To determine: The arithmetic and geometric average return.
Introduction:
Total return refers to the total income from an investment. The total income includes the periodic incomes and the increase or decrease in the value of an asset.
Arithmetic average return refers to the
Geometric average return refers to the return after compounding the average returns for multiple years.
Answer to Problem 21QP
The arithmetic average return is 17.68% and the geometric average return is 16.15%.
Explanation of Solution
Given information:
Refer Question and Problems 21 for price and dividend details.
The formula to calculate the total percentage returns:
The formula to calculate the arithmetic average return:
Where,
“∑Xi” refers to the total of observations,
“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),
“N” refers to the number of observations.
Formula:
The formula to calculate the geometric average return:
Where,
“R” is the annual returns for the investment,
“T” is the years of returns.
Compute the percentage return for year 1:
Note: The opening price of stock of year 1 is the closing price of stock of year 2 that is $107.11 and the opening stock of price is $99.15. The dividend received in the year 2 is $1.60.
Hence, the percentage return for Year 1 is 9.6%.
Compute the percentage return for year 2:
Note: The opening price of stock of year 2 is the closing price of stock of year 3 that is $91.65 and the opening stock of price is $107.11. The dividend received in year 3 is $2.
Hence, the percentage return for Year 2 is −12.567%
Compute the percentage return for year 3:
Note: The opening stock of year 4 is the closing price of stock of year 3 that is $127.16 and the opening stock of price is $91.65. The dividend received in year 4 is $2.20.
Hence, the percentage return for Year 3 is 41.15%.
Compute the percentage return for Year 4:
Note: The opening stock of year 5 is the closing price of stock of year 4 that is $162.15 and the opening stock of price is $127.16. The dividend received in year 5 is $2.60.
Hence, the percentage return for Year 4 is 29.57%.
Compute the percentage return for Year 5:
Note: The opening stock of year 6 is the closing price of stock of year 5 that is $192.60 and the opening stock of price is $162.15. The dividend received in year 5 is $3.
Hence, the percentage return for Year 5 is 20.63%.
Compute the arithmetic average return:
Hence, the arithmetic average return is 17.68%.
Compute the geometric average return:
Hence, the geometric average return is 16.15%.
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