How to Calculate Beta

The table below shows the equity betas for the firms presented in the case (using Jan-92 to Dec-96 equal weight NYSE/AMEX/NASDAQ as market portfolio):

For the calculation of equity, beta is a necessity because there is no comparison that matches its operational profile. Beta 1.17 ke = (4.58%+1.17) =

Beta is the slope of the characteristic line. As shown in appendix1, we use the monthly historical data from April 2003 to April 2008 to graph SCL. We use S&P 500 as the market because it contains the stocks of 500 Large-Cap corporations and can reflect the market change broadly. As shown in exhibit 1, we can get the SCL: Ri-Rf = - 0.001 + 0.1649(Rm - Rf). So the beta is 0.1649 and the alpha (intercept) is -0.001. From the regression line, we find the R square is only 0.103. It reflects the degree that X variable explains Y variable is 10.3%. That is, Ri-Rf has no close relationship with Rm-Rf. In addition, due to the fact that beta is only 0.1649, it also provides the same result which Ri-Rf and Rm-Rf have no strong positive relationship. It is a good issue to consider why Wal-Mart stock return does not relate with S&P 500 return very well. From exhibit 2, we find the Wal-Mart price did not change very much while S&P 500 price went up. The major reasons may be that S&P 500 includes many high-tech stocks and those stocks performed very well during the period; therefore the volatility is greater than Wal-Mart. Moreover, maybe Wal-Mart has lower weight in S&P 500 so its trend of price change is different from S&P 500. From exhibit2, we also find Wal-Mart had good relationship with S&P 500 before 2004. To examine the situation, we use the data from 1998 to 2003 and find the SCL

The historical beta comes from historical data. This kind of beta would slope coefficient in a regression, and associated with company's stock returns and market returns. This approach is conceptually straightforward, and complications quickly arise in practice.

* Stock Beta: Exhibit 5 shows a detailed measurement of the company’s stock returns in relation to the rest of the market through 5-year historical price and index data. The analysis includes monthly returns of both the NYSE and the S&P 500 index in order to capture a comprehensive view of the market return. In each comparison, the monthly returns of the Target stock and market are plotted on Y-axis and X-axis respectively to get the regression line’s slope or beta. The analysis arrives at an average beta of 0.988 which indicates a similar movement of Target stock’s returns in comparison to the whole market over time.

The regression that we performed in excel for both stocks yielded a beta of .73576 for Reynolds, and a beta of 1.4198 for Hasbro. In question 2 we learned that although Reynolds stock was riskier independently, adding it to the portfolio made it more diversified compared to adding Hasbro, due to the fact that it was less correlated to the market portfolio. Beta is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Therefore, since the beta of Reynolds is lower than Hasbro, our beta calculations align with the fact that Reynolds stock makes the overall portfolio less risky. This finding is also intuitive when considering the nature of the companies; Reynolds is a Tobacco company meaning that is should be less sensitive to changes in market conditions than a toy company like Hasbro.

In the Fama & French paper, they found that: 1) stocks with high beta did not have consistently higher returns than low-beta stocks; 2)

Cost of Equity = Risk free rate + (Market return – risk free rate) X beta

Cost of Equity = Risk Free Rate + Beta Equity*(Average Market Return – Risk Free Rate)

Expected return on market rate Rm is provided at page 175 in Myers and it is the average nominal return on stocks for the last century, the value is 11.7%

2. Compares the returns of the asset to the market over a period of time (Beta)

We use the equation ri=(Pt-Pt-1+Dt)/Pt-1 to calculate the monthly return of stock of Charles Schwab Corp, Quick & Reilly Group and Waterhouse Investor Srvcs. Then we have two methods to calculate the Beta of Equity for each company.

13. According to these three scatterplots, three-year data and three-month data both show the beta of holding Under Armour shares should be around 1.22~1.23. However,

For estimation of betas, the above equation was run for the period from Jan, 2003 to Dec, 2006. Based on the estimated betas we have divided the sample of 63 stocks into 10 portfolios each comprising of 6 stocks except portfolio no.1, 5 and 10 having seven stocks each. The first portfolio 1 has the 7 lowest beta stocks and the last portfolio 10 has the 7 highest beta stocks. The rationale for forming portfolios is to reduce measurement error in the betas.

To calculate beta, we took the beta of assets of the company as a while and set that equal to the percentage of equity for each division and multiplied by the beta of equity for each respective division.