## Beta as an Indicator

A company’s beta is a measure of the volatility, or systematic risk, of a security, as it compares to the broader market. The beta of a company measures how the company’s equity market value changes with changes in the overall market. It is used in the capital asset pricing model (CAPM) to estimate the return of an asset.

Beta, specifically, is the slope coefficient obtained through regression analysis of the stock return against the market return. The following regression equation is employed to estimate the beta of the company:

﻿ \begin{aligned} &\Delta S_i = \alpha + \beta_i \times \Delta M + e\\ &\textbf{where:}\\ &\Delta S_i=\text{change in price of stock }i\\ &\alpha=\text{intercept value of the regression}\\ &\beta_i=\text{beta of the }i \text{ stock return}\\ &\Delta M=\text{change in the market price}\\ &e = \text{residual error term} \\ \end{aligned}﻿

Such a regression analysis can be conducted for listed companies because historical stock-return data is used. But what about private companies?

Due to the lack of market data on the stock prices of private companies, it is not possible to estimate stock beta. Therefore, other methods are required to estimate their beta.

## Calculating Beta From Comparable Public Companies

In this approach, we first need to find the average beta of the publicly-traded companies that generate income from similar operations as the private company. This will be a proxy for the industry average levered beta. Second, we need to unlever the average beta using the average debt-to-equity ratio for these comparable companies. The final step is to re-lever beta, using the private company’s target debt-to-equity ratio.

Assume we want to estimate the beta of an illustrative energy services company with a target debt-to-equity ratio of 0.5, and the following companies are the most comparable companies:

The equity-weighted average beta of the four companies is 1.64. This is close to the arithmetic average of about 1.66. The chosen method to find the average beta may depend on the specifics of the data and size range of the comparable companies.

For instance, if there are one very large company and three very small companies, then a weighted average method will be biased toward the beta of the large company. In this particular example, however, we can take the weighted average beta as it is close to the arithmetic average, which gives equal weight to each company’s equity.

The next step is unlevering the average beta. For this, we need the average debt-to-equity ratio for these companies. The weighted average debt-to-equity ratio is 0.34.

﻿ \begin{aligned} \beta_u &= \frac{\beta_L}{1 + (1 - T) \times \frac{D}{E}} \\ &= \frac{1.64}{1 + (1 - 0.35) \times 0.34} \\ &= 1.343 \\ \end{aligned}﻿

Thus, we get the unlevered beta of 1.343.

Where D/E is the average debt-to-equity ratio of the comparable companies, T is the tax rateBu the unlevered beta, and BL the levered beta.

In the final step, we need to re-lever the equity using the target debt-to-equity ratio of the private company, which equals 0.5.

﻿ \begin{aligned} \beta_L &= \beta_U \times [1 + (1 + T) \times \frac{D}{E}] \\ &= 1.343 \times [1 + (1 - 0.35) \times 0.5]\\ &= 1.78 \\ \end{aligned}﻿

In this example, the beta of the illustrative private company is higher than the average levered beta due to a higher target debt-to-equity ratio.

This method has certain pitfalls, including the fact that it neglects the difference between the size of the private company and that of the public company. Most of the time, publicly-traded companies are much larger in size compared to private ones.

## Earnings Beta Approach

Usually, listed companies are large companies that operate in more than one segment. Therefore, it may be problematic to find a comparable firm whose beta would adequately represent the business beta of the private company being valued. For instance, Apple Inc. (AAPL) has a diverse set of operations, including personal computers, smartphones, tablets, and other items. This company would likely be poorly comparable to a private company that has a single operation, such as smartphone production.

When it is difficult to obtain reliable comparable beta, a company’s earnings beta can be used as a proxy for the levered beta. In this method, the company’s historical earnings changes are regressed against the market returns. An appropriate market index can be used as a proxy for the market. For instance, if the company is operating in the U.S. market, the S&P 500 can be used as a proxy.

Beta obtained from historical data needs to be adjusted to make sure that it reflects the company’s expected future performance. To reflect the mean-reverting feature of beta (beta tends to revert to one in the long run), we need to estimate adjusted beta using the following equation:

\begin{aligned} &\beta_{\text{adj}} = \alpha + (1 + \alpha) \times \beta_h \\ &\textbf{where:}\\ &\alpha=\text{smoothing factor}\\ &\beta_h=\text{historical beta}\\ &\beta_{\text{adj}}=\text{adjusted beta}\\ \end{aligned}

The smooth factor can be derived through complex statistical analysis based on historical data, but as a rule of thumb, the value of 0.33 or (1/3) is used as a proxy.

The earnings beta approach also has some pitfalls. First, private companies do not usually have extensive historical earnings data for reliable regression analysis. Second, accounting earnings are subject to smoothing and accounting policy changes. Therefore, these may not be appropriate for statistical analysis, unless necessary adjustments have been made.

## Bottom Line

The valuation of private companies using CAPM can be problematic because there is no straightforward method for estimating equity beta. To estimate the beta of a private company, there are two primary approaches.

One approach is to obtain a comparable levered beta from an industry average or from a comparable company (or companies) that best mimics the current business of the private company, unlever this beta, and then find the levered beta for the private company using the company’s target debt-to-equity ratio. Alternatively, one can find the beta of the company’s earnings and use it as a proxy for the company after appropriate adjustments are made.