# What is Beta in Finance: Explained by Graduate Tutor

CFAs and MBAs will encounter the word beta early in their finance courses. Beta is a critical component in corporate finance. There are different types of betas and multiple aspects to betas. This article considers the various aspects of beta in finance.

## What is Beta in Finance?

The beta captures the risk profile of an asset/security/investment in relation to the market. So, it reflects how closely an investment’s returns move with that of the market returns. There are different types of assets, and so you can have different types of betas. For example, if the asset/security/investment is equity (stock), its beta is called equity beta. If the asset/security/investment is debt, its beta is called debt beta.

## What is Equity Beta in Finance?

The equity beta of a stock reflects how closely that equity stock’s returns move with that of an index/market returns. The equity beta is also referred to as the market risk of that equity because it is measured in relation to the market.

### What does an equity beta of one indicate?

An equity beta of one indicates that the stock return will move exactly in line with the market. For example, if that market provides a 10% return, a stock with an equity beta of 1 will also have a 10% return. Similarly, if the market drops by 5%, this stock will also drop by 5%.

### What does an equity beta greater than one indicate?

An equity beta of 1.5 indicates that if the market moves up by 10%, this stock will move up by 15% (10% x 1.5). On the other hand, if the market drops by 5%, this stock will drop by 7.5% (-5%1.5). You will see that it has higher peaks and deeper troughs! A stock with an equity beta greater than one will have higher volatility than the market.

### What does an equity beta less than one indicate?

Along the same lines, a stock with an equity beta of less than one will have lower volatility than the market. For example, an equity beta of 0.5 indicates that if the market moves up by 10%, this stock will increase by only 5% (10% x 0.5). On the other hand, if the market drops by 5%, this stock will drop by only 2.5% (-5%0.5). You will see that it has lower peaks and lower troughs! A stock with an equity beta lower than one will have lower volatility than the market.

## What range of values can beta have? Can equity beta go negative? What does an equity beta less than zero indicate?

MBA or CFA students may think that equity betas start from 0. However, you can have equity betas be less than 0 or negative betas. A negative beta indicates that the stock moves in the opposite direction of the market. If the market moves up, a negative beta stock moves down. For example, an equity beta of – 0.5 indicates that if the market moves up by 10%, this stock will move down by -5% (10% x -0.5). Typically, countercyclical stocks/industries have negative betas. This is because they move in the opposite direction of the business cycle.

A beta of one indicates the stock’s performance moves in line with the market. Betas can take on values greater than one too.

## If beta is a measure of risk, how is it different from variance or standard deviation?

Beta is indeed a measure of risk. However, beta is a measure of risk relative to a specific market. Whereas variance and standard deviation are measures of volatility as measured against the expected value.

In other words, beta is a bivariate measure. In comparison, variance and standard deviation are univariate measures.
Beta measures volatility relative to the market. That is why the equity beta is also referred to as the market risk. Whereas variance and standard deviation measure volatility against the mean.

## What kind of companies/industries have a beta greater than 1?

An equity beta great than 1 indicates that the company’s stock is more volatile than the market. In other words, a stock with an equity beta greater than 1 has swings, both ups, and downs, which are larger than the market’s swings.
A beta great than 1 indicates that the best fit line of the company’s stock returns vs. market returns is steeper (slope is higher). Remember the slope is the beta. You can visualize this in the graph. If you move 1 unit to the right on the x-axis, you will move more than 1 unit on the y-axis. Given that these are the returns on the company’s stock returns vs. market returns, this indicates for a given change in the market, the company’s stock price will change at a higher rate and in the same direction.

Generally speaking, industries such as retail, restaurants, air transportation, home building, auto, etc. have betas higher than 1. (Jan 21)

Professor Aswath Damodaran maintains an industry database that lists betas of various industries here.

## What kind of companies/industries have a beta less than 1?

A beta of less than 1 indicates that the company’s stock is less volatile than the market. In other words, its swings up and down are lower than the market.

A beta less than 1 indicates that the best fit line of the company’s stock returns vs. market returns is flatter than other companies (less steep slope). Remember, the slope of the trend line is the stock’s beta. You can visualize this in the graph. If you move 1 unit to the right on the x-axis, you will move less than 1 unit on the y-axis. Given that these are the returns on the company’s stock returns vs. market returns, this indicates that the company’s stock price will change at a lower rate and in the same direction for a given change in the market.

