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Journal of Business Case Studies – November/December 2010

Calculating The Beta Coefficient And

Required Rate Of Return For Coca-Cola

John C. Gardner, University of New Orleans, USA

Carl B. McGowan, Jr. Norfolk State University, USA

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ABSTRACT

In this paper, we demonstrate how to compute the required rate of return for Coca-Cola using

modern portfolio theory with data downloaded from the internet. We demonstrate how to

calculate monthly returns for the index and Coca-Cola and how to use the returns to compute the

beta coefficient and the required rate of return using the downloaded data. We show how to

validate the data for the market index and the company and how to compute the returns using the

dividend and stock split adjusted prices. We demonstrate how to graph the characteristic line for

Coca-Cola and use the graph to check that the regression was run correctly. We use Coca-Cola

and the S&P 500 Index in this paper, but any company listed on Yahoo! Finance can be used as

the example. This paper can be used as the basis of a lecture on intermediate corporate finance

or investments to demonstrate the process using a real company.

Keywords: beta; characteristic line; required rate of return; Coca-Cola; teaching note

INTRODUCTION

arkowitz1 (1952) began modern portfolio theory (MPT) which can be used to explain the

relationship between risk and return for assets, particularly stocks. Stock of companies that have

higher rates of return have higher levels of risk. In order to achieve a lower level of risk, an

investor must accept a lower expected rate of return. This concept is called the dominance principle and allows for

the creation of the efficient frontier. MPT partitions risk into non-systematic risk, which can be eliminated from a

portfolio through diversification, and systematic risk that is market wide and cannot be diversified. Non-systematic

risk is company specific and is reduced to zero in a large, well diversified portfolio. In order to determine

systematic risk for a stock, we use the market model developed by Sharpe2 (1964). The returns for a stock are

regressed as the dependent variable against a market index used as the independent variable. The slope coefficient

of the regression is the measure of systematic risk for the stock. Systematic risk measures the degree to which a

stock moves with the market. A higher beta coefficient implies that returns for the stock move more than the market

and a lower beta coefficient implies that returns for the stock move less that the market. The former are aggressive

stocks and the latter are defensive stocks.

In this paper, we show how to retrieve data from the internet, how to compute returns for both the market

index and the stock, and how to run a regression to determine the beta coefficient to measure the systematic risk for

the stock. In addition, we show how to graph the data with a trend line and statistics to verify that the first

regression is run correctly; that is, with the correct variable as the independent variable. We show how to do all of

this analysis using Excel.

1 Markowitz received The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1990.

2 Sharpe received The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1990.

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DOWNLOADING DATA FROM THE INTERNET

The data used for the analysis discussed in this paper are downloaded from the internet using the Yahoo!

finance.yahoo.com/. Once one arrives at the Yahoo!

Finance website, the S&P 500 data can be found by clicking on the “S&P500” icon and then, clicking on the

Historical Prices” icon. Click on the “Monthly” indicator to download monthly data and enter the dates. For this

paper we download sixty-one monthly, observations in order to calculate sixty monthly returns. The data columns

are: Date, Open, High, Low, Close, Average Volume, and Adjusted Close. The index and the Coca-Cola price are

adjusted for splits and dividends. Move the cursor to the bottom of the data and click on “Download to

Spreadsheet”. Save the data to a spreadsheet and repeat the process for the Coca-Cola data. Begin by entering the

Coca-Cola ticker symbol, KO, and download and save the data for the save time period.

CALCULATING RETURNS FOR THE S&P 500 INDEX AND FOR COCA-COLA3

In this paper, we use arithmetic returns to compute the beta coefficient for Coca-Cola. Arithmetic returns

are calculated by dividing the ending index or stock value, (Value1), by the beginning value, (Value0), and

subtracting one as in Equation [1]. An alternative method to calculate the return is to subtract the beginning value,

(Value0), from the ending value, (Value1), and dividing by the beginning value, (Value0), as in Equation [2]. Both

returns are adjusted for dividends and stock splits. The returns used in the regression analysis are arithmetic returns.

Return = [(Value1- Value0) – 1]

Return = [(Value1- Value0)/Value0)]

Five years of Monthly data are used to generate sixty data points4.

CALCULATING BETA FOR COCA-COLA5

Modern Portfolio Theory shows that investors are rewarded for the systematic risk of an investment and not

for the total risk of an investment because total risk includes firm specific risk that can be eliminated in a well

diversified portfolio. The specific risk of an individual stock is the slope coefficient of the characteristic line which

is the regression line between the monthly returns for the individual security and the monthly returns for the market

index. Beta coefficient lines are calculated using a sixty month regression. In this example, the beta coefficient for

Coca-Cola is calculated using sixty monthly observations of returns for Coca-Cola from 09/02/2003 to 08/01/2008

and returns for the S&P 500 Index for the same time period. Beta is the covariance between returns for Coca-Cola

and returns for the S&P 500 divided by the variance for the S&P 500.

RKO = AlphaKO + BetaKO (Rm)

RKO

the return for Coca-Cola stock

BetaKO the slope of the regression line between returns for the market and returns for Coca-Cola

AlphaKO the intercept coefficient for the regression line between returns for the market and returns for Coca-

Cola

(Rm) the return on the S&P 500 Stock market Index

(Rm – RF) the market risk premium is the additional return that stock holders receive for the additional risk of

holding stocks rather than the risk free asset, long-term government bonds.

Appendix A contains the data used to compute the Coca-Cola beta and are downloaded from Yahoo!

Finance. Column 1 shows the date and Columns 2 and 3 contain the stock split and dividend adjusted index and

price values, for the S&P 500 Index and for Coca-cola stock, respectively. The independent variable is the return for

3 See Brigham and Ehrhardt (2008, pages 223-225) for a discussion of how to compute a beta coefficient.

4 See Brigham and Ehrhardt (2008, page 223).

5 See Brigham and Ehrhardt (2008, pages 223-225) for a discussion of how to compute a beta coefficient.

[1]

[2]

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the S&P500 (Column 4) and the dependent variable is the return for Coca-Cola (Column 5). The returns are

calculated by dividing the ending index or stock value by the beginning value and subtracting one. An alternative

method to calculate the return is to subtract the beginning value from the ending value and dividing by the beginning

value. Both returns are adjusted for dividend and stock splits. The returns used are arithmetic returns.

Table 1 contains the regression results for the regression between the return for the S&P500 and for Coca-

Cola using Excel. The independent variable is the return for the S&P500 (x-axis) and the dependent variable is the

return for Coca-Cola (y-axis). Both returns are adjusted for dividends and stock splits. The adjusted R2 for the

regression is 0.23 and the F-statistic is 18.65, both of which are statistically significant at the 0.0000 level. The

regression coefficient is 0.7560 and has a t-statistic of 4.31 and is significant at the 0.0000 level.

Table 1: Coca-Cola versus the S&P 500 Regression of Arithmetic Means Returns from 09/02/03 to 08/01/08

Regression Statistics

Multiple R 0.493288

R Square 0.243333

Adjusted R Square 0.230287