### Comparing apples to apples

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I just left a meeting with a wholesaler and this issue came up:

Fund ABC has an annualized total return of 7% since 1980

Fund XYZ also has an annualized total return of 7% since 1980

If both situations started with the identical amount is there any chance that they would have different amounts now assuming there were no withdrawals or anything like that to throw a curve into the mix.

Also, can someone educate us to how you compute this figure.

e.g. If a fund does 10% year 1 and 20% year 2 is that 15% annualized average return over the 2 year period.

How about if a fund does negative 20% year 1 and plus 50% year 2? Is that also a 15% avg annual return

I realize in these examples you will not arrive at the same amount at the end so i'm unsure what the avg annual return is.

Thanks in advance for any constructive feedback.

scrim

Average Rate of Return can always be misleading, and I think people are quick to reguratate Avg. ROR’s to make an investment sound great. Looking at annual performance on a year to year basis and then computing what the ACTUAL Rate of Return tells the true story and is the ROR that a client and advisor needs to focus on.

[quote=scrim67]

I just left a meeting with a wholesaler and this issue came up:

Fund ABC has an annualized total return of 7% since 1980

Fund XYZ also has an annualized total return of 7% since 1980

If both situations started with the identical amount is there any chance that they would have different amounts now assuming there were no withdrawals or anything like that to throw a curve into the mix.

Also, can someone educate us to how you compute this figure.

e.g. If a fund does 10% year 1 and 20% year 2 is that 15% annualized average return over the 2 year period.

How about if a fund does negative 20% year 1 and plus 50% year 2? Is that also a 15% avg annual return

I realize in these examples you will not arrive at the same amount at the end so i'm unsure what the avg annual return is.

Thanks in advance for any constructive feedback.

scrim

[/quote]

Total Return = Return from point A to point B

Annualized = what it would be from year to year from point A to point B, or if shorter than a year, if it kept it up what it would be over a year's period

Ergo, ABC's and XYZ's end amounts would always be equal, even though they may have had incredibly different looking charts getting there.

For example: fund does 10% year one and ends up with 1.1 x what started with. It then goes on the next year to do an additional 20%, to end up with 1.32 x what started with. 1.32 is the total return. Annualized, it is what the fund would have to do equally both years to get 1.32. Or, 14.8912529...% As you can see, it's not the arithmetic average, or 15%, but the geometric average.

Or if the fund does -20% (.8) and then +50% (.8*1.5) you get a 20% total return (=1.2). The square root of 1.2 is 1.0954451150..., thus a 9.5445...% average return. To find the average return over a number of years (n), take the n root of the total return plus one, and then subtract one.

So, when a prospectus says the average return, it never means the arithmetic average (which would be misleading), but the geometric average (which you can take to the bank, or rather, could, assuming you have a time machine, because PPINIOFR.)

Ace

Scrim,

Of course you could have different values with the same avg annual return…really need to understand this.

If I get 5% every year for 5 years on $100,000 (assume monthly compounding), I have an avg annual return of 5% and I will end up with $128,335.87.

If I get 3%, 4%, 5%, 5%, 8%, I still have an avg annual return of 5% (again assume monthly compounding) but I have an end balance of $128,328.46.

Slightly different.

This is a close example…as volitility increases the difference increases, and it can work both ways. (Higher returns in the earlier stage can make the end values higher, and the reverse is also true etc)

Basically, it’s a selling point for stable investments, and I’m sure that is what your wholesaler was trying to convey (and sell) to you.

Ace just answered it a little more academically than me…hope that solves it for you.

[quote=BankFC]If I get 3%, 4%, 5%, 5%, 8%, I still have an avg annual return of 5% (again assume monthly compounding) but I have an end balance of $128,328.46.

[/quote]

Sorry, you're figuring on arithmetic averages, not geometric, which is legally required in communications with the public.

Ace

Scrim,

The power of compounding throws this from a simple equation to a more challenging one. If you remember the Future Value Formula:

FV=(amount invested) * (1+ Interest Rate)^n

To get an annualized rate of return you solve the equation for interest rate.

Interest Rate = the n'th root of (FV/amount invested) - 1

Maybe it is simpler than what you are making it out to be. Is the 7% return before or after the sales charge and internal expenses. Was the wholesaler trying to show the importance of low internal fees?

[quote=Ace Planner]

[quote=BankFC]If I get 3%, 4%, 5%, 5%, 8%, I still have an avg annual return of 5% (again assume monthly compounding) but I have an end balance of $128,328.46.

[/quote]

Sorry, you're figuring on arithmetic averages, not geometric, which is legally required in communications with the public.

Ace

[/quote]

Quick kill them before they start to talk about the joy of Black Scholes.