APT

For this question, you want $to$ round $upto$ two digits for the final answer. $If$ the final answer $isin$

percentage form, round $upto$ the nearest basis point.

Suppose all assets follow a two$-$factor model, where factor $1is$ the market, and factor $2is$ inflation.

Risk premium $on$ the market $isE[R^M]=8\%,$ while risk premium $on$ inflation $isE[R^{}]=-3\%.$

$(a)$ Well$-$diversified portfolio A has betas ${}_{A,M}=0\mathrm{.}6,{}_{A,}=0\mathrm{.}2.$ What $is$ its risk premium, $E[R^A],$

under APT?

$(b)$ Well$-$diversified portfolio $B$ has betas ${}_{B,M}=1,{}_{B,}=0\mathrm{.}2.$ Its expected return $isE[r^B]=8\%.$

What must risk free rate, $r^f,be,$ under APT?

$(c)$ Assuming that risk$-$free rate $is$ given $by$ the value $in$ part $(b).$ Well$-$diversified portfolio $C$ has

betas ${}_{C,M}=0\mathrm{.}5,{}_{C,}=1\mathrm{.}5.$ Its expected return $isE[r^C]=2\%.Is$ asset $C$ mispriced? $Ifso,$

what $is$ its alpha with respect $to$ the two factors?

$(d)$ Suppose $an$ investor believes that CAPM holds, with $R^M$ specified $in$ this question $as$ the market.

$Is$ asset $Bin$ part $(b)$ mispriced $in$ the eyes $of$ this investor? $Ifso,$ what $is$ its alpha?