Question

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A portfolio's performance is summarized in the table below. What is the geometric average return for...

A portfolio's performance is summarized in the table below. What is the geometric average return for the entire period?

Year Beginning of Year Price
2017 $40
2018 $45
2019 $41
2020 $44

Multiple Choice

  • 3.23%

  • 10.00%

  • 6.48%

  • 2.41%

  • 4.88%

Solutions

Expert Solution

Please note the solution.

> Concept

The geometric average return formula calculates the average rate of return on an investment that is compounded over multiple periods.

> Formula

GAR = [ (1+r1)×(1+r2)×...(1+rn)​ ]1/n − 1

Return = [ Closing Value - Beginning Value ] / Beginning Value

> Calculation

GAR =

Year Beginng Price Return
2017 40

= (45-40) / 40

= 12.50%
2018 45

= (41-45) / 45

= -8.89 %
2019 41

= (44-41) / 41

= 7.32%
2020 44 Since price of Beginning of 2021 not given

GAR = [ (1+r1)×(1+r2)×...(1+rn)​ ]1/n − 1

         = [ (1.1250) * ( 1 - 0.089 ) * (1.0732 ) ]1/3 - 1

         = [ (1.1250) * (0.911) * (1.0732 ) ]1/3 - 1

         = [ 1.0998959 ]1/3 - 1

         = 1.03224 - 1

        = 0.03225 or 3.23 % Answer

> Answer

The correct choice is Option 1 - 3.23 %.

Hope you understand the solution.

jeff jeffy answered 1 year ago
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