Consider the following data for a one$-$factor economy.$$ Both portfolios are well diversified.$$

Portfolio

E$($r$)$

Beta

A

$12\%$

$1\mathrm{.}2$

B

$8\%$

$0\mathrm{.}6$

$$Suppose the return on the risk$-$free asset is $6\%.$ You try to investigate $(1)$ whether the arbitrage opportunity exists or not and $(2)$ how to execute the arbitrage strategies.$$ Evaluate the following statements.

I. The ratios of risk premium to beta for Portfolio A and Portfolio B are equal, which implies that an arbitrage opportunity exists.

II$.$ To exploit the arbitrage opportunity, you can create a portfolio C with beta equal to $0\mathrm{.}6$ by combining Portfolio A and the risk$-$free asset in equal weights.$$

III.$$Portfolio C has the same beta as Portfolio B and it has higher return.

IV$.$ You should buy Portfolio B and simultaneously sell Portfolio C to make arbitrage profits.