assume that you invested $100 in a stock mutual fund in year 1. at the end of ye

Question

assume that you invested $100 in a stock mutual fund in year 1. at the end of year 2 it grew to be $180. at the end of year 3 it became $108. at the end of year 4 it became $200. given this investment record what is the proper geometric average annual rate of return on your initial investment of $100 over the three year period
assume that you invested $100 in a stock mutual fund in year 1. at the end of year 2 it grew to be $180. at the end of year 3 it became $108. at the end of year 4 it became $200. given this investment record what is the proper geometric average annual rate of return on your initial investment of $100 over the three year period

Explanation / Answer

Given,

Initial investment=100

amount after,

year 2=180

year 3=108

year 4=200

the returns can be calculated as

r1=180-100/100=0.8

r2=108-180/180= -0.4

r3=200-108/108=0.85

using the geometric mean return formula,

Goemetric return={(1+r1)*(1+r2)*(1+r3)}^1/3 - 1

={1.8*0.6*1.85}^1/3 - 1

=1.26-1=0.26 or 26%

hence the geometric average annual rate of return on the investment over 3 year period is 26%

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