Generally speaking, industries such as utilities, insurance, tobacco, beverages, etc., have low betas. (Jan 21)

Professor Aswath Damodaran maintains an industry database that lists betas of various industries here.

## What are the uses of beta?

The beta is used to arrive at the cost of capital in the Capital Asset Pricing Model (CAPM).
The beta of a stock is also used to estimate the amount of risk you will add to a well-diversified portfolio (remember, the beta is a measure against the market).

## What inputs/ingredients do you need to compute the beta?

Since the beta measures the relationship of the company’s stock return vs. the market return, what you need is essentially the company’s stock prices and the market levels over some time. From the company’s stock prices and the market levels, you can compute the company’s stock returns and the market returns over each period. From here, you can use any of the three methods described in this article below to arrive at the beta.

## How do you compute the beta?

The beta can be estimated from the regression line of the company’s return vs. the market return. It is essentially the slope of the best fit line in a scatter graph when plotting the company’s return vs. the market return. See the image below.

The beta can also be computed using the formula for beta in finance OR using the slope function in Microsoft Excel. We describe the various methods in detail below.

Beta = Covariance (stock return vs. market return) / market variance

## When do you need to look for comparable companies’ beta?

As seen above, you need the stock prices of the company to estimate a company’s beta. What do you do if the company you are analyzing is not a listed company!? This is when you need to look for comparable companies.
You are trying to estimate beta to capture the volatility or risk profile of the company in question. Risk is primarily driven by two factors 1) the nature of the business – which drives business risk, and 2) the capital structure of each company – which drives financial risk. You can assume that the business risk is the same or at least similar for companies in the same industry or line of business. Therefore, you look for the business risk profile of comparable companies to estimate your company’s beta.

## Where does operating risk come from?

Operating risk comes from a few sources: Cyclicality in the industry, volatility in sales, volatility in costs and degree of operating leverage. All of these can vary based on the strategies and management decisions adopted by the management. For example, two manufacturers of the same product will have different risks if one decides to manufacture in the US and the other in China.

## Why/when is beta used as a measure of “systematic risk” or “non diversifiable risk”?

The CAPM considers the expected return to be a function of the risk-free rate and a premium paid to reward you for the risk taken. The risk taken is the risk of investing in the equity market and the risk of your company’s stock price movements in relation to the equity market or portfolio.

Remember that the beta is teased out of the relationship between the market’s return and the stock’s return. The risk inherent in the market is considered “systematic risk” or “non-diversifiable risk”.

Beta can be used as a measure of “systematic risk” or “non-diversifiable risk” only when the company has no leverage. Therefore, only the unlevered beta is considered as a pure indicator of systematic risk – of that specific company.

Note some of that is also caused by the company’s decisions on its capital structure.

## How does the beta contribute to the Security Market Line (SML)?

The beta is an input in the CAPM model used to estimate the expected return on an investment/equity. The expected return line formed using the CAPM equation at different levels of beta is the Security Market Line (SML)!

## What are the drawbacks of beta?

• The beta is computed from historical data, making the beta a backward-looking measure. In investing and financial decision-making, we are making decisions about the future, and so what is ideal are forward-looking measures.
• The beta is a measure of risk relative to a portfolio or market index. Therefore, to be relevant, we much chose the appropriate market index from the investor’s perspective. Often this may not be possible, so we default to the S&P 500 or the Russel 3000. This is less than ideal and may make the beta less meaningful.
• Beta changes when you change the time periods used in the analysis. For example, you will get different betas if you use a five years of historical data instead of 20 years of historical data.
• Beta changes when you change the length of each time period used in the analysis. For example, you will get different betas if you use daily/weekly stock instead of monthly or quarterly stock prices.
• Beta only shows the impact of the portfolio’s risk profile. It does not clarify anything on the returns, which is of more importance to an investor. For example, the beta only shows a specific stock has low volatility relative to the index. But this particular stock may also have moderate returns. At the same time, another stock may have a low beta but has a better return for the shareholders.
• The beta does not show the trend or direction of movement if present in a stock. For example, a stock steadily increasing or decreasing may have the same beta! Or a beta with a steady decline in stock prices may show a low beta. So it may be portrayed as a good stock to add to a portfolio. However, while it may reduce the portfolio’s volatility, it will reduce the earnings (which is more important) due to the downward trend. So in fact, beta may mislead due to this issue.

