Question

Your mutual fund has just sent you its annual performance review. In it, you are told that the returns for the past 3 years were: a loss of 20% three years ago, a 10% gain two years ago, and a 25% gain last year.

The opening remark in the review says you will be glad to know your fund has provided an average return of 5% over the past three years. Suppose you initially invested $1,000 three years ago. If you made no additional investments and any dividends were automatically reinvested, is 5% the appropriate average annual return you earned on your investment? If not, what is the appropriate average annual rate of return over the three year? If not why not?

Answer 1

The average return of 5% as stated in the review is not appropriate.

Given that the last three year's performance is loss of 20%, gain of 10% and 25% respectively. So, if $1000 was invested three years ago, current value will be 1000*(1-20%)*(1+10%)+(1+25%)= 1100. So, annual rate of return can be calculates as ((Final Investment value/Initial Investment value)^(1/3))-1= ((1100/1000)^(1/3))-1= 3.23%. So, Appropriate annual rate of return over three years is 3.23%

The 5% stated by the mutual fund review is not appropriate, because it was stated as a sum of returns over last three years(-20%+10%+25%)/3= 5%. This way of calculation ignores the compounding effect and thus will be not appropriate to consider.