Portfolio i$\text{'}$s return is described by the following two$-$factor model:

$r_i-r_f=2\%-0\mathrm{.}8(r_m-r_f)+1\mathrm{.}4(r_e-r_f),$

where $r_m$ is the return on the market index, $r_e$ is the return on a real estate index and $r_f$ is the risk$-$free rate.

Construct a pure arbitrage trade using the market index, a real estate index, a risk$-$free asset $($such as T$-$bills$)$ and Portfolio i$.$ What are your overall weights in each asset?