Equitizing a long short portfolio

I’m confused about equitizing long short portfolio. My question: if you short an overvalued stock and long a similar undervalued stock in the same industry to get beta=0, wouldn’t you exhaust your cash proceed at this point? Where do you have the money to place in treasury to earn the interest? I understand you can get into an equity future without putting down money, but I’m confused as where the money is from to put into treasury

Maybe i’m misunderstanding your question, but I believe the problem assumes you have some money in your account at the begining:

IE You have $100 in cash which you use to buy $100 of securities, so you then have $0 in cash. You then short $100 dollars of securities to get a long/short portfolio of 100/100 and $100 in cash. The $100 from your short can be used for treasuries. (Very simplified exampe which doesn’t include maintaining margin requirements, etc.)

Ok got it. And for long-short only, the strategy is to short a stock and use the proceed to buy another stuck with the same sensitivity in the same industry right? (Assuming you have no cash in your account at the beginning?)

you have the portfolio - since you have something that is being shorted. (That cannot come out of thin air).

so there is some cash somewhere with you ( a notional amount of portfolio value).