Note that we do not adjust for differences in leverage, since regulatory constraints and the needs of the business keep the leverage of most commercial banks at similar levels.41 The beta for Deutsche Bank as a firm can be estimated as a weighted average of these two betas. Using estimating market value weights of 69% for the commercial banking and 31% for the investment banking arms (based upon the revenues that Deutsche Bank made from each in the most recent year), we arrive at a beta for Deutsche Bank's equity:42 Deutsche Bank's beta = 0.7345 (0.69) + 1.5167 (0.31) = 0.9767 This beta will change over time as the weights on the businesses change.

41 Regulators often specify capital ratios, specified in terms of book values of debt and equity that banks must meet to stay in business. Most banks stay close to these ratios though some tend to be better capitalized than others.

42 Deutsche Bank does not explicitly break down income into commercial banking and investment banking components. The firm reported 5,470 million in Euros in trading revenues (investment banking), $ 15,179 million in net interest revenues and fiduciary commissions (commercial banking).

Calculating Betas after A Major Restructuring

The bottom-up process of estimating betas provides a solution when firms go through a major restructuring, where they change both their financial mix and leverage. In these cases, the regression betas are misleading because they do not reflect fully the effects of these changes. Disney's beta, estimated from the bottom up approach, is likely to provide a more precise estimate than the beta from a regression, given Disney's acquisition of Capital Cities and its increase in leverage. In fact, a firm's beta can be estimated even before the restructuring becomes effective using this approach. In the illustration that follows, for instance, we estimate Disney's beta just before and after its acquisition of Capital Cities/ABC, allowing for the changes in both the business mix and the leverage.

Illustration 4.9: Beta of a Firm After an Acquisition: Disney / Capital Cities

In 1995, Disney announced that it was acquiring Capital Cities, the owner of the ABC television and radio network, for approximately $ 120 per share, and that it would finance the acquisition partly through the issue of $ 10 billion in debt. At the time of the acquisition, Disney had a market value of equity of $31.1 billion, debt outstanding of $3.186 billion and a levered beta of 1.15. Capital Cities, based upon the $120 offering price, had a market value of equity of $18.5 billion, debt outstanding of $ 615 million and a levered beta of 0.95.

In order to evaluate the effects of the acquisition on Disney's beta, we do the analysis in two parts. First, we examine the effects of the merger on the business risk of the combined firm, by estimating the unlevered betas of the two companies, and calculating the combined firm's unlevered beta.

Disney's unlevered beta = 1.15/(1+0.64*0.10) = 1.08 Capital Cities unlevered beta = 0.95/(1+0.64*0.03) = 0.93 The unlevered beta for the combined firm can be calculated as the weighted average of the two unlevered betas, with the weights being based upon the market values of the two firms.43

43 Unlevered betas should always be weighted based upon firm values. With levered (equity) betas, the values of equity can be used as weights.

Value of Disney = 31,100 + 3,186 = $ 34, 286 million Value of Capital Cities = 18,500 + 615 = $ 19, 115 million Unlevered Beta for combined firm = 1.08 (34286/53401) + 0.93 (19115/53401)

Then, we examine the effects of the financing of the merger on the betas, by calculating the debt/equity ratio for the combined firm after the acquisition. Since Disney is assuming the old debt of Capital Cities, we add that debt to Disney's existing debt and add the additional $ 10 billion in debt used to fund this acquisition:44

Debt = Capital Cities Old Debt + Disney's Old Debt + New Debt

= $ 615 + $ 3,186 + $ 10,000 = $ 13,801 million Equity = Disney's Old Equity + New Equity used for Acquisition = $ 31,100 + $ 8,500 = $ 39,600 million where New Equity = Total Cost of Acquisition - New Debt Issued

= $ 18,500 - $ 10,000 = $ 8,500 million Notice that the equity in Capital Cities of $18,500 million disappears after the acquisition and is replaced with new debt of $ 10,000 million and new Disney equity of $ 8,500 million. The debt/equity ratio can then be computed as follows -

D/E Ratio = 13,801/39600 = 34.82% This debt/equity ratio in conjunction with the new unlevered beta for the combined firm yields a new beta of

C. Accounting Betas

A third approach is to estimate the market risk parameters from accounting earnings rather than from traded prices. Thus, changes in earnings at a division or a firm, on a quarterly or annual basis, can be regressed against changes in earnings for the market, in the same periods, to arrive at an estimate of a "market beta" to use in the CAPM. While the approach has some intuitive appeal, it suffers from three potential pitfalls. First, accounting earnings tend to be smoothed out relative to the underlying value of the company, resulting in betas that are "biased down", especially for risky firms, or "biased up", for safer firms. In other words, betas are likely to be closer to one for all firms using accounting data. Second, accounting earnings can be influenced by non-operating factors, such as changes in depreciation or inventory methods, and by allocations of corporate expenses at the divisional level. Finally, accounting earnings are measured, at most, once every quarter, and often only once every year, resulting in regressions with few observations and not much power.

Illustration 4.10: Estimating Accounting Betas — Bookscape Books

Bookscape Books, even though it is a private business, has been in existence since 1980 and has accounting earnings going back to that year. Table 4.10 summarizes accounting earnings changes at Bookscape and for the S&P 500 for each year since 1980. Table 4.10: Earnings for Bookscape versus S&P 500


S&P 500


Lessons From The Intelligent Investor

Lessons From The Intelligent Investor

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