:

$\backslash$table$[[,\backslash$table$[[$Unearned Revenue$],[($in $ million$)]],$Stock Return,$\backslash$table$[[$Market Capitalisation$],[($in $ billion$)]]],[,$Mar$-,$Apr$-,,$Mar$-,$Apr$-],[,$Feb$-24,24,24,$Feb$-24,24,24,],[$Stock $1,12\mathrm{.}00,15\mathrm{.}00,14\mathrm{.}00,0\mathrm{.}12,0\mathrm{.}07,-0\mathrm{.}04,7\mathrm{.}00],[$Stock $2,8\mathrm{.}00,10\mathrm{.}00,11\mathrm{.}00,-0\mathrm{.}05,-0\mathrm{.}08,-0\mathrm{.}06,5\mathrm{.}00],[$Stock $3,15\mathrm{.}00,14\mathrm{.}00,16\mathrm{.}00,0\mathrm{.}09,0\mathrm{.}06,0\mathrm{.}03,9\mathrm{.}00],[$Stock $4,22\mathrm{.}00,18\mathrm{.}00,21\mathrm{.}00,0\mathrm{.}04,0\mathrm{.}06,0\mathrm{.}05,12\mathrm{.}00],[$Stock $5,13\mathrm{.}00,9\mathrm{.}00,7\mathrm{.}00,-0\mathrm{.}08,-0\mathrm{.}09,-0\mathrm{.}02,6\mathrm{.}00],[$Stock $6,7\mathrm{.}00,5\mathrm{.}00,8\mathrm{.}00,-0\mathrm{.}06,0\mathrm{.}01,-0\mathrm{.}03,8\mathrm{.}00]]$

$($a$)(10$ marks$)$ Using the information provided in the table, implement a value$-$weighted tercile hedge portfolio. If you invested $$100$ in the value$-$weighted tercile hedge portfolio at the start of March $2024,$ how much would you have $($in dollars$)$ at the end of April $2024?($Please use the market capitalisation provided in the table above for portfolio weights. You are not required to make adjustments to market capitalisation to account for changes due to stock returns.$)$