Most common mistakes when calculating a CAPM beta

In the aim of conducting a business or an asset valuation

The Weighted Average Cost of Capital has entered the court of justice where it is used to discount or capitalize cash flows or earnings in order to estimate damages and compensations. However, in many instances, judging by the reliability of a WACC assessment is a true challenge that unfortunately, cannot be left to individual lacking expertise. When calculating a WACC, valuers and appraisers have to estimate the cost of equity. To do so, most practitioners resort to the numerous existing financial databases. However, their estimations do not converge (with ratios of 1 to 3 or more, it is a euphemism) and their methodologies are seldom transparent. An alternative option is to calculate a beta on your own. This allows your methodology to be transparent and incidentally demonstrates your expertise. The most employed (but not the least contested) model to do so is the capital asset pricing model (CAPM), which requires a particular input : the beta.

I have been teaching corporate finance for 30 years. I am currently teaching to future chartered accountants in France and I am also an examiner of their national exam. My experience of 10,000 hours of teaching corporate finance, about 300 written exams and corrected, and 25 years of participation in the national (French) CPA exams has exposed me to thousands of copies. It follows that I have been a continuous observer of how knowledgeable - or at least trained - people at a graduate management or finance level put the beta calculation into applications. This unique experience has given me the chance to identify the most common mistakes that are made by lay practitioners when estimating the cost of equity. In this post, I share those with you.

This post will be of interest to all DSCG students preparing the French CPA exam, but also to all novice valuers seeking to improve their practices and to all users of expert valuers’ and appraisers’ works. This post is, however, of little interest to financial analysts or actuaries who make different uses of the beta.

As a reminder, the CAPM model is the following :

With:

§ E (ROEi), the expected profitability of asset i

§ Rf, the risk-free rate of return

§ Rm, the market rate of return

§ βi, the beta of security i

How do you put this model in practice? How do you estimate the risk-free rate of return ? How do you estimate the market rate of return ? How you we estimate the beta ?

In this post, I’ll focus on the following question: what knowledge do you need in order to calculate a beta ?

To compute a beta on your own, you will need:

· Knowledge in modern finance theory,

· Knowledge in financial markets,

· Knowledge in mathematics,

· Knowledge in statistics, some excellent mathematicians have only limited skills in statistics,

· Knowledge in excel to make your life easier…

In each domain of knowledge, I list the common mistakes that I could witness in copies, and in valuations made by more or less expert valuers. In bold, I highlight what seems to be the most common mistakes in a domain of knowledge.

**Knowledge in modern finance theory** will help you understanding what you are doing, but also the limitations of your calculation. CAPM is a model attempting to capture what return shareholders are expecting from their investment in a financial asset. Hence, it is only an predicted estimation and in no manner, it is an observation.

The beta measures how an individual asset moved in comparison to the overall financial market movements. It does not measure the risk of the asset; it rather measures the contribution of an individual asset to the risk of the market portfolio. Notably the portfolio is taken as a representation of the market and is not fully diversified.

When calculating a CAPM beta, top mistakes related to finance theory are:

1- Interpreting the beta as a measure of the idiosyncratic risk (asset-specific risk),

2- Considering that the beta is a stable measure over time.

ð Beta moves over periods, therefore the period of observation (and data collection) is instrumental.

**3- Thinking that the beta is an output of the CAPM.**

4- Confusing top down betas and bottom-up betas, thus not being able to describe the nature of the risks captured in the betas.

ð Top down betas are calculated from stock and index prices whereas bottom up betas are estimation based on samples of comparable companies.

5- Making inappropriate use of the unlevered beta.

ð Unlevered beta is the beta of a company that would finance its investment with equity only.

**Knowledge in financial markets** will help you to identify on which financial market the financial instrument is listed and the appropriate stock market index amongst the large variety of existing indexes. Several rules govern that selection, they relate to the coverage of the index, to the index components and to the index methodology.

The most challenging input of the CAPM model is the market premium. It is provided by many data providers, who use different methodologies and unfortunately, rarely disclose those. Thus, the market premium estimations are very different from one data provider to another. This may cause some consistency problem across all your inputs. Moreover, the updating pace is different across providers and some databases are only updated once a year. For example, the famous Damodaran’s open data is very useful for finance teachers but much less relevant for practitioners.

When calculating a CAPM beta, top mistakes related to financial markets are:

1- Defining an index coverage that does not match your scope of interest.

2- Forgetting to check the components of the index.

3- Using a market period which calculation methodology that differs from your methodological choices (periodicity, profitability measures, matching average calculation procedures, etc.).

**4- Using unreliable or incompatible data sources.**

5- Using inconsistent risk-free rate of return and risk premium inputs.

6- Confusing historical approaches and implied approaches.

7- Selecting a risk-free rate of return that is not risk-free.

8- Selecting inconsistent time series lengths.

**Knowledge in mathematics **is also necessary. The market model is a simple regression explaining the market model that estimates the profitability of a financial instrument as a function of the market profitability. The CAPM, however, explains the profitability of the financial instrument as a function of its beta. Knowledge in mathematics will also help you to produce the correct time series needed to run the model. Time series require specific precautions when estimating averages, this is an issue in mathematics and statistics.

When implementing the CAPM, you’ll need to make methodological choices : how to deal with time series, how to calculate profitability, averages, pick a valuation model, a market price and a growth rate.

When calculating a CAPM beta, top mistakes related to mathematics are:

1- Introducing beta as an output of the CAPM.

2- Picking an inappropriate valuation model.

3- Picking an inappropriate growth rate or market price.

4- Lacking understand that implied cost of equity is derived from forecasts that do not make this assumption explicit.

5- Mismatching the number of observations in the time series.

**6- Calculating the profitability in the wrong direction because the downloaded series was ante chronologic.**

7- Calculating a beta on too short a period.

8- Calculating a beta on too long a period.

**Knowledge in statistics** is required in order to compute the beta. One needs to understand what a variance and a covariance are and mean, i.e., how they can be interpreted. The understanding of the differences between the theoretical and the empirical variance is also a necessity.

When calculating a CAPM beta, top mistakes related to statistics are:

1. Mismatching (geometrical/ arithmetical) profitability calculations method and average calculation methods.

2. Employing a theoretical variance and an empirical covariance, and conversely.

3. Forgetting to check the fit of the regression and other indicators of its quality, before drawing conclusions.

4. Misunderstanding biased estimations.

5. Calculating a biased beta.

**6. Calculating the descriptive statistics based on the observed prices and not on their variations.**

**Knowledge in accounting and financial reporting** is necessary because one can only rely on the entity’s financial statements. This requires understanding of the modalities of recognition of equity and liabilities, of their evaluation and reevaluation, and also of the way they are impaired. This information is either expressed at book value, or at market value, or at fair value. Market value of a financial debt is of particular interest when one wishes to compute a levered or unlevered beta.

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