Understanding Beta of a Stock in Excel

Beta of a stock is a measure of how much the stock’s returns change in relation to the market’s returns. It tells you how risky or volatile the stock is compared to the market as a whole. For example, if a stock has a beta of 1.5, it means that it is 50% more volatile than the market. If the market goes up by 10%, the stock is expected to go up by 15%. If the market goes down by 10%, the stock is expected to go down by 15%. A stock with a beta of 0.5, on the other hand, is 50% less volatile than the market. If the market goes up by 10%, the stock is expected to go up by 5%. If the market goes down by 10%, the stock is expected to go down by 5%. A stock with a beta of 0 is not affected by the market at all. Its returns are independent of the market’s movements.

Beta is calculated by using historical data on the stock’s and the market’s returns. It is the slope of the line that best fits the scatter plot of the stock’s returns versus the market’s returns. Beta can also be used in the capital asset pricing model (CAPM), which is a formula that estimates the expected return of a stock based on its risk and the risk-free rate. According to CAPM, the higher the beta of a stock, the higher the return that investors demand for investing in it. You can learn more about beta and CAPM from these sources.

Basic Theory:

Beta is a measure of a stock’s systematic risk, indicating how much the stock price tends to move in relation to a benchmark index, typically the market index (e.g., S&P 500). A beta of 1 suggests the stock tends to move with the market, while a beta greater than 1 indicates higher volatility, and a beta less than 1 suggests lower volatility.

Procedures:

The formula to calculate beta is:

$\text{Beta} = \frac{\text{Covariance(Ri, Rm)}}{\text{Variance(Rm)}}$

where:

$\text{Covariance(Ri, Rm)}$ is the covariance between the stock’s returns (Ri) and the market returns (Rm).
$\text{Variance(Rm)}$ is the variance of the market returns.

Comprehensive Explanation:

Let’s consider a scenario where Stock XYZ’s returns are being compared to the S&P 500 index. We have historical monthly returns for both the stock and the market.

Scenario:

Stock XYZ Returns: 1%, 2%, 3%, -1%, 0.5%
S&P 500 Returns: 0.8%, 1.5%, 2%, -0.5%, 1%

Calculation:

Calculate the average returns:
- Stock XYZ: $\text{Average(Ri)} = \frac{1\% + 2\% + 3\% - 1\% + 0.5\%}{5} = 1.1\%$
- S&P 500: $\text{Average(Rm)} = \frac{0.8\% + 1.5\% + 2\% - 0.5\% + 1\%}{5} = 1.16\%$
Calculate Covariance:
- $\text{Covariance(Ri, Rm)} = \frac{\sum{(Ri - \text{Average(Ri)}) \times (Rm - \text{Average(Rm)})}}{n-1}$
- Substituting values, we get $\text{Covariance(Ri, Rm)} = 0.0091$
Calculate Variance of Market Returns:
- $\text{Variance(Rm)} = \frac{\sum{(Rm - \text{Average(Rm)})^2}}{n-1}$
- Substituting values, we get $\text{Variance(Rm)} = 0.0032$
Calculate Beta:
- $\text{Beta} = \frac{0.0091}{0.0032} = 2.8438$

Excel Table:

Month	Stock XYZ Returns	S&P 500 Returns
1	1%	0.8%
2	2%	1.5%
3	3%	2%
4	-1%	-0.5%
5	0.5%	1%

Result:

The beta for Stock XYZ, based on this scenario, is approximately 2.84. This indicates that the stock is expected to be about 2.84 times as volatile as the overall market.

Other Approaches:

Using Regression Analysis:
- Excel’s built-in regression analysis can be used to directly calculate beta.
Online Tools:
- Various online financial tools and platforms provide beta values for stocks.
Using Beta from Financial Websites:
- Many financial websites provide beta values for stocks, saving you the trouble of manual calculations.