Question $1[5$ points$]$: Suppose that two factors have been identified for the Canadian economy: the growth rate of industrial production, IP$,$ and the inflation rate, IR$.$ IP is expected to be $3\%,$ and IR $5\%.$ A stock with a beta of $1$ on IP and $0\mathrm{.}5$ on IR currently is expected to provide a rate of return of $12\%.$ If industrial production actually grows by $5\%,$ while the inflation rate turns out to be $2\%,$ what is your revised estimate of the expected rate of return on the stock?

Question $2[20$ points$]$: The SML relationship states that the expected risk premium on a security in a onefactor model must be directly proportional to the security$\text{'}$s beta. Suppose that this were not the case. For example, suppase that expected return rises more than proportionately with beta as in the figure below.

a$.$ How could you construct an arbitrage portfolio? $($Hint: Consider combinations of portfolios A and B$,$ and compare the resultant portfolio to $C.$ You should specify the exact weight of the portfolio as a function of ${}_A,{}_B,$ and ${}_C)$

b$.$ Some researchers have examined the relationship between average returns on diversified portfolios and the $$ and ${}^2$ of those portfolios. What should they have discovered about the effect of ${}^2$ on portfolio return? Briefly explain.

Question $3[10$ points$]$: What are the three core assumptions of the Arbitrage Pricing Theory, and what do they suggest about the risk$-$return relationship of well$-$diversified portfolios? $($Please provide a concise response.$)$