Beta and Alpha in Business Valuation are two letters from the Greek alphabet often used in arcane discussions between business valuers.
They are very different factors in considering the value of a subject company.
Beta and Alpha in Business Valuation are crucial factors.
Beta is used to moderate the equity risk premium within the capital asset pricing model (CAPM).
The concept behind CAPM is that the required returns reflect the systematic or systemic risk within the market. There is not one level of market systematic risk.
It is not possible to measure directly the systematic risk. A proxy is used to meet this challenge. That proxy is a relative volatility measurement. It compares the price movements of the shares in a portfolio or the stock of an individual company with those of the market.
Some stocks, such as utility companies, will be expected to display less volatility in their price movements than the entire market. Other stocks will have greater price movements. In simple terms, the assumption is that the more volatile the stock, the higher the risk. The higher the risk, the higher the return that is required by investors.
The particular base market (New York Stock Exchange, NASDAQ, Nikkei or London Stock Exchange) will be given a Beta of 1.0. All stocks within that market will be measured by reference to that base point.
The Beta is measured by regressing a stock’s returns against the market’s returns. The formula for the Beta is:
In the above formula, is the standard deviation of the returns on the stock (price changes and dividends) and is the standard deviation of the market returns.
The time periods used for inputs into the above formula can be daily, weekly or monthly. The period covered is normally in the range 3 to 5 years.
There are many challenges with Beta:
For an individual company the price movements will reflect both systematic risk (that is price movements reflecting the market) and unsystematic risk (price movements caused by factors specific to the individual company).
Betas are necessarily historical measurements. There is an implicit assumption that history will repeat itself at least to the extent that future price volatility will mirror the past.
Betas are based upon the volatility of equities. A highly leveraged company will be expected to show higher volatility in stock prices than a company which is identical in every way apart from having lower leverage. There is therefore a second factor to adjust: the Beta can be unlevered to give the Beta assuming that there is no debt in the capital structure. This then produces what is known as the asset Beta.
Having calculated the Beta on the basis of a capital structure which is wholly equity, the Beta is then relevered to reflect the actual capital structure of the subject company.
This is a means of achieving a greater consistency of measurement as the volatily consistent with the debt level is stripped out of the calculations and replaced with the actual capital structure.
A commonly used pair of formulas for the above adjustments are the Hamada formulas. The unlevering formula is:
β_U= β_L
__________
(1+ (1-t)(D/E) )
In the above formula βU is the unlevered Beta; βL is the actual, levered Beta; t is the rate of tax; D and E refer to the debt and equity respectively.The relevering formula is a simple reorganisation of the above formula:
β_L= β_U (1+ (1-t)(D/E))
Whereas Beta is enveloped by the fine filigree work of detailed calculation, as summarised above, Alpha is a very different concept.
Alpha has two alternative but related meanings:
- For market participants and fund managers, Alpha is that elusive whisp of returns over and above the expected returns. Stock pickers seek to demonstrate value by showing that they can deliver these returns. This cannot be achieved simply by increasing the risk: the expected returns are the market returns as adjusted for the Beta within the portfolio.
- The second meaning is that used by business valuers. The company specific risk is very often a large factor added to the CAPM in an attempt to reflect those qualitative differences between the subject company and the guideline public company. As the differences are qualitative, such as depth of management, geographic spread, etc., the business valuers’ Alpha is extremely difficult to quantify.