Are you calculating beta(β) in valuation the right way?

"If you know what beta (β) is and how to calculate it, skip to point 3."

1. What is beta (β)?

Beta is a measure of risk of a stock/security/portfolio relative to the risk of the entire market.

Risk of the entire market is the risk that affects the overall market, not just a particular stock or industry and is also known as systematic risk. Systematic risk is the risk which cannot be minimized by diversification.

On contrary, Individual Investment's risk is the risk that affects only a particular stock or industry and is also known as unsystematic risk. Unsystematic risk is the risk which can be minimized by diversification.

"Diversification - Don't put all your eggs in one basket, diversify it."

Fact: We can only reduce/minimize the risk; we cannot eliminate it.

2. How to calculate beta (β)?

First of all, know that beta (β) is of two types: Levered beta and Unlevered beta.

1. Levered Beta: It is the beta which measures the risk of a stock/security/portfolio relative to the systematic risk of the entire market and includes the impact of a company's capital structure and leverage. And also known as Equity Beta.

• Calculation - Levered Beta: It can be calculated by using historical prices of a stock and calculate daily returns or the returns for the frequency of period you want to calculate beta i.e., daily, monthly, yearly, etc. And then use any of the method given below for calculating levered beta.
• Covariance and Variance method:

= COVARIANCE.S(Ri,Rm) / VAR.S(Rm)

where,

Ri = Return on stock/security/portfolio

Rm = Return on market

• Slope Method:

= SLOPE(Ri,Rm)

• Correlation Method:

= CORREL(Ri,Rm)*(STDEV.S(Ri) / STDEV.S(Rm))

NOTE: All formulas are excel formulas. And use sample for statistical formulas rather than population, as the data with us is not the whole population, we just have the sample of the returns of the stock as well as the market. But for other scenarios, choose as the case may be.

2. Unlevered Beta: It is the beta which measures the risk of a stock/security/portfolio relative to the systematic risk of the entire market and excludes the impact of a company's capital structure and leverage. And also known as Asset Beta.

• Calculation - Unlevered Beta:

Unlevered Beta = Levered Beta / (1 + (1-tax rate) * Debt / equity)

Unlevered beta can be levered by interchanging this formula i.e.,

Levered Beta = Unlevered Beta * (1 + (1-tax rate) * Debt / equity)

3. Why beta (β) is important in valuation, especially DCF?

Beta is an important element in calculating Weighted average cost of capital (WACC) through CAPM Model (Capital Asset Pricing Model) and hence due care should be taken while performing valuation using Discounted Cash Flow method of Income Approach to valuation. As WACC is the rate, with which Unlevered Free Cash Flows (UFCF) or Free Cash Flow to the Firm (FCFF) are discounted, to arrive at the Enterprise value of the company which is being valued.

4. But the question arises, is this beta (β) from these methods justified to be used in valuation?

All the three methods return the same beta, but the answer is "NO". Because of the following reasons:

• As beta (β) is calculated for a period (sample of returns for a period rather than whole population of returns) and in that period, there might be some noise and volatility in the stock which is due to some non-recurring big announcement or the big news which affects the stock's price, and the beta might not reflect the correct risk estimate of the company which is being valued. Outlier effect.
• And due to this, there is an inherent standard error in calculating beta (β). Standard error of beta (β) is an estimate of the standard deviation of the sampling distribution of the beta. It indicates the extent to which a company's true beta (β) may differ from its estimated beta.
• The section - calculation of unlevered beta, shows that either unlevered or levered beta should be known, for calculation of either of them. And this creates a room for subjectivity of how we are calculating one of these beta's and also how we are calculating debt/equity ratio, might affect the beta estimate.

NOTE: Remember, Debt/equity is the only ratio in which market values are taken into account for calculating it.

For equity, market value is market capitalization i.e., current share price multiplied by fully diluted shares outstanding.

For Debt, if market value is identifiable then take that, but in general due to lack of information, the book value of debt is assumed to be its market value on the ground that, it is the contractual amount that company owes currently, and it makes sense.

5. So how can we justify the beta (β), so that it can be used in valuation?

Although, due to inherent limitations in calculating beta (β) i.e., standard error of beta (β), we cannot calculate true beta (β), but we can converge towards it by using industry average for beta (β). And we use industry average for beta (β) calculation because of the following reasons:

• Using industry average for beta (β) can smooth out the noise and volatility that may affect the beta (β) estimates of individual investments, especially if they have a short or irregular trading history.
• Moreover, using Industry average for beta (β) can provide a consistent and comparable benchmark for different investments within the same industry, as it reflects the average risk profile of the industry.
• To minimize the inherent standard error in calculating beta (β).

6. How to calculate Industry average for beta (β)?

So, should we take directly, the average of the industry beta (β)?

"NO".

Although, the companies are operating in the same industry for which we are calculating beta (β), but all have different capital structure and leverage which can affect the beta (β) estimate.

Therefore, we should be Un-levering and Re-levering the beta (β) of the industry as per the following steps:

1. First, we have to find beta (β) for similar firms using stock prices i.e., levered Beta (β) using the formula for levered beta (β) mentioned above.
2. Un-lever the beta (β) for each firm using the unlevered beta (β) formula mentioned above.
3. Now, take the average of unlevered beta's. This is the industry's average beta (β) assuming no debt.
4. Then, Re-lever it for the firm you are valuing, using its own debt/equity, by using the formula for levered beta (β) mentioned above.

That's it.

In general, for private companies, beta (β) is calculated using industry average because it does not have the price history to calculate beta (β). But in case of public companies also, while valuation modeling, beta (β) should be calculated using industry averages for valuation purposes because of its inherent limitations in calculating it.

So, next time use the industry average for beta (β) calculation to reflect the correct valuation of the company which you will be valuing.

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Author: Mohit Bhatnagar, FMVA? #ValuationInsights