## What is financial risk premium?

This increase in risk due to financial leverage is called a financial risk premium. This is the premium required to take on the financial risk.

## *How does financial leverage increase risk? Name two ways financial leverage increases risk?

First financial leverage increases the chance that the company is unable to repay it’s debt obligations on the promised schedule. Default on debt obligations allows the debtor to force the company into bankruptcy, causing the equity value to drop significantly.

Second, the increase in financial leverage creates a fixed payment obligation (interest cost on the debt taken is fixed and usually payable each time-period). Free cash flow to equity is arrived at after the debt payments are covered. Therefore, this causes larger swings in the cash flows to equity, increasing volatility reflected as risk. (Excel illustration)

## What is operating risk?

Operating risk is the risk inherent in a business or company. For example, if you run a burger chain, a risk you face is the consumer becoming health conscious and deciding not to eat burgers. This risk applies to all burger chains. If you are investing in cruise lines, the risk of an airborne pandemic like the SARS virus is an operating risk. This risk applies to all cruise lines. The operating risk of global supply chain disruption is a risk that applies to all retailers who buy goods from overseas. Increase in fuel price is a risk all firms in the transportation sector need to live with.

Operating risks are more or less similar to all companies in an industry unless a company follows a different business strategy.

## Where does operating risk arise from?

Operating risk comes from a few sources: Cyclicality in the industry, volatility in sales, volatility in costs and degree of operating leverage. All of these can vary based on the strategies and management decisions adopted by the management. For example, two manufacturers of the same product will have different risks if one decides to manufacture in the US and the other in China.

## Why/when is beta used as a measure of “systematic risk” or “non diversifiable risk”?

The CAPM considers the expected return to be a function of the risk-free rate and a premium paid to reward you for the risk taken. The risk taken is the risk of investing in the equity market and the risk of your company’s stock price movements in relation to the equity market or portfolio.

Remember that the beta is teased out of the relationship between the market’s return and the stock’s return. The risk inherent in the market is considered “systematic risk” or “non diversifiable risk”.

Beta can be used as a measure of “systematic risk” or “non-diversifiable risk” only when the company has no leverage. Therefore, only the unlevered beta is considered as a pure indicator of systematic risk – of that specific company.

Note some of that is also caused by the company’s decisions on its capital structure.

## How does the beta contribute to the Security Market Line (SML)?

The beta is an input in the CAPM model used to estimate the expected return on an investment/equity. The expected return line formed using the CAPM equation at different levels of beta is the Security Market Line (SML)!
See image

## What are the steps required to compute the equity beta of a stock?

### Method 1) Estimating beta using a scatter graph, trend line and regression equation.

Estimating the beta of equity by calculating stock and market returns and plotting a scatter graph to arrive at the regression line is the first method introduced in business school. This method is helpful for MBA and CFA students to see and experience what the beta represents and means. So it is taught in all introductory and intermediate finance courses in a business program. MBA and CFA students also have finance assignments to pick a company, collect stock and market prices, compute returns, and plot scatter graphs to arrive at the equity betas. We outline the steps required to estimate an equity beta using a scatter graph below.

#### Step 1: Gather stock price and market index data

The first step is to gather the data required to compute the equity beta of the company. The data required are 1) the stock prices and 2) market index levels over the evaluation period.

The evaluation period, the duration of each time unit, and the index you are evaluating the company against are essential decisions at this point. Your beta value will vary based on these assumptions.

This data is available from any of the major data providers, including Yahoo Finance, Morningstar, Bloomberg, etc.

#### Step 2: Compute the equity returns and market returns in each period

The next step is to compute the returns from the stock and the market for every period you are evaluating. This can be done using the formula (ending price-starting price)/starting price or (ending price/starting price)-1.

#### Step 3: Plot a scatter graph

You can plot a scatter graph of the Equity returns vs. market returns in each period. The equity returns are the dependent variable and so should be on the y-axis. The market returns are the independent variable and so should be on the x-axis.

#### Step 4: Plot the trend line and regression equation

We can then use Microsoft Excel to plot a linear trend line on the scatter plot. This trend line is also called the least square line or the line of best fit because this is the line that has the minimum sum of squares of the distances from the scatter points and the line.

