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In fact, if the marginal investor is globally diversified, Titan Cements beta should have been estimated against a global indexIndex Domination and Beta Estimates There are a number of indices that are dominated by one or a few stocks. One of the most striking cases was the Helisinki Stock Exchange (HEX) in the late 1990s. Nokia, the telecommunications giant represented 75% of the Helisinki Index, in terms of market value. Not surprisingly, a regression of Nokia against the HEX yielded the results shown in Figure 8.3. The regression looks impeccable. In fact, the noise problem that we noted with Boeing, arising from the high standard errors, disappears. The beta estimate has a standard error of 0.03, but the results are deceptive. The low standard error is the result of a regression of Nokia on itself, since it dominates the index. The beta is meaningless to a typical investor in Nokia, who is likely to be diversified, if not globally, at least across European stocks. Worse still, the betas of all other Finnish stocks against the HEX become betas estimated against Nokia. In fact, the beta of every other Finnish stock at the time of this regression was less than 1. How is this possible, you might ask, if the average beta is one? It is the weighted average beta that is one, and if Nokia which comprises three quarters of the index has a beta greater than one (which it does), every other stock in the index could well end up with a beta less than one. Titan Cements is a cement and construction company in Greece. Reproduced below in Figure 8.4 is the beta estimate for Titan obtained from a beta service (Bloomberg) from January 1996 to December 2000. Note that the index used is the Athens Stock Index. This is a fairly conventional choice since most services estimate betas against a local index. Based upon this regression, we arrive at the following equation. The beta for Titan Cements, based upon this regression, is 0.93. The standard error of the estimate, shown in brackets below, is only 0.08, but the caveats about narrow indices apply to the Athens Stock Exchange Index. Drawing on the arguments in the previous section, if the marginal investor in Titan Cements is, in fact, an investor diversified across European companies, the appropriate index would have been a European stock index. The Bloomberg beta calculation with the MS European Index is reported below in Figure 8.5. the decline in beta to 0.33 and the increase in the standard error of the beta estimate. In fact, if the marginal investor is globally diversified, Titan Cements beta (as well as Boeings beta in the previous illustration) should have been estimated against a global index. Using the Morgan Stanley Capital Index (MSCI), we get the regression beta of 0.33 in Figure 8.6. In fact, the beta estimate and the standard error look very similar to the ones estimated against the European index. Estimating the Historical Beta for Private Firms The historical approach to estimating betas works only for assets that have been traded and have market prices. Private companies do not have a market price history. Consequently, we cannot estimate a regression beta for these companies. Nevertheless, we still need estimates of cost of equity and capital for these companies. You might argue that this is not an issue because you do not value private companies but you will still be confronted with this issue even when valuing publicly traded firms. Consider, for instance, the following scenarios. * If you have to value a private firm for an initial public offering, you will need to estimate discount rates for the valuation. * Even after a firm has gone public, there will be a period of time lasting as long as two years when there will be insufficient data for a regression. * If you are called upon to value the division of a publicly traded firm that is up for sale, you will not have past prices to draw upon to run a regression. * Finally, if your firm has gone through significant restructuring - divestitures or recapitalization - in the recent past, regression betas become meaningless because the company itself has changed its risk characteristics. Thus, regression betas are either unavailable or meaningless in a significant number of valuations. Some analysts assume that discounted cash flow valuation is not feasible in these scenarios and use multiples. Others make assumptions about discount rates based upon rules of thumb. Neither approach is appealing. In the next section, we will develop an approach for estimating betas that is general enough to apply to all of these companies. risk.xls .This spreadsheet allows you to run a regression of stock returns against market returns and estimate risk parameters. The Limitations of Regression Betas Much of what we have presented in this section represents an indictment of regression betas. In the case of Boeing, the biggest problem was that the beta had high standard error. In fact, this is not a problem unique to Boeing. Figure 8.7 presents the distribution of standard errors on beta estimates for US companies. With the Nokia regression, we seem to cure the standard error problem but at a very large cost. The low standard errors reflect the domination of the index by a stock and result in betas that may be precise but bear no resemblance to true risk. Changing the market index, the return period and return interval offer no respite. If the index becomes a more representative index, the standard errors on betas will increase, reflecting the fact that more of the risk in the stock is firm-specific. If the beta changes as the return period or interval changes, it creates more uncertainty about the true beta of the company. In short, regression betas will almost always be either too noisy or skewed by estimation choices to be useful measures of the equity risk in a company. The cost of equity is far too important an input into a discounted cash flow valuation to be left to statistical chance. B. Fundamental Betas A second way to estimate betas is to look at the fundamentals of the business. The beta for a firm may be estimated from a regression but it is determined by decisions the firm has made on what business to be in, how much operating leverage to use in the business and by the degree to which the firm uses financial leverage. In this section, we will examine an alternative way of estimating betas for firms, where we are less reliant on historical betas and more cognizant of their fundamental determinants. 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 of the firm and (3) the firms financial leverage. Although we will use these determinants to find betas in the capital asset pricing model, the same analysis can be used to calculate the betas for the arbitrage pricing and the multi-factor models as well. Type of Business betas measure the risk of a firm relative to a market index, the more sensitive a business is to market conditions, the higher its beta. Thus, other things remaining equal, cyclical firms can be expected to have higher betas than non-cyclical firms. Companies involved in housing and automobiles, two sectors of the economy which are very sensitive to economic conditions, should have higher betas than companies in food processing and tobacco, which are relatively insensitive to business cycles. We can extend this view to a companys products. The degree to which a products purchase is discretionary will affect the beta of the firm manufacturing the product. Firms whose products are much more discretionary to their customers should have higher betas than firms whose products are viewed as necessary or less discretionary. Thus, the beta of Procter and Gamble, which sells diapers and daily household products, should be lower than the beta of Gucci, which manufactures luxury products. 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 fixed costs relative to total costs is said to have high operating leverage. A firm with high operating leverage will also have higher variability in operating income than would a firm producing a similar product with low operating leverage. Other things remaining equal, the higher variance in operating income will lead to a higher beta for the firm with high operating leverage. Can firms change their operating leverage? While some of a firms 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. For instance, firms have made cost structures more flexible by * negotiating labor contracts that emphasize flexibility and allow the firm to make its labor costs more sensitive to its financial success; * entering into joint venture agreements, where the fixed costs are borne or shared by someone else; and * sub-contracting manufacturing and outsourcing, which reduce the need for expensive plant and equipment. While the arguments for such actions may be couched in terms of offering competitive advantage and flexibility, they do also reduce the operating leverage of the firm and its exposure to market risk. 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 Sales For firms with high operating leverage, operating income should change more than proportionately when sales change. Size, Growth and Betas Generally, smaller firms with higher growth potential are viewed as riskier than larger, more stable firms. While the rationale for this argument is clear when talking about total risk, it becomes more difficult to see when looking at market risk or betas. Should a smaller software firm have a higher beta than a larger software firm? One reason to believe that it should is operating leverage. If there is a set-up cost associated with investing in infrastructure or economies of scale, smaller firms will have higher fixed costs than larger firms, leading in turn to higher betas for these firms. With growth firms, the argument for higher betas rests on the notion of discretionary versus non-discretionary purchases. For a high growth firm to deliver on its growth, new customers have to adopt the product or existing customers have to buy more of the product. Whether they do so or not will depend, in large part, on how well-off they feel. This, in turn, will make the profits of high growth firms much more dependent on how well the economy is doing, thus increasing their betas. |
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