Can someone please let me know: 1. I go long 1mil of the "market" to get beta = 1 and so can expect say 5% equity risk premium (return over riskfree rate). 2. I go long 1mil of ABC which has a beta = 1.4 and short 1mil of XYZ which has beta = 0.4 to get a net beta = 1. This trade has zero-cost. What is my expected return?

Same as the market: 5% equity risk premium (return over riskfree rate). Assuming you can borrow money and stock at the same interest rate, blah blah blah GAT

Shouldn't this be equal to the equity risk premium + (or -) the alpha you generate? By entering into specific trades as opposed to taking broad market exposure, OP assumes he's able to generate alpha (If this is realistic / statistically significant or not is a different question)

Yeah sure. But thread title was 'CAPM' and under the assumptions of CAPM there is no alpha. So my answer is 'Under CAPM if my beta is 1 my expected return is the risk premium'. In fact the trade mentioned (long high beta, short low beta) will probably lose money since the empirical evidence is that low beta outperforms high beta. GAT

so you are saying one can get equal return (say market) by incurring full cost or no-cost. I would like to know what theory (CAPM, APT, blah blah) says about that. Now what if I go long 1mil of ABC (beta = 2) and short 2mil of XYZ (beta = 0.5), netting beta = 1. Still market return (5%) plus short interests? Am trying to understand how theory unifies such countless "equivalent" factor portfolios with differing costs.

http://people.stern.nyu.edu/ashapiro/courses/B01.231103/FFL09.pdf Got this from a 10 second search of the Interwebs, using this catchy thing called a Search Engine. I input the phrase, "CAPM practice problems" and found a whole world of stuff.

It might help if you were a little more precise in your questioning and said why you want the answer to this question. Perhaps you could give a more specific example? Are you interested in factor investing? Or do you just want to know the theory? Theory is theory; it states a bunch of assumptions and if they are true, stuff happens. But the assumptions aren't true in reality. GAT

Am trying to understand how theory unifies such countless "equivalent" factor portfolios with differing costs.

It is a model based on market equilibrium. It is presumed that the supply of financial assets equals demand and the market situation is perfectly competitive and, therefore, the interaction of supply and demand will determine the price of the assets. At higher risk, greater profitability so that if we could measure and grant values at the level of risk assumed, we could know the exact percentage of potential returns of the different assets.