$6$ A U$.$K$.$ equity composite contains four portfolios, A$,$ B$,$ C and D$.$ Consider the following data for the four portfolios:

$\backslash$table$[[,\backslash$table$[[$Cash Flow$],[$Weighting$],[$Factor$]],$A$,$B$,$C$,$D$],[$Market Value as of May $31,,200\mathrm{.}00,300\mathrm{.}40,312\mathrm{.}0,164\mathrm{.}00],[$External cash flows,$0\mathrm{.}80,20\mathrm{.}00,,,],[$June $6,0\mathrm{.}6667,,-25\mathrm{.}00,,20\mathrm{.}00],[$June $10,0\mathrm{.}20,13\mathrm{.}00,,,-12\mathrm{.}00],[$June $24,,250\mathrm{.}00,220\mathrm{.}50,313\mathrm{.}30,187\mathrm{.}35],[$Market Value as of June $30,,,,,]]$

$($i$)$ Calculate the returns of Portfolio A$,$ Portfolio B$,$ Portfolio C and Portfolio $D$ for the month of June using the Modified Dietz formula.

$($ii$)$ Calculate the June composite return by asset weighting the individual portfolio returns using beginning$-$of$-$period values.