Question
In: Finance
The data is for stock ZZZ; price and dividend history are as follows: Year Beginning-of-Year Price Dividend...
The data is for stock ZZZ; price and dividend history are as follows:
Year Beginning-of-Year Price Dividend Paid at Year-End
2015 $118 $3
2016 126 3
2017 110 3
2018 115 3
What are the arithmetic and geometric average time-weighted rates of return for the investor?
| A. |
Arithmetic mean is 2.09% and the geometric average is 1.70% |
|
| B. |
Arithmetic mean is 2.09% and the geometric average is 1.90% |
|
| C. |
Arithmetic mean is 2.39% and the geometric average is 1.70% |
|
| D. |
Arithmetic mean is 2.09% and the geometric average is 1.90% |
Solutions
Expert Solution
Answer: Option (A)
| Year(i) | Beginning Price | Ending Price # | Capital Gain^ | Dividend | Total Return | Returns(Ri) | (1+Ri) | |
| 2015 | $ 118 | $ 126 | $ 8 | $ 3 | $ 11 | 9.32% | 1.0932 | |
| 2016 | $ 126 | $ 110 | $ (16) | $ 3 | $ (13) | -10.32% | 0.8968 | |
| 2017 | $ 110 | $ 115 | $ 5 | $ 3 | $ 8 | 7.27% | 1.0727 | |
| 2018 | $ 115 | NA | NA | $ 3 | ||||
| Sum | 6.28% | Product | 1.0517 |
| # Ending Price of 2015 will become the Beginning Price of 2016 |
| ^Capital Gain = Ending Price - Beginning Price |
| Total Return = Dividnd + Capital Gain |
| Return = Total Return / Beginning Price |
Note: Return for the year 2018 is not considered as Year End Price is not given (Due to which Capital Gain Computation is not available)
| Arthematic Mean = Sum of Observations / No. of Observations |
| Arthematic Mean = 6.28 / 3 |
| Arthematic Mean = 2.09% |
| Geometric Mean = [((1 + R1) × (1 + R2) × ... × (1 +Rn))^(1/n)] - 1 |
| Geometric Mean = [((1 + 0.0932)(1 - 0.1032)(1 + 0.0727))^(1/3)] - 1 |
| Geometric Mean = [(1.0517)^(1/3)] - 1 |
| Geometric Mean = 1.017- 1 |
| Geometric Mean = 1.7% |
jeff jeffy answered 2 years agoRelated Solutions
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