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Total Beta

Total beta measures both market risk and firm-specific risk.

A typical market beta measures the additional risk an investment adds to a diversified portfolio.  The market beta is attributable to only the market risk. Market risk being all that diversified investors care about, firm-specific risk having been diversified away.

With a private business, the owner is often the only investor and does not have the ability to create a diversified portfolio.  All their money is tied up in the one business.  As a consequence, an owner in a private business does care about firm-specific risk, a lot!

Alternative beta calculation

Market beta can be calculated using the above formula.  The correlation coefficient (R) is multiplied by the ratio of the standard deviation of a stocks returns (the dependent variable y) to the standard deviation of the market’s returns (the independent variable x).

The correlation coefficient represents how much of a stock’s performance can be explained by the market’s performance.  The standard deviation represents how much the returns deviate from the average returns.  A higher standard deviation, a higher deviation from the mean, which implies greater stock volatility and so higher risk.

A regular market beta measures only the additional risk, the market risk, the company adds to an already diversified portfolio. Total beta measures both market and firm-specific risk.

Total beta formula

Total beta is simply the ratio of the standard deviation of the stocks returns to the standard deviation of the market returns. Therefore, using the market beta equation, total beta (as illustrated above) is equal to the market beta divided by the correlation coefficient, R.

On the assumption that an investor in a private business is unable to diversify away firm-specific risk, then firm-specific risk needs to be incorporated into the cost of equity when valuing a private business.

Peter Butler and Keith Pinkerton published an initial article in 2006, explaining how Total Beta can be used to quantify company-specific risk and that article is attached. Clearly, if the regression analysis is unreliable total beta is also unreliable, but that logic also applies to market beta.

 A host of articles relating to the Butler and Pinkerton model (both supporting articles and criticisms) can be found at the ever helpful BVR website here: https://data.bvresources.com/defaulttextonly.asp?f=bpmarticles.

Simon is a CA Business Valuation specialist, Chartered Accountant and a Certified Fraud Examiner. Simon specialises in providing valuation services. Prior to founding Lotus Amity, he was a Corporate Finance and Forensic Accounting partner with BDO Australia. Simon provides valuation services in disputes, for raising finance, for restructuring, transactions and for tax purposes.

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