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a. You want to estimate the market model for an individual stock and a mutual fund. First, go to finance.yahoo.com and download the adjusted prices
a. | You want to estimate the market model for an individual stock and a mutual fund. First, go to finance.yahoo.com and download the adjusted prices for the last 61 months for an individual stock and a mutual fund, and the S&P 500. Next, go to the St. Louis Federal Reserve website at www.stlouisfed.org. You should find the FRED database on this website. Look for the 1-Month Treasury Constant Maturity Rate and download this data. This will be the proxy for the risk-free rate. When using this rate, you should be aware that this interest rate is the annual interest rate, while we are using monthly stock returns, so you will need to adjust the 1-month T-bill rate. For the stock and mutual fund you select, estimate the beta and alpha of the stock using the market model. When you estimate the regression model, find the box that says Residuals and check this box when you do each regression. Because you are saving the residuals, you may want to save the regression output in a new worksheet. | |||||||||
1) Are the alpha and beta for each regression statistically different from zero? | ||||||||||
2) How do you interpret the alpha and beta for the stock and the mutual fund? | ||||||||||
3) Which of the two regression estimates has the highest R squared? Is this what you would have expected? Why? | ||||||||||
b. | In part a, you asked Excel to return the residuals of the regression, which is the epsilon in the regression equation. If you remember back to statistics, the residuals are the linear distance from each observation to the regression line. In this context, the residuals are the part of each monthly return that is not explained by the market model estimate. The residuals can be used to calculate the appraisal ratio, which is the alpha divided by the standard deviation of the residuals. | |||||||||
1) What do you think the appraisal ratio is intended to measure? | ||||||||||
2) Calculate the appraisal ratio for the stock and the mutual fund. Which has a better appraisal ratio? | ||||||||||
3) Often, the appraisal ratio is used to evaluate the performance of mutual fund managers. Why do you think the appraisal ratio is used more often for mutual funds, which are portfolios, than for individual stocks? |
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