Beta (β)

How to Calculate Beta (β) in Finance

Beta (β) represents a company’s sensitivity to market volatility – otherwise referred to as systematic risk – compared to the broader market, which is used as the standard benchmark.

An integral component of the capital asset pricing model (CAPM), beta quantifies the relationship between systematic risk and the expected return.

Moreover, there are two distinct types of beta measured in corporate finance:

• Levered Beta → Inclusive of Capital Structure (D/E) Effects
• Unlevered Beta → Removed Capital Structure (D/E) Effects

From the perspective of investors, the beta coefficient is the exposure of an asset (or security) to systematic risk and determines whether it is more or less volatile than the market as a whole.

The most frequent use-case of beta in corporate finance is the capital asset pricing model (CAPM), in which beta is a critical component of calculating the cost of equity – i.e. the required rate of return for equity investors.

Beta provides a method to estimate the degree of an asset’s systematic (non-diversifiable) risk.

The process of manually calculating the beta of a company involves the following steps:

1. Calculating the covariance between the expected returns on the security and the returns of the overall stock market (market indices such as the S&P 500 are often used as the proxy)
2. Dividing that figure by the variance of expected returns on the stock market

How to Interpret Beta (β) and Market Sensitivity?

The general rules of thumb for interpreting beta are as follows.

• β = 1: Shares are just as risky as the market (no market sensitivity)
• β > 1: Shares are riskier than the market (high market sensitivity)
• β < 1: Shares are less risky than the market (low market sensitivity)
• β = 0: Shares have no correlation to the market (no market sensitivity)

The overall stock market is said to have a beta of 1.0, so companies with a beta of 1.0 should be expected to provide returns at an identical rate to the overall stock market, on average.

But if a company has a beta of 2.0, it should expect to realize returns that rise twice as fast (or decline twice as fast) compared to the broader market.

Levered vs. Unlevered Beta: What is the Difference?

Before discussing the differences between levered beta vs. unlevered beta, it’d be best to take a step back by defining the two types of risks.

Since unsystematic risk is company-specific and can be diversified away, especially if the portfolio contains investments in a wide range of industries with different traits, unsystematic risk is ignored in the capital asset pricing model (CAPM).

However, systematic risk is the market risk that cannot be diversified away.

As a result, the market will require higher potential returns and more compensation for assuming systematic risk (which increases the cost of equity).

Simply put, systematic risk is caused by external factors that are beyond the control of a specific company or organization.

All securities, some more than others, are exposed to systematic risk, which is otherwise known as “non-diversifiable” risk as it cannot be reduced by increasing the number of portfolio holdings.

Levered Beta Formula

Often referred to as the “equity beta”, a levered beta is the beta of a firm inclusive of the effects of the capital structure.

Generally speaking, a higher debt-to-equity ratio should cause the risk associated with a company’s equity shares to increase – all else being equal. The more debt on a company (and the higher the debt-to-equity ratio), the higher the risk of default (and the equity holders possibly getting left with nothing).

When calculating levered beta, the formula consists of multiplying the unlevered beta by 1 plus the product of (1 – tax rate) and the company’s debt to equity ratio (D/E).

Unlevered Beta Formula

Unlevered beta, on the other hand, removes the effects of using financial leverage to isolate the risk related to a company’s assets. Since unlevered beta represents pure business risk, it should NOT incorporate financial risk.

For that reason, unlevered beta is often called “asset beta” because it measures the expected volatility of the security (and underlying company) as if the capital structure is comprised of only equity financing.

The levered beta of a firm is different than the unlevered beta as it changes in positive correlation with the amount of debt a firm has in its financial structure.

When it comes to unlevered beta, you can essentially assume that the company is financed entirely with equity with no debt financing – and all free cash flows (FCFs) belong to the equity holder(s).

As a result of removing the debt component from the levered beta, you can understand the actual contribution of a company’s equity to its risk profile.

To calculate unlevered beta, the formula divides the levered beta by [1 plus the product of (1 minus the tax rate) and the company’s debt/equity ratio]. Typically, a company’s unlevered beta can be calculated by taking the company’s reported levered beta from a financial database such as Bloomberg and Yahoo Finance and then applying the formula below.

Criticism of Beta as a Measure of Risk

The use of beta as a proxy for risk has received widespread criticism from many practitioners, who believe it to be a flawed measure of risk.

The standard process for estimating beta is through a regression model that compares the historical stock returns to the market benchmark returns (e.g. S&P 500) for a specified duration, with the slope of the regression line corresponding to the beta.

