please do the following: $($ii$)$ The returns on securities in a market are modelled using a $2-$ factor model: $Ri=ai+bi111+$ bi$2$l$2+$ ci The following data, concerning three securities$,$ are known: Security i Ri bi$1$ bi$2112\%0\mathrm{.}51\mathrm{.}228\%1\mathrm{.}00\mathrm{.}839\%0\mathrm{.}7-1\mathrm{.}0($a$)$ Derive an equation for the arbitrage pricing plane in Ri $-$ bi$1-$ bi$2$ space. $($b$)$ A fourth security exists with R$4=$ a$,$ b$41=$ b$,$ b$42=$ c Explain carefully if and why an opportunity for arbitrage arises. $($c$)$ Construct an arbitrage portfolio from securities $1,2,3$ and $4($stating relevant proportions$)$ to exploit this arbitrage portfolio.$($i$)($a$)$ State the no $-$ arbitrage principle. $($b$)$ Explain why only a few arbitrageurs are required in a market to enforce the no $-$ arbitrage condition. $($ii$)$ The returns on securities in a market are modelled using a $2-$ factor model: $R_i=a_i+b_{i1}{I}_1+b_{i2}{I}_2+c_i$ The following data, concerning three securities$,$ are known: $($a$)$ Derive an equation for the arbitrage pricing plane in $\frac{\frac{?}{?}}{b}ar(R{)}_i-b_{i1}-b_{i2}$ space. $($b$)$ A fourth security exists with $\frac{\frac{?}{?}}{b}ar(R{)}_4=a,b_{41}=b,b_{42}=c$ Explain carefully if and why an opportunity for arbitrage arises.$($ii$)$ The returns on securities in a market are modelled using a $2-$ factor model: $R_i=a_i+b_{i1}{I}_1+b_{i2}{I}_2+c_i$ The following data, concerning three securities$,$ are known: $($a$)$ Derive an equation for the arbitrage pricing plane in $\frac{\frac{?}{?}}{b}ar(R{)}_i-b_{i1}-b_{i2}$ space. $($b$)$ A fourth security exists with $\frac{?}{?}\frac{b}{b}ar(R{)}_4=a,b_{41}=b,b_{42}=c$ Explain carefully if and why an opportunity for arbitrage arises.

$($ii$)$ The returns on securities in a market are modelled using a $2-$factor model:

$R_i=a_i+b_{i1}{I}_1+b_{i2}{I}_2+c_i$