International Finance and Accounting Handbook

• Step 5: Finally, we estimate the current market values of debt and equity of the
  firm and use this debt-to-equity ratio to estimate a levered beta.

The betas estimated using this process are called bottom-up betas.

THE CASE FOR BOTTOM-UP BETAS. At first sight, the use of bottom-up betas may seem to
leave us exposed to all of the problems we noted with regression betas. After all, the
betas for other publicly traded firms in the business are obtained from regressions.
Notwithstanding these bottom up betas represent a significant improvement on re-
gression betas for the following reasons:

• While each regression beta is estimated with standard error, the average across
  a number of regression betas will have much lower standard error. The intuition
  is simple. A high standard error on a beta estimate indicates that it can be sig-
  nificantly higher or lower than the true beta. Averaging across these errors re-
  sults in an average beta that is far more precise than the individual betas that
  went into it. In fact, if the estimation errors on individual firm betas are uncor-
  related across firms, the savings in standard error can be stated as a function of
  the average standard error and the number of firms in the sample.

where n is the number of firms in the sample. Thus, if the average standard error

in beta estimates for software firms is 0.50 and the number of software firms is

100, the standard error of the average beta is only 0.05 (0.50/ ).

• A bottom-up beta can be adapted to reflect actual changes in a firm’s business
  mix and expected changes in the future. Thus, if a firm divested a major portion
  of its operations last week, the weights on the businesses can be modified to re-
  flect the divestiture. The same can be done with acquisitions. In fact, a firm’s
  strategic plans to enter new businesses in the future can be brought into the beta
  estimates for future periods.


• Firms do change their debt ratios over time. While regression betas reflect the
  average debt-to-equity ratio maintained by the firm during the regression period,
  bottom-up betas use the current debt to equity ratio. If a firm plans to change its
  debt-to-equity ratio in the future, the beta can be adjusted to show these changes.


• Finally, bottom-up betas wean us from our dependence on historical stock
  prices. While we do need these prices to get betas for comparable firms, all we
  need for the firm being analyzed is a breakdown of the businesses it is in. Thus,
  bottom-up betas can be estimated for private firms, divisions of business and
  stocks that have just started trading in financial markets.

COMPUTATIONAL DETAILS. While the idea behind bottom-up betas is fairly simple, there
are several computational details that are deserving of attention:

• Defining comparable firms. First, we have to decide how narrowly we want to
  define a business. Consider, for instance, a firm that manufactures entertainment

1100

Standard errorBottom-up beta

Average standard errorComparable firms

1 n

9.2 ESTIMATING DISCOUNT RATES 9 • 23