Beta Formula Calculation

Beta is a measure of the stock’s volatility 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 –

Top 3 Formula to Calculate Beta

Let us discuss each of the beta formulas in detail –

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#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 stock return and the market return, which is taken as a benchmark value. We must also know the variance of the market return.

We can also calculate Beta by using the slope function in excel. The Microsoft Excel SLOPE functionExcel SLOPE FunctionThe Slope function returns the slope of a regression line based on the data points recognized by known _y values and known _x values.read more returns the slope of a regression lineRegression LineA regression line indicates a linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis. The correlation is established by analyzing the data pattern formed by the variables.read more based on the data points 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

#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. The result is then multiplied by the correlation of the security’s return and the market’s return.

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

Step by Step Beta Calculation

Examples of Beta Formula

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

  • First, download Historical prices and NASDAQ index data from the past three 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/).#2 – For Google Prices, Please visit this URL – finance.yahoo.com 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 donu2019t have use of those for beta calculations in excel. Then, prepare the beta coefficient excel sheet, as shown below. We put both the data on one sheet. Then calculate Daily Returns we get. Return = Closing Share Price – Opening Share Price / Opening Share Price 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:Using the variance-covariance method, we get the Beta as 0.16548 (Beta Coefficient) Calculate Beta using SLOPE Function available in excel Using this SLOPE function method, we again get the Beta as 1.2051 (Beta Coefficient)

You can download the data from yahoo finance, as I have done below.#1 – For NASDAQ Dataset, Please visit this link – (finance.yahoo.com/).#2 – For Google Prices, Please visit this URL – finance.yahoo.com

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 donu2019t have use of those for beta calculations in excel.

In this case, we need to use the two formulas (formulas of variance and covariance in excel), as shown below:Using the variance-covariance method, we get the Beta as 0.16548 (Beta Coefficient)

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

Using Correlation Method – Example #1

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

Solution:

Use the following data for the calculation of the beta.

So, the calculation of the beta –

Beta of XYZ = 0.82 x (0.2212 ÷ 0.2221)

Beta of XYZ = 0.817

In this case, Company XYZ is considered less risky than the market NASDAQ with its beta of 0.817.

Example #2

We will discuss some examples using data from the industry.

Calculation of Beta of Google using correlation and covariance in excel

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, with its beta of 0.165.

Example #3

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 

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 following the market value.

A higher beta indicates that the stock is riskier, and a lower beta indicates that the stock is less volatile than the market. Most Betas generally fall between the values 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 market beta is 1.

Beta is used in the formulae of the capital asset pricing model (CAPM), which calculates 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 expects a market return.

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

  • Formula of Levered Beta Equity Beta FormulaGini CoefficientUnlevered Beta Formula