Ten Questions about Bottom-up Betas

  1. What is a bottom-up beta?

A bottom-up beta is estimated by starting with the businesses that a firm is in, estimating the fundamental risk or beta of each of these businesses and taking a weighted average of these risks.

  1. What are the steps involved in estimating bottom-up betas?

There are four steps:

Step 1: Break your company down into the businesses that it operates in. A firm like GE operates in 26 businesses but Walmart is a single business company. Do not define your business too narrowly or you will run into trouble in step 2.

Step 2: Estimate the risk (beta) of being in each business. This beta is called an asset beta or an unlevered beta.

Step 3: Take a weighted average of the unlevered betas of the businesses you are in, weighted by how much value you get from each business.

Step 4: Adjust the beta for your company's financial leverage (Debt to equity ratio)

  1. What should we use as comparable firms?

While the narrow version of comparable firm defines it to be another firm in the same business that your firm is in, the broader definition of comparable firm includes any firm whose fortunes are tied to your firm's success and failure (or vice versa). From a practical standpoint, try the following. Define "comparable firm" narrowly as a firm that is very similar to your firm. (Thus, if your firm makes entertainment software, look for other firms that are entertainment software firms as well.) If you get a large enough sample (see answer to question 4), stop. If not, try expanding your sample, using any or all of the following tactics:

i.               Define comparable more broadly (all software as opposed to entertainment software).

ii.              Look for global listings of companies in the same business; all entertainment companies listed globally would be an example.

iii.            Look up and down the supply chain for other companies that feed into your company and that your company feeds into. Thus, you may start looking for software retailers that get the bulk of their revenues from entertainment software.

  1. How big a sample of firms do we need?

Think of this question in the following way. Any sample size greater than one is an improvement on a regression beta. However, the more firms that you have in your sample, the greater the potential savings in error. With a sample of 4, your standard error will be cut by half; with a sample of 9, by two-thirds; with a sample of 16, by 75%.... Try to get to double digits for your sample size, if you can. If you cannot, settle for 6-8 firms and you are still saving a substantial amount in terms of estimation error.

There is clearly a trade-off between how tightly you define "comparable firm" and your sample size. If you define comparable narrowly (firms like just like yours in terms of size and what they do), you will get a smaller sample. If you can get to double digits with a narrow definition, stay with it. If your sample size is too small, try one of the techniques suggested in the answer to question 3 to expand your sample.

  1. Once we have comparable firms, how do we estimate the unlevered (asset) betas?

Simply put, you average their regression betas and clean up those betas for financial leverage and cash holdings. In practical terms, here are some issues that you wil face:

  1. Do the regression betas for the comparable firms all have to be over the same time period and against the same index?

In a perfect world, yes.! However, as your sample size increases, you can afford to get sloppy with these details, hoping that the law of large numbers bails you out. Thus, if you have 100 global firms in your sample, with betas estimated against local indices, you can get away using an average of these 100 betas since some are likely to be over estimated and some under estimated.

  1. Once we have the regression betas for the firms, should we use simple or weighted averages?

Use simple averages. Otherwise, you will be attaching the beta of the largest firm or firms in your group to all of the firms in the sample. Microsoft's beta will become every software company's beta.

  1. Why do we need to correct for financial leverage?

Your company can have a very different policy on how much debt to use than the typical firm in the sample. Regression betas are levered betas but they reflect the financial leverage of the companies in the sample (and not your company). You have to take out the financial leverage effect (unlever the beta) to come up with a pure play or business beta.

Unlevered beta = Regression beta / (1 + (1-tax rate) D/E)

  1. Should we unlever each firm's beta and then average or average and then unlever?

I prefer to average first and then unlever. Individual firm regression betas are noisy (have large standard error) and unlevering them only compounds the noise. Averaging first should reduce the noise, leading to better beta estimates.

  1. What tax rate and debt to equity ratio should I use for the sector?

To be safe, go with a marginal tax rate and use either the median D/E ratio or the aggregate D/E ratio for the sector. (There are always strange outliers with D/E ratios that make simple averages go haywire.)

  1. Why do I need to adjust for cash and how do I do it?

The regression beta for a company reflects all of its assets (including cash). Thus, if a firm is 60% software and 40% cash, its regression beta will be lower because cash is riskless. Since we want a pure software business beta, we should be cleaning up the betas for cash holdings. If we assume that cash has a beta of zero, this adjustment is trivial:

Cash-adjusted beta = Unlevered beta / (1 – Cash/ Firm Value)

Firm value = Market value of Equity + Market value of Debt

  1. Is it possible to adjust these unlevered betas for operating leverage?

It is possible, but only if you know what costs are fixed and what are variable not only for your firm but for all of the firms in your sample. If you do have that information, you can break the unlevered beta down into a business component (reflecting the elasticity of demand for your company) and an operating leverage component:

Business Risk beta = Unlevered beta/ (1 +Fixed Costs/ Variable Costs)

The problem from a practical standpoint is getting the fixed and variable cost breakdown.

  1. How do we weight these unlevered betas to arrive at the beta for the company?

The weights should be market value weights of the individual businesses that the firm operates in. However, these businesses do not trade (GE Capital does not have its own listing) and you have to estimate the market values. You can use weight based on revenues or earnings from each business but you are assuming that a dollar in revenues (earnings) has the same value in every business. An alternative is to apply a multiple of revenues (earnings) to the revenues (earnings) from each business to arrive at an estimated value. This multiple can be estimated for the comparable firms (from which you estimated the betas). Since you are interested in the value of the business (and not the value of equity), you should look at EV multiples (and not equity multiples). If you use revenues, use an EV/ Sales multiple.

  1. How do we adjust for financial leverage?

The standard adjustment for financial leverage is to assume that debt has no market risk (a beta of zero) and to use what is called the "Hamada" adjustment:

Levered Beta = Unlevered beta (1 + (1- tax rate) (Debt/Equity))

You can use the current debt to equity ratio for the firm you are analyzing or even a target debt to equity (if you feel that change is on the horizon) in making this computation.

If you feel uncomfortable about the assumption that debt has no market risk, estimate a beta for debt and compute the levered beta as follows

Levered Beta = Unlevered Beta (1 + (1-t)(D./E)) – Beta of debt (1-t)(D/E)

The tricky part is estimating the beta of debt.

  1. Can bottom-up betas change over time for a company?

Yes, and for two reasons. One is that the mix of businesses can change over time, leading to a different unlevered beta. The other is that the debt to equity ratio for the firm can change over time, leading to changes in the levered beta.

  1. Why is a bottom-up beta better than a regression beta?

Bottom up betas are better than a regression beta for three reasons