Assume that you are using a two-factor APT model, with factors P and Q, to find the fair (model-) expected return on a well-diversified portfolio Z that has an actual expected return of 20%. Portfolio Zs factor loadings (i.e., Zs betas on each of the two factors) and the factors risk premiums are shown in the table below. Portfolios for factors P and Q are tradable (i.e., you can take long or short positions in them). Assume that the factor loading of P on Q is 0 (and the factor loading of Q on P is also, by extension, 0 too). The risk-free rate is 4%.

Factor	Zs factor loading (Beta)	Factor Risk Premium
P	1.5	12.0%
Q	0.6	-3%

There is an arbitrage opportunity.

1) What is the alpha of portfolio Z?

Create a strategy that takes advantage of the mispricing that exists. Create your strategy your strategy so that it goes either long or short $1 invested in Portfolio Z.

2) Following on from the above: with a strategy that goes either long or short $1 in Portfolio Z, what should the amount invested in Portfolio Z be? (use + for long and - for short)

3) with a strategy that goes either long or short $1 in Portfolio Z, what should the amount invested in the risk-free asset be? (use + for long and - for short)

4) with a strategy that goes either long or short $1 in Portfolio Z, what should the amount invested in Factor Portfolio P be? (use + for long and - for short)

5) with a strategy that goes either long or short $1 in Portfolio Z, what should the amount invested in Factor Portfolio Q be? (use + for long and - for short)

6) What is the arbitrage return (in %) per dollar bought/sold of Portfolio Z.