The following information is provided for a stock market in which asset returns respond to

two factors:

Notation: $b_{j1}$ and $b_{j2}$ for $j=A,B$ denote the responses of the rates of return on assets $A$

and $B$ to the factors $1$ and $2$;${}_j$ is the expected rate of return on each of the assets.

a$.$ If the APT holds in this market, calculate the risk premia $$ corresponding to the two

factors.

b$.$ Construct a portfolio which gives unit weight to the first factor and zero weight to the

second factor. Hence provide an interpretation for the risk premia in the APT.

Hint: If a portfolio $P$ has weights equal to ${}_A$ and ${}_B$ in assets A and $B,$ respectively,

then the proportion in the risk$-$free asset ${}_f$ is $(1-{}_A-{}_B).$

Also, the portfolio beta to the factors is given by:

$b_{p1}={}_A{b}_{A1}+{}_B{b}_{B1}$

$b_{p2}={}_A{b}_{A2}+{}_B{b}_{B2}$

c$.$ Assume that there is another asset, Asset $C,$ that is also traded in this market and

yields an average return of $12\%$ with $b_{c1}=1\mathrm{.}0$ and $b_{c2}=0\mathrm{.}5.$ What inference would

you draw about the asset market from this information?