Answer:
a. The arithmetic average time-weighted rates of return for the investor is 2.93%, while the geometric average time-weighted rates of return for the investor is 2.08%
b. The total cash flow for each year are as follows:
January 1, 2015 Total Cash Flow = -$700
January 1, 2016 Total Cash Flow = -$457
January 1, 2017 Total Cash Flow = $156
January 1, 2018 Total Cash Flow = $979
Explanation:
Note: This question is not complete and the data in need are merged together. The complete question with the sorted data is therefore provided before answering the question. See the attached pdf file for the complete question with the sorted data.
The explanation to the answer is now given as follows:
a. What are the arithmetic and geometric average time-weighted rates of return for the investor? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
The formula for calculating each of the arithmetic and geometric return are given as follows:
Arithmetic average return = Sum of returns/ number of years ……………….. (1)
Geometric average return = n * ((1+r1)*(1+r2)*(1+r3)…(1+rn)^(1/n) - 1 .……….. (2)
Where;
n = years 1, 2, 3….
r1, r2, r3…are the returns for year 1, 2, 3….
Return for each year = (capital gains + dividend) / Previous year Beginning-of-Year Price
Where;
Capital gains = Current year Beginning-of-Year Price – Previous year Beginning-of-Year Price
Therefore, we have:
Return for each year = ((Current year Beginning-of-Year Price – Previous year Beginning-of-Year Price) + dividend) / Previous year Beginning-of-Year Price ………………. (3)
Using equation (3), we have:
2016 Return = ((159 - 140) + 4) /140 = 0.164285714285714
2017 Return = ((132 - 159) + 4} /159 = -0.144654088050314
2018 Return = ((137 - 132) + 4) /132 = 0.0681818181818182
Using equation (1), we have:
Arithmetic mean = (2016 Return + 2017 Return + 2018 Return) / 3 = (0.164285714285714 - 0.144654088050314 + 0.0681818181818182) / 3 = 0.0292711481390727, or 2.92711481390727%
Approximating to 2 decimal places, we have:
Arithmetic mean = 2.93%
Using equation (2), we have:
Geometric mean = ((1 + 2016 Return) * (1 + 2017 Return) * (1 + 2018 Return))^(1/3) - 1
Geometric mean = ((1 + 0.164285714285714) * (1 - 0.144654088050314) * (1 + 0.0681818181818182))^(1/3) - 1
Geometric mean = 1.02081923500671 - 1
Geometric mean = 0.02081923500671, or 2.081923500671%
Approximating to 2 decimal places, we have:
Geometric mean = 2.08%
Therefore, the arithmetic average time-weighted rates of return for the investor is 2.93%, while the geometric average time-weighted rates of return for the investor is 2.08%.
b. Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2015, to January 1, 2018.
Note: See the attached excel file for the chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2015, to January 1, 2018.
In the attached excel file, Beginning-of-Year Price for January 1, 2015 and January 1, 2016 are used as negative figures because the purchase of stock will result in a cash outflow.
