Question

The beginning share price for a security over a three-year period was $50. Subsequent year-end prices were $62, $58 and $64. The arithmetic average annual rate of return and the geometric average annual rate of return for this stock was

A. 9.30% and 8.58%, respectively.
B. 9.30% and 7.89%, respectively.
C. 9.30% and 7.03%, respectively.
D. 9.30% and 6.37%, respectively.

Answer 1

Arithmetic average rate of return = 9.30 %

geometric average annual rate of return = 8.58%

correct option is A 9.30 % and 8.58%

Step-by-step explanation:

given data

beginning share price = $50

time = 3 year

end year 1 prices = $62

end year 2 prices = $58

end year 3 prices = $64

to find out

arithmetic average annual rate of return and the geometric average annual rate of return

solution

we get here return for each period that is express as

Period 1 =
`(end\ year1)/(beginning)` ...........1

Period 1 =
`(62-50)/(50)`

Period 1 = 24%

and

Period 2 =
`(end\ year2)/(beginning1)`

Period 2 = Period 1 =
`(58-62)/(62)`

Period 2 = -6.45%

and

Period 3 =
`(end\ year3)/(beginning2)`

Period 3 =
`(64-58)/(58)`

Period 3 = 10.34%

so

here Arithmetic average rate of return will be

Arithmetic average rate of return = (24% + -6.45% + 10.34%) ÷ 3

Arithmetic average rate of return = 9.30%

and

geometric average annual rate of return will be here as

geometric average annual rate of return =
`((1+r1) *(1+r2)*(1+r3))^(1/3)` - 1 ................2

geometric average annual rate of return =
`((1+0.24) +(1-0.0645)+(1+0.1034))^(1/3)` - 1

geometric average annual rate of return = 8.58%