# Beta Calculator

## Related Converters

Our beta calculator allows you to determine the volatility of returns of an individual stock with respect to the whole market. It is calculated by comparing the returns of the stock to the returns of a market index such as the S&P 500.

## Beta in Finance:

“In the stock market context, beta is a measure of the volatility of a stock relative to the overall market”

A higher beta of a company indicates that there a greater risks and expected returns. If the market stock is higher than 1.0 beta, then it can be interpreted as more volatile than the S&P 500.

## How to Use our Beta Calculator?

Our beta portfolio calculator is designed with a user-friendly interface that allows you to get fast calculations. You need to insert some values that are given as follows:

#### What you put?

• Put the company’s return and market returns in the designated fields

#### What you Get?

• Beta Value: Get the beta values that help you to indicate the stock sensitivity to market movement.
• Volatility Insights Table: How beta reflects the stock in relation to market fluctuations can be understood in the form of a table.
• Risk Assessment: Get the verification of how the beta value has contributed to assessing the risks that are associated with the market stock.

## Formula:

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

Where:

• Covariance _ The comparison of market and security returns
• Variance _ Measure of how security data points can differ from one to another
• Rm _ Overall market return
• Re _ Return of the security

## How to Calculate Equity Beta?

The volatility of a stock relative to the market can be measured easily by using a stock beta calculator because it helps you to make informed investment decisions. If you come for manual calculation you can use the example below:

### Numeric illustration:

Suppose you are considering investing in a small technology company and you know small companies tend to have higher betas than larger companies. Therefore, you consider the company's return and market returns.

• Company Returns: 12, 8, 15, -5, 10
• Market Returns: 8, 6, 10, -3, 9

#### Solution:

The dataset includes both the dependent and independent variables:

Obs. $$r_M$$ $$r_S$$
1 8 12
2 6 8
3 10 15
4 -3 -5
5 9 10

Based on the given sample values, generate the table below for the estimated regression coefficients

Obs. $$r_M$$ $$r_S$$ Xᵢ² Yᵢ² Xᵢ · Yᵢ
1 8 12 64 144 96
2 6 8 36 64 48
3 10 15 100 225 150
4 -3 -5 9 25 15
5 9 10 81 100 90
Sum = 30 40 290 558 399

The sum of squares calculated from the above table is

$$SS_{XX} = \sum^n_{i=1}X_i^2 - \dfrac{1}{n} \left(\sum^n_{i=1}X_i \right)^2$$

$$= 290 - \dfrac{1}{5} (30)^2$$

$$= 110$$

$$SS_{YY} = \sum^n_{i=1}Y_i^2 - \dfrac{1}{n} \left(\sum^n_{i=1}Y_i \right)^2$$

$$= 558 - \dfrac{1}{5} (40)^2$$

$$= 238$$

$$SS_{XY} = \sum^n_{i=1}X_iY_i - \dfrac{1}{n} \left(\sum^n_{i=1}X_i \right) \left(\sum^n_{i=1}Y_i \right)$$

$$= 399 - \dfrac{1}{5} (30) (40)$$

$$= 159$$

The formula provided determines the coefficient of the slope

$$\hat{\beta}_1 = \dfrac{SS_{XY}}{SS_{XX}}$$

$$= \dfrac{159}{110}$$

$$= 1.445$$

### What is a Zero Beta Portfolio?

A zero beta portfolio is a portfolio that is used for zero systematic risks and it would have the same expected returns as the risk-free rate.

### Why do Investors Use the Equity Beta Calculator?

Our beta coefficient calculator proves helpful for many investors like:

• Look at the risks to identify stocks in the overall market
• Create a portfolio that is exactly related to the risk tolerances
• Decide when you need to sell and buy stocks.

### In Finance Can Beta Be Negative?

When the general market price falls then an investment that is used to enhance the price is known as negative beta. It is a rare chance to have a negative beta because it is an indication of an inverse relation to the market.

## Citations:

Indeed.com: What is beta in finance? How beta works, Beta formula, Types of beta coefficient values, Who uses beta? Benefits of using beta.

Wikipedia: Beta (finance), Interpretation of values, Importance as a risk measure, Technical aspects, Choice of the market portfolio and risk-free rate, Empirical estimation, The use in performance measurement.