# Arbitrage in a Single Index Model

Simple question really, but I'm very confused by the starting point. Let's assume that we have a portfolio whose excess returns can be described by the following equation from the single index model:

E(R) = .04 + 1.4*(Risk Premium of the Market)

Obviously, alpha is .04, beta is 1.4. This portfolio is underpriced, as it lies outside the Security Market Line and has a positive alpha.

Now, if I wanted to exploit this and earn that .04 alpha, I understand I'd create some sort of tracking portfolio to mimic the 1.4 beta. This is where I'm confused, I see these questions and they state that we'd borrow .4 at the risk free rate and buy a portfolio with 1.4 beta. This is where all my questions start.

How does this make any sense?? Firstly, what's the base assumption of how much money we have? 1 unit? This means 1 unit lets us buy a portfolio of beta = 1? If we borrow .4 at the risk-free rate, how does that allow us to buy a 1.4 beta portfolio (doesn't this assume price is strictly proportional to beta and NOTHING else?)

Any insight would be very much appreciated.