Finance Beta Formula Example

Beta is a crucial concept in finance, measuring a stock’s volatility relative to the overall market. It essentially quantifies how much a stock’s price tends to move up or down compared to the market as a whole. A beta of 1 indicates that the stock’s price will move in line with the market; a beta greater than 1 suggests the stock is more volatile than the market, and a beta less than 1 implies it’s less volatile.

The formula for calculating beta is:

Beta (β) = Covariance (Stock Return, Market Return) / Variance (Market Return)

Let’s break down each component:

• Covariance (Stock Return, Market Return): This measures how the returns of the stock and the market move together. A positive covariance indicates that the stock and market tend to move in the same direction, while a negative covariance suggests they move in opposite directions.
• Variance (Market Return): This measures the dispersion or volatility of the market’s returns around its average return. A higher variance indicates greater market volatility.

Let’s illustrate with an example. Suppose we want to calculate the beta of Stock ABC. We have the following monthly return data for Stock ABC and the S&P 500 (our market proxy) over the past year:

(Simplified for illustration – real-world calculations require robust datasets)

Month	Stock ABC Return (%)	S&P 500 Return (%)
Jan	2	1
Feb	-1	-0.5
Mar	3	1.5
Apr	-0.5	-0.25
May	1.5	0.75
Jun	-2	-1
Jul	2.5	1.25
Aug	-1.5	-0.75
Sep	3.5	1.75
Oct	-2.5	-1.25
Nov	4	2
Dec	-3	-1.5

Steps (simplified):

1. Calculate the average monthly return for Stock ABC and the S&P 500.
2. Calculate the deviations from the mean for each month for both Stock ABC and the S&P 500.
3. Calculate the covariance: Multiply the deviations of Stock ABC and S&P 500 for each month and sum the results. Then divide by (number of months – 1).
4. Calculate the variance of the S&P 500: Square the deviations of the S&P 500 for each month, sum the results, and divide by (number of months – 1).
5. Calculate Beta: Divide the covariance by the variance.

Let’s assume, after performing these calculations (using statistical software is recommended), we find:

• Covariance (Stock ABC Return, S&P 500 Return) = 2.0
• Variance (S&P 500 Return) = 1.0

Then, Beta (β) = 2.0 / 1.0 = 2.0

This result suggests that Stock ABC is twice as volatile as the S&P 500. If the S&P 500 increases by 1%, Stock ABC is expected to increase by 2%. Conversely, if the S&P 500 decreases by 1%, Stock ABC is expected to decrease by 2%. A beta of 2 indicates a relatively high level of systematic risk for Stock ABC.

It’s important to note that beta is a historical measure and may not accurately predict future volatility. Also, beta only captures systematic risk (risk that cannot be diversified away) and doesn’t account for company-specific or unsystematic risk.