Question

Louis owns a stock that has an average geometric return of10.50 percent and an average arithmetic return of 11.00 percent over the past six years. What average annual rate of return should Louis expect to earn over the next four years?

Answer 1

Answer:

Average annual rate of return should Louis expect to earn over the next four years is 10.7%

Explanation:

The formula we are going o use is:

$Expected\ Return=\{(\frac{R-1}{N-1})*i_{g}\}+\{(\frac{N-R}{N-1})*i_{a}\}$

Where:

R is the number of years over which Louis expect to earn.

N is the number of years of average arithmetic return.

i_{g} is the average geometric return=10.50%=0.105.

i_{a} is the average arithmetic return =11%=0.11.

Solution:

$Expected\ Return=\{(\frac{R-1}{N-1})*i_{g}\}+\{(\frac{N-R}{N-1})*i_{a}\}\\Expected\ Return=\{(\frac{4-1}{6-1})*0.105\}+\{(\frac{6-4}{6-1})*0.11\}\\Expected\ Return=0.107$

Average annual rate of return should Louis expect to earn over the next four years is 10.7%