Beta Formula

Beta Formula (Table of Contents)

• Beta Formula
• Calculate Beta by Correlation Formula
• Calculate Beta Manually
• Calculation of Beta for the stock profile
• Beta Calculator
• Beta Formula in Excel (With Excel Template)

Beta Formula

Beta is the very important element in the stock analysis it measures risk in stock or in the stock portfolio. Beta is very volatile as it depends on the stock market and we know very well that the stock market is very much volatile. Beta not only evaluate the risk associated with a particular stock but also used to evaluate the expected rate on returns and Discounted cash flow evaluation. Beta is the covariance of the return of an asset divided by variance of the return of the benchmark over a certain time period and formula for this can be written as:-

Where,

• R_e = Stock Return
• R_m = Market Return

Calculation of Beta by above Beta Formula-

Beta can be calculated using above beta formula by following below steps:-

• Get past security price for an asset of the company.
• Get past security price for comparison benchmark.
• Calculate the percentage change periodically for both asset and benchmark.
• Calculate variance by- VAR.S(Sum of all the percentage changes of the asset).
• Calculate Covariance by- COVARIANCE.S(Sum of all the percentage changes of the asset, the Sum of all the percentage changes of the benchmark).
• Divide Covariance by variance to get the Beta.

Examples

Let’s see an example to calculate Beta.

A company has below asset and benchmark price from Jan-2018 to Dec-2018.

Date	Assets Price	Benchmark Price	Percentage of Change in Asset	Percentage of Change in Benchmark
1-Jan-18	232	1274	0.92	0.15
1-Feb-18	446	1460	-0.34	-0.24
1-Mar-18	294	1110	0.09	0.24
1-Apr-18	321	1376	1.27	-0.04
1-Jun-18	730	1316	-0.11	-0.01
1-Jul-18	648	1300	0.08	0.04
1-Aug-18	703	1351	0.04	0.03
1-Sep-18	728	1396	-0.05	0.03
1-Oct-18	689	1440	-0.68	-0.2
1-Nov-18	220	1148	1.71	0.09
1-Dec-18	597	1247	-1	-1

Then calculate the percentage of change in asset and percentage of change in the benchmark.

Variance is Calculated as:

Covariance is calculated as:

Beta is calculated as:

So, the value of Beta is 0.24 which company is less volatile than the market.

Calculate Beta by Correlation Formula

Beta formula in term of correlation can be written as:-

Where,

• σ_e= Standard deviation of returns of the benchmark
• σ_m = Standard deviation of returns of asset

Above formula is used to calculate Beta by dividing the standard deviation of returns of the asset by standard deviation of returns of benchmark which is multiply by correlation of asset return and benchmark return.

Now, let us calculate Beta by correlation formula.

Suppose an investor wants to invest in a company, he wants to calculate Beta of the company and compare it with S&P 500 EFT Trust correlation between two is 0.62, the standard deviation of returns of the company is 22% and standard deviation of returns of S&P is 30%.

• Beta = Correlation(R_a – R_m) *( σ_{e /} σ_m)
• Beta = 0.62 * (0.22 / 0.30)
• Beta= 0.45

So, the value of Beta is 0.45 which company is less volatile than the market.

Calculate Beta Manually

Beta can be calculated manually by following below steps:-

• Find the risk free rate-

It is the rate of return on investment done.

• Find the rate of return of stocks and rate of return on market-

If any of the value is in negative that will leads to a value of beta as negative which means loss.

• Find return on risk is taken on stock-

It is the stock’s rate of return minus risk free rate.

• Find return on risk is taken on the market-

It is the market’s rate of return minus risk free rate.

• Divide return on risk is taken on the stock by return on risk taken on the market-

This will provide you value for Beta.

Let us an example to calculate Beta manually,

A company gave risk free return of 5%, the stock rate of return is 10% and the market rate of return is 12% now we will calculate Beta for same.

Return on risk taken on stocks is calculated using below formula

• Return on risk taken on stocks = Stock Rate of Return – Risk Free Return
• Return on risk taken on stocks = 10% – 5%
• Return on risk taken on stocks = 5%

Return on risk taken on Market is calculated using below formula

• Return on risk taken on Market = Market Rate of Return – Risk Free Return
• Return on risk taken on Market = 12% – 5%
• Return on risk taken on Market = 7%

Beta is Calculated using below formula

• Beta = Return on risk taken on stocks/ Return on risk taken on Market
• Beta = 5 /7
• Beta = 0.71

So, value for beta is 0.71 which company is less volatile than the market.

Calculation of Beta for the stock profile

Now, let us see a calculation of Beta for the stock profile.

Beta is calculated for stock and for a stock portfolio value of each stock Beta is added up according to their weights to create the portfolio beta. The formula for same is as follows:-

The beta of Portfolio = Weight of Stock * Beta of Stock + Weight of Stock * Beta of Stock…so on

Let us see an example to calculate the same.

An investor has a portfolio of $100,000, the market value of HCL is $40,000 with a Beta value of HCL is 1.20, and market value of Facebook is $60,000 with Beta value is 1.50. The beta of the portfolio will be:-

Weight of HCL is calculated as:

• Weight of HCL = 40,000 / 100,000
• Weight of HCL = 0.40

Weight of Facebook is calculated as:

• Weight of Facebook = 60,000 / 100,000
• Weight of Facebook = 0.60

Beta of Portfolio is calculated as:

The beta of Portfolio = Weight of Stock * Beta of Stock + Weight of Stock * Beta of Stock…so on

• Beta of Portfolio = (0.40*1.20) + (0.60*1.50)
• Beta of Portfolio = 0.48 + 0.9
• Beta of Portfolio = 1.38

The beta of the portfolio is 1.38, which means the stock is highly risky and volatile.

Beta Measurement and its Relation with Market

Value of Beta defines the risk associated with the company, Beta tells whether investment in the company is risky or not and how much it is depended on the market. Beta measures the stock rise in relation to the stock market. Beta value and its interpretation are as follows:-

• If Beta = 1, then risk in stock will be the same as a risk in the stock market. It means the stock is volatile like the stock market.
• If Beta >1, then the level of risk is high and highly volatile as compared to the stock market.
• If Beta > 0 and Beta < 1, then the stock price will move with the market. However, the stock price will be less risky and less volatile.

Uses of Beta Formula

There are many uses of Beta and its formula and they are as follows:-

• It helps in risk analysis of the stock.
• Beta helps to calculate rate on returns.
• It also helps in the evaluation of discounted cash flow.
• Beta provides a real picture of the investment portfolio.

Beta has some disadvantages as it depended on past performance but in reality past performance has no guarantee of future and it cannot give an accurate value. But, still, Beta is highly used by investment bankers and investors to calculate risk.

Beta Calculator

You can use the following Beta Calculator

Beta Formula in Excel (With Excel Template)

Here we will do the same example of the Beta formula in Excel. It is very easy and simple.

You can easily calculate the Beta using Formula in the template provided.

Beta using the correlation formula is calculated as:

Return on risk taken on stocks is calculated as:

Return on risk taken on Market is calculated as:

Beta is Calculated using below formula

Weight of HCL is calculated as:

Weight of Facebook is calculated as:

Beta of Portfolio is calculated as:

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