R Squared




Here again, the risk parameters estimated for Deutsche Bank are a function of the index used in the regression. The standard error is lowest (and the R squared is highest) for the regression against the DAX; this is not surprising since Deutsche is a large component of the DAX. The standard error gets larger and the R squared gets lower as the index is broadened to initially include other European stocks and then to global stocks.

In Practice: Which index should we use to estimate betas?

In most cases, analysts are faced with a mind-boggling array of choices among indices when it comes to estimating betas; there are more than 20 broad equity indices ranging from the Dow 30 to the Wilshire 5000 in the United States alone. One common practice is to use the index that is most appropriate for the investor who is looking at the stock. Thus, if the analysis is being done for a U.S. investor, the S&P 500 index is used. This is generally not appropriate. By this rationale, an investor who owns only two stocks should use an index composed of only those stocks to estimate betas.

The right index to use in analysis should be determined by the holdings of the marginal investor in the company being analyzed. Consider Aracruz and Deutsche Bank in the earlier illustration. If the marginal investors in.these companies are investors who holds only domestic stocks - just Brazilian stocks in the case of Aracruz or German stocks in the case of Deutsche - we can use the regressions against the local indices. If the marginal investor is a global investor, a more relevant measure of risk may emerge by using the global index. Over time, you would expect global investors to displace local investors as the marginal investors, because they will perceive far less of the risk as market risk and thus pay a higher price for the same security. Thus, one of the ironies of our notion of risk is that Aracruz will be less risky to an overseas investor who has a global portfolio than to a Brazilian investor with all of his or her wealth in Brazilian assets.

Standard Procedures for Estimating Risk Parameters in the Arbitrage Pricing and Multi-factor Models

Like the CAPM, the arbitrage pricing model defines risk to be non-diversifiable risk, but, unlike the CAPM, the APM allows for multiple economic factors in measuring this risk. While the process of estimation of risk parameters is different for the arbitrage pricing model, many of the issues raised relating to the determinants of risk in the CAPM continue to have relevance for the arbitrage pricing model.

The parameters of the arbitrage pricing model are estimated from a factor analysis on historical stock returns, which yields the number of common economic factors determining these returns, the risk premium for each factor and the factor-specific betas for each firm.

Once the factor-specific betas are estimated for each firm, and the factor premia are measured, the arbitrage pricing model can be used to estimated expected returns on a stock.

j=i where,

Rf = Risk-free rate

Pj = Beta specific to factor j

Factor Analysis: This is a statistical technique, where past data is analyzed with the intent of extracting common factors that might have affected the data.

E(Rj) - Rf = Risk premium per unit of factor j risk k = Number of factors

In a multi-factor model, the betas are estimated relative to the specified factors, using historical data for each firm.

B. Fundamental Betas

The beta for a firm may be estimated from a regression but it is determined by fundamental decisions that the firm has made on what business to be in, how much operating leverage to use in the business and the degree to which the firm uses financial leverage. In this section, we will examine an alternative way of estimating betas, where we are less reliant on historical betas and more cognizant of the intuitive underpinnings of betas.

Determinants of Betas

The beta of a firm is determined by three variables -(1) the type of business or businesses the firm is in, (2) the degree of operating leverage in the firm and (3) the firm's financial leverage. While much of the discussion in this section will be couched in terms of CAPM betas, the same analysis can be applied to the betas estimated in the APM and the multi-factor model as well.

Type of Business Since betas measure the risk of a firm relative to a market index, the more sensitive a business is to market conditions, the higher is its beta. Thus, other things remaining equal, cyclical firms can be expected to have higher betas than non-cyclical firms. Other things remaining equal, then, companies involved in housing and automobiles, two sectors of the economy which are very sensitive to economic conditions, will have higher betas than companies which are in food processing and tobacco, which are relatively insensitive to business cycles.

Building on this point, we would also argue that the degree to which a product's purchase is discretionary will affect the beta of the firm manufacturing the product. Thus,

Cyclical Firm: A cyclical firm has revenues and operating income that tend to move strongly with the economy - up when the economy is doing well, and down during recessions.

the betas of food processing firms, such as General Foods and Kellogg's, should be lower than the betas of specialty retailers, since consumers can defer the purchase of the latter's products during bad economic times.

It is true that firms have only limited control over how discretionary the product or service that they provide is to their customers. There are firms, however, that have used this limited control to maximum effect to make their products less discretionary to buyers, and by extension, lowered their business risk. One approach is to make the product or service a much more integral and necessary part of everyday life, thus making its purchase more of a requirement. A second approach is to effectively use advertising and marketing to build brand loyalty. The objective in good advertising, as we see it, is to make discretionary products or services seem like necessities to the target audience. Thus, corporate strategy, advertising and marketing acumen can, at the margin, alter the business risk and betas over time.

^ 4.7: Betas and Business Risk

Polo Ralph Lauren, the upscale fashion designer, went public in 1997. Assume that you were asked to estimate its beta. Based upon what you know about the firm's products, would you expect the beta to be a. greater than one b. about one c. less than one Why?

Degree of Operating Leverage The degree of operating leverage is a function of the cost structure of a firm, and is usually defined in terms of the relationship between fixed costs and total costs. A firm that has high operating leverage (i.e., high fixed costs relative to total costs) will also have higher variability in operating income than would a firm producing a similar product with low operating leverage.32 Other

32 To see why, compare two firms with revenues of $ 100 million and operating income of $ 10 million, but assume that the first firm's costs are all fixed whereas only half of the second firm's costs are fixed. If revenues increase at both firms by $ 10 million, the first firm will report a doubling of operating income

Operating Leverage: This is a measure of the proportion of the operating expenses of a company which are fixed costs.

things remaining equal, the higher variance in operating income will lead to a higher beta for the firm with high operating leverage.

While operating leverage affects betas, it is difficult to measure the operating leverage of a firm, at least from the outside, since fixed and variable costs are often aggregated in income statements. It is possible to get an approximate measure of the operating leverage of a firm by looking at changes in operating income as a function of changes in sales.

Degree of Operating leverage = % Change in Operating Profit / % Change in


For firms with high operating leverage, operating income should change more than proportionately, when sales change.

Can firms change their operating leverage? While some of a firm's cost structure is determined by the business it is in (an energy utility has to build expensive power plants, and airlines have to lease expensive planes), firms in the United States have become increasingly inventive in lowering the fixed cost component in their total costs. Labor contracts that emphasize flexibility and allow the firm to make its labor costs more sensitive to its financial success, joint venture agreements, where the fixed costs are borne by someone else, and sub-contracting of manufacturing, which reduce the need for expensive plant and equipment, are only some of the manifestations of this phenomenon. While the arguments for such actions may be couched in terms of competitive advantage and flexibility, they do reduce the operating leverage of the firm and its exposure to "market" risk.

Illustration 4.3: Measuring Operating Leverage for Disney Corporation

In table 4.5, we estimate the degree of operating leverage for Disney from 1987 to


Table 4.5: Degree of Operating Leverage: Disney


Net Sales

% Change in Sales

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