Estimating Beta: Bottom Up Approach

Beta is a measure of the volatility or systematic risk of a security or portfolio compared to the market index as a whole. It is used in the capital asset pricing model (CAPM), which describes the relationship between systematic risk and expected return of a stock. A stock that swings more than the market over time has a beta above 1.0. If a stock moves less than the market, the stock's beta is less than 1.0.Thus it is considered that a company with higher beta has a greater risk and also greater expected returns.

The most common method of calculating beta is through regression analysis.

Beta of the stock = Covariance of stock with market portfolio/ Variance of the market portfolio

Even though this method of calculating beta is extensively used, it is not the most accurate. It has been observed that the regression beta, especially in emerging markets like India, has a high standard error attached to it. If the standard error is abnormally high, then the value of the beta maybe erroneous and not be fit for valuation purpose .Let’s say if the beta of the stock is 1.2 with a standard error of 0.5 then this data is flawed to the extent that it could be anywhere in the range of 0.7-1.7.

Also,we can't take a specific time period because it can be of 6 months,1 year, 2 years,5 years and so on and it completely depends upon the analyst who is computing the result and for each time regression results can differ a lot. Also it can depend on which return interval should be used because it can be daily,weekly & monthly.

There are also circumstances when the regression beta is not available. This situation can arise in the case of startups and private firm. The data for calculating regression beta may not be available even after the company has gone public due to lack of sufficient historic data.

As an alternative the bottom-up approach of calculating beta is available. Although this approach includes additional workings as against a relatively simple calculation of top-down (regression) beta, the beta arrived from this method is more reliable. Every business entity has a different structure with respect to its operating model and capital structuring. The bottom up approach considers this difference. This is the main factor which makes bottom up beta superior than the regression beta.

 Bottom-up beta can be computed by examining:

1. The nature of the business

2. Operating leverage of the company (Fixed Cost/Total Cost)

3. Financial leverage of the company (Debt/Equity)

Let’s understand bottom up beta by an example of Company X which operates in a steel industry and 14 other comparable companies of that specific industry:

Unleveraged beta = Regression beta/ {1+ (1-tax-rate)*debt-equity ratio}

Unleveraged beta = 1.16/ 1 + (1-.0.0975)*1.77 = 0.44

The above results in the effect of the financial leverage being eliminated. However the effect of operating leverage also needs to be addressed.

Business beta = Unlevered beta/ {1+ (fixed to variable ratio)}

Business beta = 0.44/ {1+ (0.13)} = 0.38

The figure of 0.38 purely reflects the risk of operating in the steel industry without taking into consideration leverage of any sort. This number forms the base from which Company X’s beta will be calculated.

Step 2: Unlevered beta of Company X (adjusted for its operating leverage)

Business beta = 0.38(calculated above)

Fixed/variable cost ratio = 0.32

Unlevered Beta of Company X = 0.38 * (1+0.32) = 0.50

Step 3: Levered Beta of Company X (adjusted for its financial leverage)

Unlevered beta = 0.50 (calculated above)

Debt-equity ratio = 0.4

Effective Tax rate = 30.66%

Levered beta = Unlevered beta * {1+ (1 - effective tax rate) * debt-equity ratio}

Levered beta of X = 0.50 * {1+ (1-0.30)*0.4} = 0.64

The bottom-up beta for Company X which captures the nature of the business in which it operates, its operating leverage and the financial leverage works out to be 0.64.

The explanation is that the regression beta is of a larger sample base (14 companies in this case) which reduces the standard error in statistical estimation. Assuming the regression beta for Company X has a standard error of 0.50. . Thus, the standard error =Individual error / Square root of number of samples (0.50/√14 =0.13).Thus,the average industry regression beta would have a much lower error.

Conclusion:

Overall, bottom-up betas are designed to be a better measure of the market risk associated with the industry or sector of the business. It is estimated from the betas of firms in a specified business, thereby addressing problems associated with computing the cost of capital.

First, by eliminating the need for historical stock prices to estimate the firm’s beta, the standard error, created by regression betas, is reduced. Second, the problem of a changing product mix is eliminated because the business computes a different cost of capital for each product line. Third, the levered beta is computed from the company’s current financial leverage, rather than from the average leverage over the period of the regression. 

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