An asset has had an arithmetic return of 10.6 percent and a geometric return of
ID: 2762438 • Letter: A
Question
An asset has had an arithmetic return of 10.6 percent and a geometric return of 8.6 percent over the last 82 years. What return would you estimate for this asset over the next 5 years? 19 years? 26 years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
An asset has had an arithmetic return of 10.6 percent and a geometric return of 8.6 percent over the last 82 years. What return would you estimate for this asset over the next 5 years? 19 years? 26 years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Explanation / Answer
Since, an arithmetic mean refered to expected rate of return while geometric mean refered to growth rate.Now, we compute future annual returns.We have,
(a) For 5 Years:
Future annual return = Expected return (1+growth rate)time
Future annual return for 5 years = 10.6 ( 1 + 0.086)5
Future annual return for 5 years = 10.6 x (1.086)5 = 10.6 x 1.51 = 16.00
(b) For 19 Years:
Future annual return = Expected return (1+growth rate)time
Future annual return for 19 years = 10.6 ( 1 + 0.086)19
Future annual return for 5 years = 10.6 x (1.086)19= 10.6 x 4.79 = 50.77
(c) For 26 Years:
Future annual return = Expected return (1+growth rate)time
Future annual return for 26 years = 10.6 ( 1 + 0.086)26
Future annual return for 5 years = 10.6 x (1.086)26= 10.6 x 8.54 = 90.52
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