(, (Solving a comprehensive problem) Use the end-of-year stock price data in the popup window, B. to answer the following questions for the Harris and Pinwheel companies. a. Compute the annual rates of return for each time period and for both firms b. Calculate both the arithmetic and the geometric mean rates of return for the entire three-year period using your annual rates of return from part a. (Note: you may assume that neither firm pays any dividends.) c. Compute a three-year rate of return spanning the entire period (i.e., using the ending price for period 1 and ending price for period 4). d. Since the rate of return calculated in part c is a three-year rate of return, convert it to an annual rate of return by using the following equation: ( Three-Year Rate of Return w]+[*** Annual Rate of Return e. How is the annual rate of return calculated in part d related to the geometric rate of return? When you are evaluating the performance of an investment that has been held for several years, what type of average rate of return (arithmetic or geometric) should you use? Why? a. Enter the annual rate of return for each year for Harris in the table below. (Round to two decimal places.) Time Annual Rate of Return Annual Rate of Return Value of Harris Stock $11 9 1 1 2 Value of Pinwheel Stock $22 32 29 24 3 4 13 17 Enter the annual rate of return for each year for Pinwheel in the table below. (Round to two decimal places.) Time Value of Annual Rate Value of Annual Rate Harris Stock of Return Pinwheel Stock of Return 1 $11 $22 2 9 - 18.18% 32 3 13 44.44% 29 4 17 30.77% 24 % b. The arithmetic average rate of return earned by investing in Harris stock over this period is %. (Round to two decimal places.) The arithmetic average rate of return earned by investing in Pinwheel stock over this period is %. (Round to two decimal places.) The geometric average rate of return eamed by investing in Harris stock over this period is % (Round to two decimal places.) The geometric average rate of returneamed by investing in Pinwheel stock over this period is % (Round to two decimal places.) c. The three-year rate of return spanning the entire period for Harris is % (Round to two decimal places.) The three-year rate of return spanning the entire period for Pinwheel is % (Round to two decimal places.) d. The annual rate of return converted from the three-year rate in partc for Harris is %. (Round to two decimal places.) The annual rate of return converted from the three-year rate in part for Pinwheel is % (Round to two decimal places.) e. How is the annual rate of return calculated in part d related to the geometric rate of return? (Select the best choice below.) A. The annual rate of return calculated in part d is nothing but the arithmetic average rate of return calculated in a different way. OB. The annual rate of return calculated in part d is not related to the geometric average rate of return. C. The annual rate of return calculated in part d is nothing but the geometric average rate of return calculated in a different way. OD. The annual rate of return calculated in part d is the same as the geometric rate of return in this problem but this is only a coincidence When you are evaluating the performance of an investment that has been held for several years, what type of average rate of return (arithmetic or geometric) should you use? Why? Select the best choice below.) O A. Arithmetic average return better describes the average annual rate of return over a period because it is a simple average so it answers the question concerning the expected rate of return over a period. OB. Geometric average return better describes the average annual rate of return over a period because it is a simple average, so it answers the question concerning the expected rate of return over a period. OC. The arithmetic rate of return should be used. It better describes the average annual rate of return over a period because it compounds at the same rate while the geometric rate of return is best used for a single period. OD. The geometric rate of return should be used. It better describes the average annual rate of return over a period because it compounds at the same rate while the arithmetic rate of return is best used for a single period
