$($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:

Ri $=$ ai $+$ bi$1$I$1+$ bi$2$I$2+$ ci

The following data, concerning three securities$,$ are known:

Security i Ri bi$1$ bi$2$

$112\%0\mathrm{.}51\mathrm{.}2$

$28\%1\mathrm{.}00\mathrm{.}8$

$39\%0\mathrm{.}7-1\mathrm{.}0$

$($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 $\frac{?}{\text{b}\text{a}\text{r}}(R{)}_i-b_{i1}-b_{i2}$ space.

$($b$)$ A fourth security exists with

$\frac{?}{\text{b}\text{a}\text{r}}(R{)}_4=a,b_{41}=b,b_{42}=c$

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.