Question

You have found an asset with a 13.60 percent arithmetic average return and a 10.44 percent geometric return. Your observation period is 30 years. What is your best estimate of the return of the asset over the next 5 years? 10 years? 20 years?

Answer 1

Answer:

Return on assets  =  10.87 %

Return on assets  =  11.42%

Return on assets  =  12.51 %

Explanation:

given data

arithmetic average return = 13.60 percent = 0.1360

geometric return = 10.44 percent = 0.1044

observation period N = 30 years

solution

we will use here Blume formula for return of the asset  for 5 , 10 and 20 year

Return on assets = Arithmetic average return × (N - T) ÷ (N - 1) + Geometric average × (T - 1) ÷ (N - 1)   ....................1

here N is observation period and t is time period i.e 5, 10 and 20

put here value for all 3 we get

Return on assets = $\frac{5-1}{30-1}*0.1360 +\frac{30-5}{30-1}*0.1044$  

Return on assets  = 0.108759 = 10.87 %

and

Return on assets  = $\frac{10-1}{30-1}*0.1360 +\frac{30-10}{30-1}*0.1044$

Return on assets  = 0.114207 = 11.42%

and

Return on assets  =  $\frac{20-1}{30-1}*0.1360 +\frac{30-20}{30-1}*0.1044$

Return on assets  = 0.125103 = 12.51 %