# How to Calculate the Beta of a Combined Firm

Beta is a measure of how much a stock moves relative to movements in the overall stock market. Technically, it is the covariance of returns of the stock and the overall market (represented by an index such as the Standard & Poor's 500) divided by the variance of the market.

## Meaning of Beta

If a stock has a beta of 1.0, then if the market goes up one point, the stock will also go up one point. If a stock has a beta of zero, an upward or downward movement in the market will result in no movement in the stock. If a stock has a beta of negative 1.0, if the market moves up one point, the stock will move down one point. If a stock has a beta of 2.0, if the market moves up one point, the stock will move up two points.

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Keep in mind that beta is measured based on historical returns, meaning that beta is not a perfect indicator of future performance. If a stock has a two-year beta of 1.0, what this really says is that over the past two years, when the market has moved up one point, the stock also has moved up one point.

## Weighted-Average Beta

If two firms are merged into one firm, the combined firm's beta is based on the weighted average of the market capitalizations of the two predecessor firms. Market capitalization refers to the total equity value of a company and is calculated by multiplying the number of shares a company has outstanding by each share's market value, or trading price. Alternatively, you can estimate a company's market value by performing a valuation of its equity, usually by applying a valuation multiple to a metric like earnings or revenues. For example, the price-to-earnings ratio is one of the better known valuation ratios. If a company records earnings of \$1 million and the average price-to-earnings ratio of comparable companies is 10.0, the equity value of the company would equal \$10 million (P/E ratio of 10.0 multiplied by annual earnings of \$1 million).

If two firms combined via a merger and each company had a market capitalization of \$1 million, the total market capitalization of the newly combined firm equals \$2 million. If Firm A has a beta of 1.0 and Firm B has a beta of 2.0, the newly combined firm's beta equals 1.5 (1/(1+1) multiplied by 1.0 plus 1/(1+1) multiplied by 2.0).

Using the same predecessor firm betas, if Firm A's market capitalization equaled 25 percent of the newly combined entity's market capitalization, Firm B's market capitalization must equal 75 percent. In this case, the newly combined firm's beta would equal 1.75 (0.25 multiplied by 1.0 plus 0.75 multiplied by 2.0; or 0.25 plus 1.5).