# What does leverage have to do with beta? [closed]

Given a portfolio $P$ with return $R$ and market-beta $\beta$, we have

$$E (R - R_f) = \beta (E R_M - R_f)$$

Now, what does leveraging $P$ have to do with $\beta$? How it is affected if we leverage the portfolio up or down?

For example, say I want a portfolio of beta 1. Then I divide through by $\beta$ to get $$E(R - R_f)/\beta$$

... but what exactly is this? How do I obtain a portfolio using leverage that gives a beta of one?

• You leverage by borrowing or lending money. If $\beta$ is less than one you have to borrow money, if greater than one you lend. For example if $\beta$ of the stock is 2 you put half your money in treasury bills (or a bank account) the other half in the stock; that gives you a beta of 1 overall (because the bank account has a beta of zero and the overall beta is the weighted average of 2 an 0). – Alex C Aug 6 '18 at 15:45