Fama decomposition

(a) In Proposition 11.10, take $\operatorname{Var}(q)=1$, $\operatorname{Var}(p)=4$ and $\operatorname{Cov}(p,q)=-1.5$, in squared percent per month. Compute $b$. (b) Show that if $p$ and $q$ are uncorrelated, then $b=\operatorname{Var}(q)/(\operatorname{Var}(q)+\operatorname{Var}(p))\in[0,1]$, so a negative $b$ is impossible. (c) With $a=0$ and $b$ from (a), compute the expected carry return for a rate differential of 2% a year. (d) Why does a positive expected carry return not contradict market efficiency?