Calculating and analysing the drivers of Equity Beta

Equity beta is a valid measure of investment risk and an important metric in equity analysis. However, don’t just plug into your models the equity beta given by a data provider – beta should be analysed and adjusted by investors with the same diligence that is applied to performance metrics.

We present an interactive equity beta analysis model to assist investors in better understanding the drivers of equity beta and its application in equity valuation. The model features the calculation of beta (and its volatility and correlation components) for any investment for which price data is available in Microsoft Excel.

It is generally accepted that investors are risk averse and consequently require a higher rate of return from more risky investments. A higher required return translates into a higher discount rate in DCF valuations, and a lower enterprise or equity valuation multiple. What is less clear is how risk should be measured and how risk can be translated into a required return.

The best known and widely used method to identify a risk-adjusted discount rate is the Capital Asset Pricing Model (CAPM). The model gives the investor required return as the sum of the return on risk free assets (government bonds) and the premium investors demand to invest in a diversified ‘market portfolio’ of risky assets (i.e. equities), scaled by a beta factor.

Investment required return = Risk free rate + Equity risk premium x Investment beta

Although CAPM has solid theoretical foundations, the model is based on a number of fairly restrictive assumptions including:

Risk can be measured by the volatility (standard deviation) of investment returns.

Returns are normally distributed.

Markets are ‘perfect’ where investors are able to effectively diversify and there are no distortions due to, for example, taxation.

A market portfolio can be identified that applies to all investors.

CAPM has merit despite the restrictive assumptions and its limitations

These assumptions (and challenge of obtaining empirical evidence that CAPM actually works) has led to criticisms of the model and various attempts to extend and modify the theory. Nevertheless, we think that an unadjusted CAPM still has merit. Subjective adjustments by investors to the CAPM result may be just as effective as complex additional modelling.

To use CAPM in practice it is important that investors understand, and can effectively estimate, the beta of equity securities¹, which is the main purpose of this article. We do not consider here the other difficult component: the equity risk premium. See our article ‘Intrinsic value and the equity risk premium’ for more on this subject.

Equity beta

An equity beta² can be described in a variety of ways, including the slope of a regression of stock returns on market returns and the ratio of the covariance of stock and market returns relative to the variance of the market. We do not believe either of these descriptions provide investors with much insight into risk, or provide a basis on which to make judgements for valuation. Our preferred formulation of beta (which is mathematically equivalent to the others we mention) is based on correlation and standard deviation (volatility).

Beta = Correlation of stock and market returns x stock volatility / market volatility

This calculation emphasises the total risk of a stock (volatility) and the non-diversifiable element of this risk (correlation x volatility). It is this non-diversifiable (also called systemic or systematic) risk of a stock which affects the risk of a diversified portfolio that includes the investment. If sufficient investors are well diversified, such that prices reflect only non-diversifiable risk (which we think is a reasonable assumption), then equity beta should matter.

While beta may not fully explain how investors factor risk into equity valuation, we think that the importance of both volatility and correlation³ can be clearly observed in equity markets, and with this the relevance of beta for equity analysis and valuation. However, do not simply plug a historical beta obtained from one of the data providers into your models without further analysis and investigation.

Understanding historical betas, their drivers and historical development facilitates better forecasts

The equity beta that should be included in the calculation of a discount rate should reflect risk during the relevant period of discounting. This means betas should be forward looking, much like DCF valuations require forecasts of cash flows rather than historical cash flows (although a historical beta is more likely to be relevant for equity valuation than a historical cash flow). The first step to forecast a beta is to understand historical betas and their volatility and correlation components. This includes understanding why these values differ depending on the dataset of prices used, the statistical margin of error involved, and how changes in beta over time relate to changes in the business and its financing.

The calculation and analysis of equity beta

We have developed a simple model to illustrate the type of historical beta analysis that we think is useful. The blue inputs in the model below change the sample of data used for the beta calculation, with the ability to separately change the time period used in the charts.

The downloadable version has further instructions and explanations and includes links to Microsoft Excel ‘Rich Data’ which enable beta calculations for most global stocks and the selection of different indices. The data access requires an Excel 365 subscription – older versions of Excel do not work. However, because we cannot embed an Excel model with live data links in this web page, the version below includes cached data only for Carnival Corp (one of the companies we discuss below).

Please note that the model is intended for educational use only. The model has some approximations due to the limitations of Microsoft Excel price data, including having to use ETF proxies for indices. A link to other data sources would have probably been better, but we used the freely available data in Excel so that all of our readers can use the model. Nevertheless, we believe the model works well and effectively illustrates the sort of historical risk analysis that investors should be aiming for.

