Question
In: Finance
Find the arithmetic annual mean rate of return and the geometric annual mean rate of return. Which one should be used?
| Year | Beginning value | Ending value |
| 1 | 110 | 115 |
| 2 | 115 | 138 |
| 3 | 138 | 110,4 |
Find the arithmetic annual mean rate of return and the geometric annual mean rate of return. Which one should be used?
Solutions
Expert Solution
| Year | Beginning value | Ending value | Return |
| 1 | 110 | 115 | =115/110 - 1 = 0.04545454545 |
| 2 | 115 | 138 | =138/115 - 1 = 0.2 |
| 3 | 138 | 110.4 | =110.4/138 - 1 = -0.2 |
Arithmetic annual mean return = (0.04545454545 + 0.2 - 0.2)/3
Arithmetic annual mean return = 0.01515151515
Arithmetic annual mean return = 1.515151515%
Geometric annual mean return = (Ending value in year 3)/(Beginning value in year 1)^(1/3) - 1
Geometric annual mean return = (110.4/110)^(1/3) - 1
Geometric annual mean return = 1.0036363636^(1/3) - 1
Geometric annual mean return = 1.0012106549 - 1
Geometric annual mean return = 0.0012106549
Geometric annual mean return = 0.12106549%
Geometric annual mean return should be used because it takes compounding into effect, while the arithmetic average return does not.
jeff jeffy answered 2 years agoRelated Solutions
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