Tamisha McQuilkin Unit 4 Assignment GB550 Financial Management Dr. Prondzinski May 17, 2011 24-2 Security A has an expected rate of return of 6%, a standard deviation of returns of 30%, a correlation coefficient with the market of -0. 25, and a beta coefficient of -0. 5. Security B has an expected return of 11%, a standard deviation of returns of 10%, a correlation with the market of . 75, and a beta coefficient of 0. 5. Which security is more risky? Why? Using SML: rA= rrf + (rm – rrf)bi Security A is riskier because of its negative correlation to the market.
Also its beta is negative causing to believe its risk will increase over time. 24-8 You are given the following set of data: Historical Rates of Return| | | Year| NYSE| Stock Y| 1| 4. 0%| 3. 0%| 2| 14. 3| 18. 2| 3| 19| 9. 1| 4| -14. 7| -6. 0| 5| -26. 5| -15. 3| 6| 37. 2| 33. 1| 7| 23. 8| 6. 1| 8| -7. 2| 3. 2| 9| 6. 6| 14. 8| 10| 20. 5| 24. 1| 11| 30. 6| 18. 0| | Mean = 9. 8%| 9. 8%| | ? = 19. 6%| 13. 8%| a. Construct a scatter diagram showing the relationship between returns on Stock Y and the market.
Use a spreadsheet or a calculator with a linear regression function to estimate beta. ? = 0. 62 b. Give a verbal interpretation of what the regression line and the beta coefficient show about stock Y’s volatility and relative risk as compared with those of other stocks. This graph shows that stock Y’s volatility follows the basic trend of the market (NYSE). The regression line and beta coefficient shows a positive correlation between stock Y and the market with an upward trending regression line and positive beta coefficient of 0. 62.
Also, the plots of stock Y lie closer to the regression line than the market leading to believe that stock Y is less risky than the other stocks in the market. c. Suppose the regression lines were exactly as shown by your graph from part b but the scatter of points were more spread out. How would this affect (1) the firm’s risk if the stock held in a one-asset portfolio and (2) the actual risk premium on the stock if the CAPM holds exactly? If the plots were more spread out on the regression line it would show that the firm’s risk would increase as this shows a greater amount of volatility and greater risk.
The actual risk premium on the stock if the CAPM held exactly would be equal to the required rate of return. d. Suppose the regression line were downward sloping and the beta coefficient were negative. What would this imply about (1) Stock Y’s relative risk, (2) its correlation with the market, and (3) its probable risk premium? If the regression line were downward sloping and the beta coefficient were negative stock Y’s relative risk would increase stock Y’s correlation with the market would have an inverse relationship and its probable risk premium would decrease.