Interactive model: The calculation and analysis of equity beta

— iPhone and iPad users: This model formats best if viewed in Google Chrome —

This is an interactive model – inputs shown in blue can be changed

To see the full model, including further explanations about its use, and to be able to access live price data for most global stocks, please use the downloadable excel version. You will need an Excel 365 subscription that supports “rich data” to access live price data. This model is for educational use only and we go not provide any warranty of its accuracy. See our disclaimer here.

DOWNLOAD THIS MODEL

Please enter your email address to receive an excel version of this model

Margin of error and choice of data set

All historical beta factors are based on a sample of price data. In our model you can choose any historical time period over which to calculate beta of up to 10 years (5 years for the charts) and any frequency of returns from 1 day to 21 day (approximately monthly) returns. There is no one correct historical beta, merely different estimates based on different samples.

A key feature of our model is the presentation of a 95% confidence interval⁴ for the components of beta, as well as for the beta itself. The combination of time period and frequency determines the number of data points used in the calculation. A higher number of data points reduces the statistical margin of error, which we illustrate for US Pharma company Pfizer in the table below.

Pfizer Inc. – Equity beta estimates based on different data samples

Data derived from The Footnotes Analyst beta analysis model using a global index.

Notice how the 95% confidence interval is narrower for longer time periods and a shorter return interval. However, longer, and more frequent, is not necessarily the best approach. A longer period increases the risk that the price changes reflect a business with characteristics that differ from those today and, consequently, the beta estimate is more out of date.

We calculate historical betas primarily to estimate current or future levels of risk; more recent data increases the likelihood that the historical measure has predictive value. For Pfizer there is some evidence that beta has fallen over the last few years, even after allowing for the wider margin of error. Here is a chart showing a time series of a 3 year / daily data beta.

Pfizer Inc. – Equity beta

To reproduce this chart, use the stock ticker XNYS:PFE in the downloadable model and select the global MSCI index for the US time zone. We used daily data and a 3 year interval.

Although using daily price changes produces the lowest margin of error, in cases where there is limited liquidity in a stock, daily data can underestimate the stock volatility and correlation, and consequently understate beta. It is often more reliable to use a longer interval to calculate returns for small-cap stocks.

In addition to the sample size, the margin of error for beta factors is affected by the combination of correlation and volatility. Low correlation but high volatility tends to produce a much larger margin of error for beta. This is illustrated by the chart below which shows the historical equity beta for Californian utility company PG&E.

PG&E Corporation – Equity beta

To reproduce this chart and see the related correlation and volatility data, use the stock ticker XNYS:PCG in the downloadable model and select the global MSCI index for the US time zone. We used daily data and a 2 year interval.

PG&E has historically had a relatively stable beta of about 0.5 with a low margin of error. However, the company was implicated in a series of Californian forest fires, most notably the deadly November 2018 ‘Camp fire’, which ultimately cost the company billions in compensation. The uncertain outcome of this at the time resulted in a large increase in stock volatility, which at one point reached an annualised 120%. However, most of this increase in risk was company specific (idiosyncratic) and hence diversifiable, which resulted in a lower correlation coefficient – correlation fell from about 0.4 to less than 0.1. The combination of lower correlation and higher volatility produced the significant increase in the margin of error for the beta calculation that can be seen in the chart from 2019 to 2021.

The forest fire related compensation claims against PG&E are now resolved, such that correlation has returned to closer to its historical norm. However, volatility and the equity beta remains elevated, which is probably the result of the higher financial leverage due to the cost of compensation claims, although this was subsequently mitigated by an issue of new equity shares.

Global or local index

In addition to different samples of price data, the other factor that affects a beta calculation is the selection of the index to which stock returns are compared. This index could be global, regional, or local. As with the price sample, there is no one correct approach. For major markets, particularly the USA, the choice of a local or global index often makes little difference. However, this is not always the case, particularly for smaller markets that may be less diversified.

Use a global index if equity markets are integrated, and particularly for large-cap stocks

A key consideration in selecting the index is whether global equity markets are integrated or segregated. In an integrated market investors diversify internationally, compare stocks with global peers and select stocks based on their global risk and return characteristics. In a segregated market investment decisions and portfolios are considered within that market. Clearly there are investors with both a global and local view, the question is whether global investors are sufficient to ensure that stock pricing, and the risk included in that stock pricing, is global.

