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you cant. you do need a market portfolio as a reference to compute beta. e.g S&P 500 or another index could be used as a proxy for the market portfolio. using different market portfolios will give different betas for the same stock.

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Beta Question

Question regarding Beta. Beta is defined as the covariance of the asset's returns with the returns on the overall portfolio divided by the portfolio's variance.

So in order to determine Beta, you need to have a portfolio. How does someone just find the Beta of one stock with out an overall portfolio?

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