Question $1.$

Suppose that a two$-$factor model, where the factors are the stock market $($Factor $1)$ and the

growth rate of industrial production $($Factor $2),$ correctly describes the return generating

processes of all assets and the corresponding two$-$factor APT correctly prices three well$-$

diversified portfolios, $A,B,$ and $C.$

a$.$ What are i$)$ the risk premiums of the two factors and ii$)$ the risk$-$free rate?

$(4$ marks$)$

b$.$ Another well$-$diversified portfolio $D$ has sensitivities $0$ and $1$ to factor $1$ and

factor $2,$ respectively. What is the APT$-$consistent expected return on Portfolio

D$?$

$(4$ marks$)$

c$.$ Suppose that Portfolio D$\text{'}$s expected return is $8\%.$ Given your answers above,

design an arbitrage strategy involving Portfolios A$,$ B$,$ C$,$ and D$.($Hint: an

arbitrage strategy requires no initial investment, has no risk and yet generates a

positive return.$)$

$(4$ marks$)$

$($Total for Question: $12$ marks$)$