# What does negative beta mean in CAPM

## Beta factor of stocks - explanation & calculation

Author: Pit Wilkens - Content checked by: Philipp Berger

The beta factor, also known as "beta", is a statement about how much a stock fluctuates compared to the overall market. In capital market theory, the beta factor based on the Capital Asset Pricing Model (CAPM) plays a special role. The beta factor measures the systematic risk (also: market risk) of an investment.

### Beta Factor Definition

The beta describes the expected reaction of a security to changes in the price of the benchmark index, i.e. how high the volatility of a share is compared to the stock market. In addition to being used in the context of individual stocks, a beta factor can also be formed for securities portfolios. Investors usually use the weighted mean of the individual betas for this.

The beta factor can be used to diversify a portfolio in a targeted manner. In addition, the beta also shows the correlation between a value and its benchmark index.

### Beta factor calculation

The beta factor is calculated by dividing the covariance between the market return and the security return by the variance in the market return. This consideration always takes place for a fixed period of time, that is, the beta factor can vary over different periods of time. This results in the following formula:

Beta factor = \ frac {covariance (Ri; Rm)} {variance (Rm)}

where Ri = individual security return and Rm = average market return.

Important: The beta factor does not have to be determined exclusively by calculation. A derivation based on a comparison group (also: peer group or benchmark) is also possible. For this purpose, the arithmetic mean of the individual beta factors is determined in order to infer the beta of another company.

### Derivation of the beta factor

The beta factor is a statistical unit of measurement and can be derived and determined using appropriate calculation methods. The starting point here is the return on an individual share in relation to the market return. A straight line is then determined using simple linear regression. This straight line shows the average ratio between the individual stock return and the total market return.

Excursus: As Covariance the linear relationship between two variables is understood. The covariance is similar to the correlation. However, the covariance is not available in a standardized form, so that an analysis is only possible with the help of the correlation coefficient. The correlation coefficient is also an important key figure for interpreting the beta. A covariance of 0.4 shows that there is a positive relationship between two values, but not how strong the relationship is.

The Variance is determined in a previous step on the covariance. It indicates how high the expected deviation of a variable from its expected value is. For example, if a stock portfolio has a standard deviation (also: expected value) of 5%, the variance measures how often values ​​are outside this corridor.

### What is the significance of the beta factor?

On the basis of the mathematical principles, it becomes clear that the beta factor can help investors estimate how much a security, e.g. a share, fluctuates compared to the overall market. A meaningful benchmark index is necessary when determining the beta to achieve target-oriented results. Comparing a European stock with a US index, for example, makes little sense.

In addition to an isolated risk assessment, an investor can use the beta to assess how buying or selling a specific stock will affect their entire portfolio. For example, a low beta stock lowers the risk of a portfolio. Conversely, the expected return on lower beta securities is relatively low. If the investor has previously defined his desired risk profile for the portfolio, he can use the beta factors of individual values ​​to increase or decrease his overall risk in a targeted manner.

### Systematic vs. unsystematic risk

The beta factor offers a way of assessing the systematic risk. However, an investor cannot reduce this risk. Every participant in the capital market is exposed to this risk and, according to capital market theory, receives the market risk premium in return.

• The systematic risk consists, for example, of global economic or political, i.e. non-company-specific factors. These can have an impact on a wide range of companies - this systematic risk can therefore not be further reduced through diversification.
• On the other hand, that can unsystematic risk can be reduced if there is sufficient spread. This risk is also known as individual risk because it relates to individual industries or companies.

### Beta factor - interpretation

Based on the possible results, the beta factor can be divided into different values. These can each enable a specific statement to be made regarding the risk of the respective security.

In portfolio theory, the so-called market portfolio is mentioned again and again. It is a fictitious portfolio that contains all securities of one class. In the case of stocks, it would therefore be assumed for computational reasons that all stocks in the world form the market portfolio for stocks. In practice, however, market-wide indices such as the MSCI World or the S&P 500 are used. These adequately map the economically relevant companies and require little effort to put them together.