To plot a linear trend line on the scatter plot, you first click on and select the scatter plots and right-click to get the trend line. Next, please check the “Display equation” option to display the algebraic equation of the trend line. This algebraic equation is your regression equation showing you the relationship between the y variable (stock returns) and the x variable (market returns).

#### Step 5: Arriving at your beta

The slope of the trend line is your beta. The slope is seen in the regression equation as the coefficient of the x variable or market.

### Method 2) Estimating beta using the statistics formula

You can also arrive at the beta using the formula approach. This method is maybe faster than computing the beta using the scatter graph and regression line.

Step 1 and Step 2 are the same as in the previous method (described above).

Once you have computed the equity and market returns in each period, you will compute the variance of the market and the covariance of the stock and the market. You can use any tool or software like R, Python, Microsoft Excel, etc. to do these computations. You only need to apply variance and covariance formulas on each period’s equity returns and market returns using software/tool. Then, apply the market variance and stock-market covariance results to the formula to arrive at the beta.

### Method 3) Using the Microsoft Excel ‘Slope’ function to estimate beta

You can also arrive at the beta using the slope function Microsoft Excel. This method is maybe faster than either of the methods discussed above – computing the beta using the scatter graph and regression line or the beta formula in finance.

Once again, Step 1 and Step 2 are the same as in the previous method (described above). Gathering the raw data and computing the returns cannot be avoided.

Once you have computed the equity and market returns in each period, you use the slope line to arrive at the beta. Remember again that the equity returns are the dependent variable and so should be on the y inputs. The market returns are the independent variable and should be the x inputs.

Note: remember the beta computed using stock prices is considered the equity beta. It contains all the risks involved in the equity investment in relation to the market portfolio. The equity beta includes any financial risk from the financial leverage/capital structure employed by the company.

## Why do you compute unlevered betas from equity betas?

We compute the equity beta of a stock from the share price. The share price set by the market accounts for all the risk embedded in the stock. The risk the market accounts for includes business risk and financial risks associated with the stock. Removing the financial risks associated with the equity beta, called un-levering the beta, leaves you with only the business risks and will be referred to as unlevered beta.

## How do you arrive at industry beta?

We know the business risk of a company is related to the business risks inherent in the business. Different companies in an industry will have different capital structures and therefore their betas will include both financial risks and business risks. When you unlever their equity betas, you are left with only the business risks. To understand the risk profile of an industry, you will average the unlevered betas of companies in an industry. This average of the unlevered betas in an industry will reflect the general risk profile of that industry.

## How do you compute unlevered betas from levered betas?

You can use this formula to computed the unlevered beta. It accounts for the amount of debt in the capital structure and the interest tax shield provided by debt.

Unlevered Beta = Equity Beta / (1+ [(1 – Applicable Tax Rate) (ratio of debt to equity)]

The average of the unlevered betas of comparable companies in an industry is often called industry beta or asset beta.

## Re-levering the beta to accounting for target D/E ratio

If you want to estimate the beta of a company that is not listed or a proposed project, you will need to add the financial leverage appropriate to your company/project to the industry beta. This process is called re-levering the industry beta. You can use the formula below to relever the industry beta with the target capital structure (the proposed debt/equity ratio).

Levered Beta = Levered Beta / (1 + [(1 – Tax Rate) (debt/equity)]

## What is the beta of a portfolio?

The beta of a portfolio is the weighted average beta of all the individual assets in the portfolio. For example, let us assume a portfolio has three stocks A, B, C, in proportions 50%, 30%, and 20%, respectively. And these three stocks A, B, and C, have betas 1.5,1.2, and 0.8, respectively. Then the portfolio beta will be 1.27.

The interpretation of a portfolio’s beta is the same as that of an individual company’s beta (see links here). The portfolio beta reflects how closely that portfolio’s returns move with that of the market returns. A beta greater than one indicates it will have higher volatility than the market. A beta of less than one means it will have lower volatility than the market. And a beta equal to one indicates it will have the same volatility as the market, etc.

We can think of a portfolio as 100% of the firm’s equity assets and 100% of the firm’s debt assets. Just like the beta of a portfolio is the weighted average beta of all the individual assets in the portfolio, the asset beta can also be thought of the weighted average beta of the individual portfolio components – debt beta and equity beta.

