How are a mutual fund's annual returns calculated?

Question

I've invested in a mutual fund was going over the statement, and was just curious how they arrive at an average annual return for the life of the fund. I know you do NOT simply use an arithmetic average of each year's return.

Do they look at what you'd have at the end of the time period and then annualize a return based on that? I'm really curious how it is calculated.

Answer 1

It's a geometric average to account for the compounding effect. The general form is:

[1+(Current Capital - Original Capital) / Original Capital)]^(n periods per year / number of periods) -1


Which is kind of a mess. Let me give an example:

NAV at purchase: $10
Current NAV: $12
Life of fund: 30 months

Average Annual Return:
[1+(12-10/10)]^(12/30)-1
=[1.2^(12/30)]-1
= 0.757
= 7.57%