Since past performance is not necessarily an accurate indicator of future performance, the “backward-looking” aspect of the beta calculation is one notable drawback.

Seth Klarman Comments on Beta

“The reality is that past security price volatility does not reliably predict future investment performance (or even future volatility) and therefore is a poor measure of risk.”

– Seth Klarman, Margin of Safety

Another concern is that the capital structure (debt/equity ratio) of companies, which is a key determinant of volatility (and market performance), changes over time as companies mature and new developments in industries emerge.

Beta reflects a company’s business risk over the period used in the regression model, which can be misleading if the company has undergone significant changes in terms of its business model, target customer, etc.

Lastly, beta is typically based on the historical average financial leverage (i.e. capital structure) over the regression period, rather than the current debt-to-equity mix.

But despite the frequent criticism, the usage of beta in academia and on the job has remained, largely due to the lack of a more suitable alternative.

Warren Buffet Criticism of Beta: Limitations of Risk Measure

One vocal proponent against the use of beta in finance is Warren Buffett.

According to Buffet, beta is ineffective because the model mistakenly assumes volatility as a risk when significant price declines could represent some of the most profitable opportunities to purchase undervalued securities.

Therefore, rather than viewing volatility as a sign that the stock is risky and less valuable, one should perform a fundamental analysis to determine if the shares are indeed underpriced – and then the focus should be on the “margin of safety” (i.e. downside protection).

^{Warren Buffet Commentary on Risk (Source: Graham-and-Doddsville)}

To Buffet, the concept of risk instead represents “the possibility of harm or injury” (i.e. losing your initial capital) from inadequate research and/or ignorance.

Beta Calculator

We’ll now move on to a modeling exercise, which you can access by filling out the form below.

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1. Levered Beta and Capital Structure Assumptions

In the first part of our tutorial, we’ll calculate the unlevered beta starting from the levered beta.

Here, we look at three companies with different assumptions for the levered beta and varying capital structures.

The only constant assumption across all companies is the 35.0% tax rate.

For each company, the following assumptions will be used throughout the exercise:

Company A Assumptions

• Levered Beta =1.00
• Debt = $120mm
• Equity = $600mm

Company B Assumptions

• Levered Beta = 1.20
• Debt = $50mm
• Equity = $500mm

Company C Assumptions

• Levered Beta = 0.80
• Debt = $200mm
• Equity = $400mm

Since we have the debt and equity figures for each company, the calculation of the debt/equity ratio is straightforward:

Debt to Equity Ratio (D/E)

• Company A = 0.2x
• Company B = 0.1x
• Company C = 0.5x

2. Calculate Unlevered Beta from Levered Beta

Based on the financial data we’ve collected so far, the pattern between levered beta and the debt/equity ratio should be clear.

Generally speaking, the lower the levered beta, the higher the debt/equity ratio tends to be – albeit there are several exceptions to the rule, which are often related to management irresponsibility and favorable credit market conditions.

However, for the most part, less volatile companies typically have more consistent free cash flow (FCF) generation and can raise more debt financing because lenders are more comfortable given the company’s track record of profitability.

Lower volatility relative to the market can often be perceived as a positive sign that the company (i.e. the borrower) could withstand a downturn in the economy and still meet its interest payments and mandatory amortization requirements on time – which are qualities that risk-averse lenders seek.

Returning to our calculation of unlevered beta, all that remains is to plug our assumptions into the formula we discussed earlier.

The unlevered beta for each company is as follows:

• Company A = 0.88
• Company B = 1.13
• Company C = 0.60

From our formula, in which we de-levered beta (i.e. removed the effects of leverage), we are now left with the business-specific risk of each company, as intended.

3. Levered Beta Calculation (Re-Levered)

In the next section, we’ll calculate the levered beta using the formula we went over earlier.

While the levered betas were hardcoded assumptions, if done properly, the hardcoded values and the calculated values (converting unlevered beta back into levered beta) should match.

To have a clean model to work with, we’ll first link the required assumptions from the section above to have a separate section (and a more dynamic model).

Considering we already have all the required inputs, the only real row where we’ll be actively entering a formula is “Levered Beta” (Row 31).

The levered beta for each company is as follows:

• Company A = 1.00
• Company B = 1.20
• Company C = 0.80

In conclusion, the levered betas that we arrived at match the stated levered beta assumptions from earlier, confirming that our formulas were entered properly.