### Beta factor = 1

With a beta of 1, it can be assumed that the respective share moves in the same way as the overall market.

### Beta factor <1

Shares with a beta of less than 1 are considered to be less volatile compared to the overall market. The inclusion of such an asset in a portfolio therefore generally lowers its overall risk. Typical industries with a beta less than 1 are, for example, utilities or the pharmaceutical industry. These are therefore sometimes also referred to as “defensive sectors”.

### Beta factor> 1

A beta greater than 1 means: The security moves with greater fluctuations than the market as a whole. Beta factors above 1 are common in growth stocks and typical cyclical industries such as automotive and aerospace. These stocks are usually assigned an increased risk, but also sometimes greater chances of price gains. More recent studies show, however, that stocks with a beta greater than 1 are regularly not sufficiently compensated for the higher risk ("Betting against beta", Andrea Frazzinia, Lasse Heje Pedersen)

### Beta factor <0

Shares with a beta equal to or less than 0 - in terms of volatility - evidently have no positive correlation with the overall market. A beta of 0 means that the security is uncorrelated to the overall market. A beta <0 means that there is a negative relationship between volatility in the security compared to the overall market.

### Function of beta in theory and practice

Since the beta factor is a statistical key figure, there are basic assumptions that do not necessarily correspond to reality. For example, just like the beta factor, the CAPM assumes that stock market returns are normally distributed. This means that most of the values ​​in a statistical survey are in a relatively small corridor (so-called standard deviation). In a normal distribution, approx. 68% of all measured values ​​are within one standard deviation.

However, a normal distribution of stock returns cannot be observed in practice. In particular extreme events, so-called black swans, occur in practice both in the negative and in the positive case more frequently than would be permissible in theory.

### Difference Between Levered and Unlevered Beta

• The beta discussed so far is available as a levered beta, also known as Equity beta or Stock beta known. It is therefore a beta view of an entire company - including the individual capital structure (external and own capital). A comparison of betas of different stocks and thus different companies is therefore not necessarily precise if the respective capital structure of the individual company is disregarded. The levered beta thus includes both the business risk and the risk that arises from taking on debt.
• The Asset beta, also called delevered beta orunlevered beta on the other hand, only relates to the equity, i.e. the state of the company through no debt. It includes business risk but not leverage risk.

The intention behind identifying this Unlevered betas is the adjustment of the calculation for the financing risk. The unlevered beta is not intended to be used to evaluate an individual company, but rather to enable a beta that is as accurate as possible for a comparison group (“peer group”).

example: Company A is to be rated by an analyst. It is an automobile company. For the assessment, the analyst would like to use the CAPM, among other things, and needs a beta factor for this. When evaluating a company, industry beta is often used. The analyst therefore uses the beta factors of ten direct competitors of a similar size. Since every company has an individual capital structure, it does not make sense to simply take the mean of the betas. The beta factors are therefore “unlevered” so that an unlevered beta can be determined for the benchmark. Then the beta is adjusted to the debt share of company A and used for the calculation. This process is also called "releving".

### Example - beta factors from DAX companies

Investors usually do not have to determine a beta factor themselves. Rather, it is important that the calculation method and the derivation of the beta are basically known.

In the context of this example, the different beta factors for 10 different values ​​of the German leading index are examined and analyzed in more detail. The 1-year beta is shown on 07/11/2020.

 Companies Beta factor Adidas 1,24 alliance 1,20 BASF 1,14 Bayer 0,85 Beiersdorf 0,47 BMW 1,12 Continental 1,35 Covestro 1,03 Daimler 1,59 Deutsche Bank 1,41

These companies from the DAX-30 have different beta factors, whereby similarities can be found between the industries. Bayer and Beiersdorf stand out in this selection with a beta factor below 1 and thus low volatility. Both companies are pharmaceutical groups that have developed relatively stable even during the Corona crisis (from April 2020). The other companies can be assigned to the automotive or financial sector in a broader sense. Both sectors are closely related to the economy as a whole and therefore tend to be more volatile.