Part 4: Risky Business Lastly, just for fun, El Cap Climbing Company (ECCC) is looking at determining their sensitivity to market fluctuations. Since ECCC isnt publically traded and cant look at their own stock history, they must evaluate their competitors. Black Diamond Equipment is their closest competitor, but the company doesnt have enough trading volume to make any sound conclusions. Leah identifies Callaway Golf Company (ELY) as ECCCs closest publicly-traded competitor. Even though ELY sells golf equipment, it too is a specialized company selling high-tech sports equipment. Finding Beta with CAPM Note: This information is also in your textbook. The CAPM is one of the most thoroughly researched models in financial economics. When beta is estimated in practice, a variation of CAPM, called the market model, is often used. To derive the market model, we start with the CAPM: E(Ri) 5 Rf 1 ?[E(RM) 2 Rf ] Since CAPM is an equation, we can subtract the risk-free rate from both sides, which gives us: E(Ri) 2 Rf 5 b[E(RM) 2 Rf ] This equation is deterministicthat is, exact. In a regression, we realize that theres some indeterminate error. We need to formally recognize this in the equation by adding epsilon, which represents this error: E(Ri) 2 Rf 5 b[E(RM) 2 Rf ] 1 e Finally, think of the above equation in a regression. Since theres no intercept in the equa- tion, the intercept is zero. However, when we estimate the regression equation, we can add an intercept term, which well call alpha: E(R ) 2 R 5 a 1 b[E(R ) 2 R ] 1 e The intercept term is known as Jensens alpha, and it represents the excess return. If CAPM holds exactly, this intercept should be zero. Think of alpha in terms of the SML: If the alpha is positive, the stock plots above the SML; if the alpha is negative, the stock plots below the SML. Youll first create a scatter plot and then perform a regression analysis for ELY stock and the mutual fund. Then use those results to compare and analyze the results. A. Scatter Plotting and Regression Analysis Use the following steps to create the scatter plot: 1. Go to the Part 4 Stock Data tab in your Excel spreadsheet. Highlight column KM headings, then hold down the Ctrl button and select cells K-3 through M-62. 2. Go to the INSERT tab, click on Scatter Chart, and select the first style. 3. Move the chart to the side of the data, and increase the size of the chart. Click on the Chart Title and change it to Risk Premium Analysis. 4. In the DESIGN tab, click on Quick Layout. Select the layout that gives you the y formulas and the R2. 5. Move the y formulas and the R2 to the bottom right-hand corner of the chart. Now use the following steps to create a regression analysis for ELY and for the Mutual Fund: 1. First, check to see that you have the ability to run the analysis. Go to the DATA tab in Excel, and look for the Data Analysis feature shown in the image below. 2. Click on Data Analysis. A dialog box with a list of analysis tools will open. Select Regression from the list and click OK. 3. Next, another dialog box opens for you to select your Inputs and Output for the regression. Select the input data ranges by highlighting S&P Risk Premium numbers (x-axes range) and the number for the asset youre com- paring as the y-axes range. Output to a new worksheet (do not type a name in the text box). Select the check boxes for Labels, Confidence Level, and Residuals. Click OK. 4. Your regression analysis will open in a new worksheet. Rename the worksheet based on the premium being compared to the S&P premium, for example: ELY Regression Analysis. B. Answer the following questions: 1. In this regression, Rt is the return on the stock and Rft is the risk-free rate for the same period. RMt is the return on a stock market index, such as the S&P 500 index. ?i is the regression intercept, and b is the slope (and the stocks estimated beta). e represents the residuals for the regression. The intercept, a , is often called Jensens alpha. What does it measure? If an asset has a positive Jensens alpha, where would it plot with respect to the SML? R 2 R 5 a 1 b [R 2 R ] 1 e 2. Is the alpha of either ELY or the mutual fund significantly more or less than zero? (Hint: The alpha is the intercept.) 3. How do you interpret the beta for the stock and the mutual fund? (Hint: The beta is next to the coefficient.) 4. Which of the two regression estimates has the highest R-squared? Is this what you would have expected? Use the scatterplot to explain why.