Beta Formula

Beta Formula Calculation

Beta is a measure of the volatility of the stock as compared to the overall stock marketOverall Stock MarketStock Market works on the basic principle of matching supply and demand through an auction process where investors are willing to pay a certain amount for an asset, and they are willing to sell off something they have at a specific price.read more. We can calculate beta using three formulas –

  1. Covariance/Variance Method
  2. By Slope Method in Excel
  3. Correlation Method

Top 3 Formula to Calculate Beta

Let us discuss each of the beta formulas in detail –

Beta-Formula

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Source: Beta Formula (wallstreetmojo.com)

#1- Covariance/Variance Method

Beta Formula = Covariance (Ri, Rm) / Variance (Rm)

Covariance( Ri, Rm) = Σ ( R i,n – R i,avg ) * ( R m,n – R m,avg ) / (n-1)
Variance (Rm) = Σ (R m,n – R m,avg ) ^2 / n

To calculate the covarianceCalculate The CovarianceCovariance is a statistical measure used to find the relationship between two assets and is calculated as the standard deviation of the return of the two assets multiplied by its correlation. If it gives a positive number then the assets are said to have positive covariance i.e. when the returns of one asset goes up, the return of second assets also goes up and vice versa for negative covariance.read more, we must know the return of the stock and also the return of the market, which is taken as a benchmark value. We must also know the variance of the market return.

#2 -By Slope Method in Excel

We can also calculate Beta by using the slope function in excel. The Microsoft Excel SLOPE function returns the slope of a regression line based on the data points, which are identified by % change in NASDAQ and % change of the company, which we are calculating.

% change is calculated as below:

Return = Closing Share Price – Opening Share Price / Opening Share Price
slope excel

#3 – Correlation Method

Beta can also be calculated using the correlation method. Beta can be calculated by dividing the asset’s standard deviation of returns by the market’s standard deviation of returns. The result is then multiplied by the correlation of security’s return and the market’s return.

Beta Formula = Σ Correlation (R i, Rm) * σi / σm

Step by Step Beta Calculation

Follow the below steps:

  1. First, download Historical prices and NASDAQ index data from the past 3 years.


    You can download the data from yahoo finance, as I have done below.

    #1 – For NASDAQ Dataset, Please visit this link – (finance.yahoo.com/).

    equation step 1

    #2 – For Google Prices, Please visit this URL – finance.yahoo.com

    equation step 1.2

  2. Then Sort the Prices as Done Below.


    Then we need to sort the dates of the stock prices and adjusted closing prices in ascending order of dates. We need only these two columns, and the remaining columns can be deleted as we don’t have use of those for beta calculations in excel.

    beta calculation step 2

  3. Then, prepare the beta coefficientBeta CoefficientThe beta coefficient reflects the change in the price of a security in relation to the movement in the market price. The Beta of the stock/security is also used for measuring the systematic risks associated with the specific investment.read moreThe beta coefficient reflects the change in the price of a security in relation to the movement in the market price. The Beta of the stock/security is also used for measuring the systematic risks associated with the specific investment.read moreThe beta coefficient reflects the change in the price of a security in relation to the movement in the market price. The Beta of the stock/security is also used for measuring the systematic risks associated with the specific investment.read more excel sheet, as shown below. We put both the data in one sheet.

    beta calculation step3

  4. Then calculate Daily Returns we get.


    Return = Closing Share Price – Opening Share Price / Opening Share Price

  5. Then, calculate Beta by the Variance-Covariance method.


    In this case, we need to use the two formulas (formulas of variance and covariance in excel), as shown below:

    beta calculation step5

    Using the variance-covariance method, we get the Beta as 0.16548 (Beta Coefficient)

  6. Calculate Beta using SLOPE Function available in excel


    beta calculation step6

    Using this SLOPE function method, we again get the Beta as 1.2051 (Beta Coefficient)

Examples of Beta Formula

Let’s take an example to understand the calculation of the beta equation in a better manner.

You can download this Beta Formula Excel Template here – Beta Formula Excel Template

Using Correlation Method – Example #1

An investor is looking to calculate the beta of company XYZ as compared to the NASDAQ. Based on data over the past three years, the correlation between the firm XYZ and NASDAQ is 0.82. XYZ has a standard deviation of returns of 22.12%, and NASDAQ has a standard deviation of returns of 22.21%.

Solution:

Use the following data for the calculation of the beta.

Excel 1.1

So, the calculation of the beta –

Excel 1

Beta of XYZ = 0.82 x (0.2212 ÷ 0.2221)

Beta of XYZ = 0.817

As we have seen in this case, Company XYZ is considered less risky than the market NASDAQ as its beta of 0.817.

Example #2

We will discuss some examples using data from the industry.

Now we will take an example to calculate the beta of Google and the Market index as NASDAQ. We will calculate the Beta of Google and Amazon in excel– variance/covariance method, slope function. We will see each of the beta coefficient calculations.

Calculation of Beta of Google using correlation and covariance in excel

Excel Google

We will calculate the beta of Google as compared to NASDAQ.

Based on data over the past three years, take the data from Yahoo finance and calculate Beta as below:-

  • Beta = Covariance (Ri, Rm) / Variance (Rm)
  • Beta = 0.165

In this case, Google is considered less volatile than NASDAQ as its beta of 0.165.

Example #3

We will calculate the beta of Amazon as compared to NASDAQ.

Excel Amazon

Based on data over the past three years, take the data from Yahoo finance and calculate Beta as below:

Beta = Covariance (Ri, Rm) / Variance (Rm)

Beta = 0.000135 

In this case, Amazon zero correlation with the market movements.

Relevance and Uses

Beta indicates whether an investment is more volatile or less volatile. Beta, which has a value of 1, indicates that it exactly moves in accordance with the market value.

A higher beta indicates that the stock is riskier, and a lower beta indicates that the stock is less volatile as compared to the market. Mostly Betas generally fall between the values of range 1.0 to 2.0. The beta of a stock or fund is always compared to the market/benchmark. The beta of the market is equal to 1. If a stock is benchmarked against the market and has a beta value greater than 1 (for example, we consider it as 1.6), this indicates that the stock is 60 percent riskier than the market as the beta of the market is 1.

Beta is used in the formulae of capital asset pricing model (CAPM), which is used to calculate the expected returnExpected ReturnThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + ………… + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability. read more of an asset based on the value of beta and expected market return.

Recommended Articles

This article has been a guide to Beta Formula. Here we learn how to calculate beta using the top 3 methods along with practical examples and a downloadable excel template. You can learn more about financial analysis from the following articles –