We think that equity markets are increasingly integrated and that it is best to generally use a global equity index, particularly for companies that are larger and more actively traded by international investors. An advantage of a global approach to CAPM is that it means applying a single global equity risk premium rather than having to estimate different values for different markets.

If you do use a global index, be careful to ensure that the time zone of the index and the currency in which it is presented, correspond to those of the stock. A different time zone in particular is likely to produce a spurious low result, especially when using daily returns.

Focus separately on volatility and correlation

Our analysis of the historical development of the PG&E equity beta illustrates how the drivers of volatility and correlation can differ and how changes in these risk metrics can be linked to changes in the business and its financing. We suggest that investors should separately focus on volatility and correlation when seeking to understand historical risk metrics.

What determines correlation

Most stocks have significant positive correlation with the market. For example, the average correlation of individual stocks in the US S&P 500, with a global index, is about 0.60. However, correlation also varies considerably. According to CAPM, and as evidenced by investor behaviour, differences in correlation matter.

The degree of correlation depends on the nature of the underlying business, the range of activities of the business (including geographical spread) and the size of that business. Correlation is not affected by leverage.

Stock specific risk factors: Risk factors that are company specific, such as those arising from litigation or reputational issues, tend to be uncorrelated with the equity market. As with PG&E above, these risk factors tend to increase volatility and reduce correlation, and can leave beta largely unaffected.

Type of business activities: If the profitability of a business is closely tied into the success or otherwise of the economy then correlation will be high. For example, banks tend to have high correlation. A more specialist business, or one where success depends on the outcome of a particular business venture, such as biotechnology, will tend to have lower correlation and often, as a result, a lower beta. The average correlation for the largest 25 US banks is about 0.64, whereas for the largest 25 NASDAQ listed biotechnology companies it is 0.32.

Range of business activities: Greater diversification at the stock level tends to increase the correlation with the index. Conglomerates and multi-nationals will tend to have higher correlation than companies with just one activity focused on just one market. However, this does not necessarily imply a higher equity beta because greater diversification at the stock level will likely result in lower volatility.

Size of business: Larger companies tend to have higher correlation, partly because they will tend to have a larger range of business and geographical exposure, but also because mega-cap stocks can form a significant part of an index.

What determines volatility

Volatility is determined by both the nature of a business and by how the business is structured, particularly the degree of leverage, and the size and diversification of that business.

Type of business activities: Companies that operate in sectors where there is greater business uncertainty tend to have higher stock volatility. For example, the largest 25 utility companies in the USA have average volatility of 30%, whereas the equivalent for biotechnology is 42%⁵.

Structure of the business: Companies that operate in the same sector can still have very different levels of volatility because of how that business is structured. For example, a company that has greater exposure to property assets due to an ownership rather than short-term leasing business model, will likely have lower volatility. In effect, a property ownership business model means that the business is a combination of a lower risk real estate company and a (potentially) higher risk operating business, with the real estate exposure reducing the overall risk profile⁶. The degree of outsourcing can have a similar effect.

Financial leverage: Companies with higher financial leverage (debt finance relative to market capitalisation) will have higher stock volatility. Operating risk is concentrated largely in equity capital, with limited sharing with debtholders. Higher leverage increases the degree of risk concentration. Cruise operator Carnival Corp (XNYS:CCL) is a good example. Prior to Covid-19 Carnival had an equity beta (2 year, daily returns and global index) and leverage (D/E) at Dec. 31, 2019 of 1.02x and 41% respectively. After the effects of Covid-19 related price changes drop out of the calculation⁷ the beta factor has more than doubled to a little over 2.0x. Although other factors may have contributed, it seems the main reason is the higher financial leverage. At Dec. 31, 2022 debt was 340% of market capitalisation (although the stock price increase in 2023 has reduced this to currently about 195%) and the equity beta is 2.11x. The impact of leverage on beta, and the calculation of deleveraged ‘asset betas’, is important topic in equity valuation, but not one we consider further in this article.

Carnival Corp – Equity beta and volatility

To reproduce this chart, use the stock ticker XNYS:CCL in the downloadable model and select the global MSCI index for the US time zone. We used daily data and a 2 year interval.

Pension fund investment: A further source of leverage arises from defined benefit pension funds. A pension fund deficit has a similar effect on volatility and equity beta as debt finance. Furthermore, if the fund asset allocation is not matched with the fund liabilities, additional ‘asset allocation’ risk can arise, with a further increase in volatility (and can also impact correlation). We include an interactive DCF model in our article ‘DCF and pensions: Enterprise or equity flow?’, where we demonstrate how pension leverage and pension asset allocation risk affect beta and cost of capital.

