Stock Beta. In June 2016 , Yahoo Finance reported the beta...

Stock Beta. In June 2016 , Yahoo Finance reported the beta value for Coca-Cola was .82 (Yahoo Finance website). Betas for individual stocks are determined by simple linear regression. The dependent variable is the total return for the stock, and the independent variable is the total return for the stock market, such as the return of the $\mathrm{S} \& \mathrm{P} 500$. The slope of this regression equation is referred to as the stock's beta. Many financial analysts prefer to measure the risk of a stock by computing the stock's beta value. The data contained in the file CocaCola show the monthly percentage returns for the S\&P 500 and the Coca-Cola Company for August 2015 to May 2016 . $\begin{array}{lll} & \text { S\&P } 500 & \text { Coca-Cola } \\ \text { Month } & \text { \% Return } & \text { \% Return } \\ \text { August } & -3 & 3 \\ \text { September } & 8 & 6 \\ \text { October } & 0 & 1 \\ \text { November } & -2 & 1 \\ \text { December } & -5 & 0 \\ \text { January } & 0 & 0 \\ \text { February } & 7 & 8 \\ \text { March } & 0 & -3 \\ \text { April } & 2 & 0 \\ \text { May } & -5 & -1\end{array}$ a. Develop a scatter diagram with the $\mathrm{S} \& \mathrm{P} \%$ Return as the independent variable. b. What does the scatter diagram developed in part (a) indicate about the relationship between the returns of the $\mathrm{S} \& \mathrm{P} 500$ and those of the Coca-Cola Company? c. Develop the least squares estimated regression equation. d. Provide an interpretation for the slope of the estimated equation (i.e., the beta). e. Is your beta estimate close to $.82 ?$ If not, why might your estimate be different?

Stock Beta. In June 2016 , Yahoo Finance reported the beta value for Coca-Cola was .82 (Yahoo Finance website). Betas for individual stocks are determined by simple linear regression. The dependent variable is the total return for the stock, and the independent variable is the total return for the stock market, such as the return of the $\mathrm{S} \& \mathrm{P} 500$. The slope of this regression equation is referred to as the stock's beta. Many financial analysts prefer to measure the risk of a stock by computing the stock's beta value. The data contained in the file CocaCola show the monthly percentage returns for the S\&P 500 and the Coca-Cola Company for August 2015 to May 2016 .
$\begin{array}{lll} & \text { S\&P } 500 & \text { Coca-Cola } \\ \text { Month } & \text { \% Return } & \text { \% Return } \\ \text { August } & -3 & 3 \\ \text { September } & 8 & 6 \\ \text { October } & 0 & 1 \\ \text { November } & -2 & 1 \\ \text { December } & -5 & 0 \\ \text { January } & 0 & 0 \\ \text { February } & 7 & 8 \\ \text { March } & 0 & -3 \\ \text { April } & 2 & 0 \\ \text { May } & -5 & -1\end{array}$
a. Develop a scatter diagram with the $\mathrm{S} \& \mathrm{P} \%$ Return as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the returns of the $\mathrm{S} \& \mathrm{P} 500$ and those of the Coca-Cola Company?
c. Develop the least squares estimated regression equation.
d. Provide an interpretation for the slope of the estimated equation (i.e., the beta).
e. Is your beta estimate close to $.82 ?$ If not, why might your estimate be different?

Key Concepts

Interpretation of Regression Slope (Beta)

The slope of the regression line in the context of stock analysis, referred to as the beta, quantifies the sensitivity of the stock’s returns to changes in the market's returns. It represents the expected change in the stock’s return for a one-unit change in the market return. A beta of less than one suggests that the stock tends to be less responsive to market movements, while a beta greater than one implies higher responsiveness.

Scatter Diagram

A scatter diagram is a graphical representation of the relationship between two quantitative variables. In this context, it is used to plot the market returns on one axis and the stock returns on the other. This visualization helps in assessing the direction, form, and strength of the linear relationship between the variables, and is a crucial step before fitting a regression model.

Data Limitations and Estimation Variability

When estimating parameters like beta using historical return data, differences in sample periods, data frequency, or the specific market index used can lead to estimates that differ from commonly reported values. Estimation variability can also arise from random fluctuations in returns, outlier effects, or changes in market conditions, all of which should be considered when interpreting the results.

Simple Linear Regression

Simple linear regression is a statistical method used to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered the independent (or predictor) variable, and the other is the dependent (or response) variable. The estimation of the regression line is typically done using the least squares method, which minimizes the sum of the squared differences between the observed values and the values predicted by the model.

Stock Beta

In finance, the stock beta is a measure of the volatility or systematic risk of a stock compared to the overall market. It is derived as the slope coefficient in a regression analysis where the stock's return is regressed on the market's return. A beta greater than 1 indicates that the stock is more volatile than the market, while a beta less than 1 indicates less volatility relative to the market.

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