Unlevered beta is the beta of a company, after eliminating the effects of financial leverage. Unlevered beta is often used for a company which is not publicly-traded, using the pure play method.
Beta measures the market risk of a company but can also be used to compare companies in the same industry. While calculating the beta of a company which is publicly-traded is easy as the returns of the company and of the market are known, doing the same for unlisted companies is not as straight forward.
The pure play method is a calculation which takes a comparable but listed company, and unlevers its beta (which means eliminating the effects of financial leverage in its beta and relevering with the leverage the private company has) to get the unlisted company’s risk quotient or beta.
A comparable listed company is one which faces similar business risks as the unlisted company for which we are calculating beta.