Why ‘forecast betas’ may not be forecasts

The betas that are quoted by data providers, and those presented in our model, are historical betas. They are all derived from past price changes with some, but not all, data providers providing flexibility over the sample, similar to our model above.

So-called ‘forecast’ betas are likely still be based on past data

You may find some data provider betas labelled as ‘forecast’, but this can be misleading. The calculation is still based on past data, but the result is subject to statistical adjustment. A common adjustment is to make the result closer to 1.0x by taking the weighted average of 1.0 and the ‘raw’ historical beta, commonly a 1/3 weighting for 1.0x and 2/3 for the raw beta. Alternatively, the adjustment may depend on the standard error of the beta estimate. The idea behind these adjustments is that beta factors will tend to regress towards 1.0 in the long-term and that, because beta is subject to statistical error, and we know that betas on average must be 1.0x, then a compression towards 1.0x removes some of the statistical error.

We are sceptical about the merits of these adjustments. In our view, betas are often persistently higher or lower than 1.0x, reflecting the sector and business characteristics. For example, we do not think it appropriate to move the Carnival Corp equity beta shown above to nearer 1.0x. It is above 2.0 for a good reason – high leverage. If leverage falls, then use a lower equity beta, but not before.

Mix and match – different estimates for different components

There is no reason why the same data must be used to determine each component of a beta factor. The volatility measures for the stock and index should be consistently calculated but correlation could well be based on a different data set.

For example, if a company has experienced a recent change in financial leverage, a historical volatility measure over, for example, 5 years is unlikely to result in an estimate that is relevant for a realistic current beta factor. It is better to use a period after the change in leverage (use the same period to measure market volatility). However, correlation is primarily determined by the nature and size of a business and is not impacted directly by leverage. Therefore, the correlation measure included in the beta calculation could be based on a longer period of price changes, thereby reducing the statistical margin of error (assuming, apart from leverage, the business has not changed significantly over the longer period).

Implied volatilities combined with historical correlation may give a better estimate of beta

An alternative to using a different time period is to use a forward-looking measure of volatility. If traded options are available for the stock and index, implied volatility can be included in an equity beta calculation. Unfortunately, there is no market implied measure of correlation, and this component of beta will always have to be estimated using historical price changes.

We applied this approach to Carnival Corp where the current (1 month) implied stock volatility of 40.4%, is significantly lower than the historical volatility over the last 2 years of 66.2%. Using implied volatility, the equity beta is about 1.4x, significantly lower than the historical beta of 2.0x.

Historical versus implied volatility based beta for Carnival Corp

Data derived from The Footnotes Analyst beta analysis model. Historical data sample is 2 years of daily data, and the selected index in this case is S&P 500. Implied volatility estimated at Sept 24, 2023.

Although a 1-month implied volatility⁸ may not accurately reflect the market perception of longer term equity risks for Carnival, the fact that the implied volatility beta is significantly lower than the historical measure certainly deserves further investigation. Interestingly, the lower beta estimate is consistent with our earlier observations about the recent increase in the Carnival stock price and the resulting reduction in (market value based) leverage.

It will be interesting to see whether the historical volatility based beta falls over the coming months.

Insights for investors

Beta and CAPM are relevant for investment decisions, even though they may not give the full picture of investment risk. Beta affects both valuation multiples and DCF discount rates.

Don’t simply look up betas from a data supplier. Do your own calculations and consider different data sets, but always be mindful of the statistical margin of error.

Separately analyse the volatility and correlation components of beta. Linking their historical development to changes in the business and financing helps to better understand and forecast risk.

Remember to select an index expressed in the same currency and for the same time zone as the stock or fund you are analysing. Generally, we recommend using a global index, particularly for large-cap stocks.

Don’t be afraid to mix and match the different components of beta. Implied volatilities combined with historical correlation may give a more relevant measure of equity beta.

Don’t miss new articles published by The Footnotes Analyst – subscribe here:

No advertising, no spam, just new articles. Unsubscribe anytime.

Send us a question or comment about this article:

For more articles select subject tags:

Or see suggested related articles below:

Cookie	Duration	Description
cookielawinfo-checkbox-analytics	11 months	This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Analytics".
cookielawinfo-checkbox-functional	11 months	The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional".
cookielawinfo-checkbox-necessary	11 months	This cookie is set by GDPR Cookie Consent plugin. The cookies is used to store the user consent for the cookies in the category "Necessary".
cookielawinfo-checkbox-performance	11 months	This cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Performance".
viewed_cookie_policy	11 months	The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. It does not store any personal data.