###### Overfitting and Methods of Addressing it

Overfitting is a problem that arises when the machine learning algorithm fits the... **Read More**

For public companies, beta is estimated through ordinary least squares (OLS) regression of the returns on a stock on the returns on the market. Beta estimates from such a regression are influenced by the following:

- The choice of index used to represent the market portfolio. For example, for U.S. equities, the S&P 500 index is used as the market portfolio.
- The length of the data period and the frequency of observations. The most common choice is five years of monthly data, yielding 60 observations.

The value of beta obtained through OLS regression is known as * raw* or

$$\text{Adjusted beta}=\bigg(\frac{2}{3}\bigg)(\text{Unadjusted beta})+\bigg(\frac{1}{3}\bigg)(1.0)$$

Analysts can indirectly estimate the beta of nonpublic companies using the beta of publicly traded comparable companies. This procedure must consider the effect on the beta of differences in financial leverage between the nonpublic company and the comparable. This is done in two steps:

**Step 1****:** The comparable company’s beta is unlevered to reflect the systematic risk. This is known as **asset beta** (\(\beta_{U}\)).

$$\beta_{U}=\bigg[\frac{1}{1+\big(\frac{\text{D}}{\text{E}}\big)}\bigg]\beta_\text{E}$$

Where \(D\) and \(E\) represent the nonpublic company’s debt and equity levels.

**Step 2****: **The unlevered beta (asset beta) is then re-levered to reflect the financial leverage of the comparable company.

$$\beta_{\text{E}}=\bigg[1+\frac{\text{D}}{\text{E}}\bigg]\beta_{U}$$

Analysts may use the median or average industry beta rather than a single comparable company’s beta. The un-levering and re-levering process can be applied to the asset beta using the median or average industry capital structure.

## Question

Which of the following processes is

most likelyto be applied to an asset beta to reflect the effect of financial leverage when estimating the beta of a nonpublic company?

- Adjusted beta.
- Re-levering.
- Unlevering.
## Solution

The correct answer is B.Re-levering is the process of incorporating the effect of the subject company’s financial leverage on an asset beta.

A is incorrect.Adjusted beta is the estimated beta that reflects the tendency of betas to revert to 1.0 overtime.

C is incorrect.Unlevering is the process of eliminating the comparable’s company financial leverage from its beta so that it only reflects the systematic risk. This process is used to arrive at the asset beta.

Reading 21: Return Concepts

*LOS 21 (d) Explain beta estimation for public companies, thinly traded public companies, and nonpublic companies.*