Question

You have found an asset with an arithmetic average return of 14.60 percent and a geometric average return of 10.64 percent. Your observation period is 25 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 of the asset =  13.94%

return of the asset =  13.11%

return of the asset = 11.46 %

Explanation:

given data

average return = 14.60 percent

geometric average return = 10.64 percent

observation period = 25 years

solution

we get here return of the asset over year  by Blume formula that is

return of the asset = ( T- 1 ) ÷ ( N - 1)  × geometric average + ( N -T)  ÷ ( N - 1)  × arithmetic average   ..................1

here N is observation period and T is time

put value in equation 1

return of the asset = $\frac{5-1}{25-1} *0.1064 + \frac{25-5}{25-1} * 0.1460$

return of the asset = 0.1394 = 13.94%

and

return of the assets = $\frac{10-1}{25-1} *0.1064 + \frac{25-10}{25-1} * 0.1460$

return of the asset = 0.13115 = 13.11%

and

return of the assets = $\frac{20-1}{25-1} *0.1064 + \frac{25-20}{25-1} * 0.1460$

return of the asset = 0.11465 = 11.46 %