## How does the capital structure effect your beta?

We can see that the asset beta is the weighted average of the debt beta and equity beta. Therefore, we know when the capital structure changes, the weights change, impacting the asset beta. In addition, the betas do not stay the same as weights change. When the capital structure changes to add debt /financial leverage, risk levels increase, impacting the debt beta and equity beta.

## What is the beta of the market?

The beta of the market is always equal to 1! Think about this for a moment. If you follow the process indicated above, you are plotting the same stocks on the x-axis and y-axis. So the slope will be exactly equal to 1. Or the formula method will give you the same numerator and denominator.

## What is the beta of a risk free asset?

The beta of a risk-free asset is always zero. Why is the beta of a risk-free asset is always zero? The beta reflects how the asset in question moves in relation to the market. By definition, a risk-free asset’s return should not move! Because the return on a risk-free asset does not move in relation to the market, the beta of a risk-free asset is zero.

A risk-free asset theoretically gives you the same return no matter what the market does. Therefore, if you plot the returns from the risk-free asset vs. the market return, you will see the risk-free asset’s return is a flat line. Thus, the regression line or line of best fit is also a flat line with a slope of zero!

## *Should we consider the US market or the German market or a global market in estimating a beta?

Beta measures risk in relation to a portfolio or index. And so, we must evaluate risk from the investor’s perspective. Since beta assumes that the investor is diversified, we must be evaluating risk in relation to his/her portfolio or index.
So, if you are evaluating beta for a US investor, you must compare a stock’s performance against the US market assuming his/her portfolio is mostly comprised of assets in the US market. But if you are evaluating beta for a German investor, you must compare a stock’s performance against the German market, assuming his/her portfolio is mostly comprised of assets in the German market.

However, if the US investor is globally diversified, as is the case increasingly today, we can compare the stock returns against a global index.

So the same stock, will have a different beta for a US investor and a German investor! So with a different beta, a US investor and a German investor will have different expected returns! And so different valuations!!

## Are there/do you have different kinds of betas?

Yes, you can have different kinds of betas. Beta measures the risk/volatility of an asset in relation to the overall portfolio. Since different types of assets will behave in different ways when the selected index changes, you will have different types of betas. We mainly deal with equity betas. Equity betas need to be further specified as levered betas or unlevered betas. Other types of betas include debt beta, revenue beta, portfolio beta, etc.

## What is debt beta?

Debt beta is the beta of debt. Beta evaluates the risk of an asset in relation to the market. So debt beta evaluates the risk of debt in relation to the market.

## Why is debt beta assumed to be zero? Is it right to assume debt beta zero?

The debt beta is usually significantly lower than equity beta because debt is a contractual agreement between the borrower and debt. And no changes are expected in a contractual agreement.

When you have a healthy market and a financially healthy borrower, you can expect all the contracted debt cash flows to be repaid as promised. You also have recourse to the courts to enforce the debt and interest repayment. So if there is a reasonable expectation to be repaid – or no change in cash flows are expected whatever happens in the market, your debt beta is technically zero. However, even in a healthy market and with a financially healthy borrower, there is a small probability of default, and so theoretically, the debt beta is not precisely zero but very close to zero.

## What are the risks associated with beta that the debt beta measures?

The two risks debt beta measures are:

Risk of default: While debt is a contractual agreement between the borrower and debt and can be enforced in court, there is a risk of bankruptcy and loss of all or a portion of the cash flows.

Macroeconomic risks: There are other risks such as inflation or recessions that can cause the cash flows to be worth less than expected.

## Can you have high volatility (standard deviation or variance) with a low beta?

Yes, you can have high volatility (standard deviation or variance) with a low beta. Remember that volatility measured by standard deviation or variance is a measure of fluctuations or changes in relation to the mean value. Whereas beta is a measure of fluctuations or changes in relation to the market index or the overall portfolio.

So you could have an asset whose prices vary significantly but has no relation (correlation) to the prices of the market index. An example may be timber or gold, whose prices vary, but price changes are not caused by changes in the market.

## Does beta measure diversifiable risk or non-diversifiable risk (systematic risk)?

Beta is a measure of non-diversifiable risk or systematic risk. Beta measures risk or volatility in relation to the market or portfolio. Since beta is measured in relation to the broader market risk- one that you cannot diversify away from, beta is a measure of non-diversifiable risk.