You are a hedge fund manager and need to create a portfolio that will hopefully outperform the stock market. The expected return and risk of your potential choices are:

Asset	Expected Return (%)	Standard Deviation (%)
S&P 500	8%	16%
Real Estate Fund (REITs)	12%	20%
International Stock Fund	14%	22%

	Variance-Covariance Matrix
	S&P 500	REITs	International Stock Fund
S&P 500	0.0256	0.0128	0.0176
REITs	0.0128	0.0400	0.0088
International Stock Fund	0.0176	0.0088	0.0484

The risk-free rate over this period is 3%. All given rates are annual rates.

You choose to hold 25% of your wealth in the S&P 500, 50% in REITs, and the rest in the international stock fund, but you are having doubts as to whether the CAPM is the right asset pricing model for your portfolio and now thinking about using an alternative model, such as the APT, because your portfolio is exposed to more risk factors than you thought. The betas to the risk factors and expected risk premium are:

Factor	Beta	Expected Risk Premium(%)
CAPM(Market)	?	?
Size	1.5	4.0%
Book-to- Market	0.5	6.5%

1. What is your portfolio's expected returns using APT?

2. What is the portfolio's alpha with respect to APT? [4 marks]

Please provide the detailed process. Thank you