Question

An asset has had an arithmetic return of 11.9 percent and a geometric return of 9.9 percent over the last 86 years. What return would you estimate for this asset over the next 8 years? 23 years? 39 years? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

11.74% ; 11.38%; 11.01%

Step-by-step explanation:

Given the following :

Arithmetic return (Ar) = 11.9%

Geometric return (Gr) = 9.9%

N = 86 years = Past period

A) Return in the next 8 years

T = future period = 8 years

Return = (T - 1) / (N - 1) * Geometric average + (N - T) / (N - 1) * Arithmetic average.

Return = (8 - 1) / (86 - 1) * 0.099 + (86 - 8) / (86 - 1) * 0.119

(0.0823529 * 0.099) + (0.9176470 * 0.119)

= 0.1173529301

= 0.1173529301 * 100 = 11.74%

B) over the next 23 years

T = 23 years

Return = (T - 1) / (N - 1) * Geometric average + (N - T) / (N - 1) * Arithmetic average.

Return = (23 - 1) / (86 - 1) * 0.099 + (86 - 23) / (86 - 1) * 0.119

(0.2588235 * 0.099) + (0.7411764 * 0.119)

= 0.1138235181

= 0.1138235181 * 100 = 11.38%

C.) over 39 years

F = 39 years

Return = (T - 1) / (N - 1) * Geometric average + (N - T) / (N - 1) * Arithmetic average.

Return = (39 - 1) / (86 - 1) * 0.099 + (86 - 39) / (86 - 1) * 0.119

(0.4470588 * 0.099) + (0.5529411 * 0.119)

= 0.1100588121

= 0.1100588121 * 100 = 11.01%