A companyâ€™s beta is a measure of theÂ volatility, or systematic risk, of a security compared to the market. The beta of a company measures how the companyâ€™s equity market value changes with the change of market overall.Â It is used in theÂ Capital Asset Pricing ModelÂ (CAPM) to estimate the return of an asset.

Beta 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:

Such a regression analysis can be conducted for listed companies, because we use historical stock returns for such an analysis.

But what about for private companies? Due to lack of market data on stock prices of private companies it is not possible to estimate stock beta. Therefore, other methods are required to estimate beta of the private company.

**Deriving Private Company Beta from a Comparable Public Company**

In this approach we need at first to find 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 re-levering beta, using private companyâ€™s target debt/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, andÂ the following companies are the most comparable companies:

ComparableÂ Companies, as of year-end 2014 |
Beta |
Debt |
Equity |
D/E |

Halliburton Company (HAL) | 1.6 | 7,840 | 16,267 | 0.48 |

SchlumbergerÂ Limited. (SLB) | 1.65 | 10,565 | 37,850 | 0.28 |

Helix Energy Solutions Group Inc. (HLX) | 1.71 | 523.23 | 1653.47 | 0.32 |

Superior Energy Services, Inc. (SPN) | 1.69 | 1,627.84 | 4079.74 | 0.40 |

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Averages | Â | Â | Â | Â |

Weighted average beta | 1.64 | Â | Â | Â |

Weighted average D/E | 0.34 | Â | Â | Â |

The equity-weighted average beta of the four companies is 1.64. This is close to the arithmetic average of about 1.66. The choice ofÂ method to find the average may depend on the specifics of the data and size range of the comparable companies. For instance, if there is one very large company and three very small companies, then a weighted average method will be biased toward to 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, giving equal weight to each companyâ€™s equity.

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

Thus, we get the unlevered beta of 1.343 approximately.

Where D/E is the average debt-to-equity ratio of the comparable companies, T â€“ is the tax rate, Â *B** _{u}*Â - unlevered beta, Â

*B*

*â€“ levered beta.*

_{L}In the final step, we need to re-lever the equity using the target D/E ratio of the private company, which equals 0.5.

In this example, the beta of the illustrative private company is higher than the average levered beta due to 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 public company. Most of the time, publicly-traded companies are much larger in size compared those that are private.

**Earnings Beta Approach**

Usually listed companies are large companies that operate in more than one segment, and therefore, it may be problematic to find a comparable firm that whose beta would adequately represent the business beta of the private company to be valued. For instance, Apple Inc. (AAPL) has a diverse operation segments including personal computers, cell phones, media player, tablets, etc. This company would be a biased comparable for a private company that has a single operation, such as cell phone production.

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

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

Where alpha is a smooth factor, and *B** _{h}* and

*B*

*Â are historical and adjusted beta respectively. 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.*

_{adjÂ }The earnings beta approach also has some pitfalls. First, private companies do not usually have extensive historical earnings data for reliable regression analysis.Â 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.Â

**The Bottom Line**

The valuation of private companies using CAPM can be problematic because there isÂ no straightforward method for estimating equity beta.To know more read:valuing private company. In order to estimate the beta of a private company there are two primary approaches:

- Obtaining a comparable levered betaÂ from an industry average or from a comparable company (or companies) that best mimics the current business of the private company, unlevering this beta, and then finding levered beta for the private company using the companyâ€™s target debt/equity ratio.
- Finding beta of the companyâ€™s earnings and using it as a proxy for the company after appropriate adjustments are made.