Suppose we regress firms on the market like this: r$\_$i$-$rf $=$ alpha$\_$i $+$ beta$\_$i $*($r$\_$m$-$rf$)+$ epsilon$\_$i$.$

Suppose the epsilons are uncorrelated.

Now we form a large diversified portfolio with alpha$\_$p $=0\mathrm{.}05$ and beta$\_$p $=0\mathrm{.}6.$

To arbitrage this, we either long or short $$200$ of the portfolio $($you have to decided if long or short$).$

As part of this arbitrage strategy, how much do we long$/$short of the market portfolio?