### Author Topic: If you start with \$10k, and end with \$10k four years later, average return 25%?  (Read 2967 times)

#### extremedefense

• Posts: 63
• Location: DFW - Texas
##### If you start with \$10k, and end with \$10k four years later, average return 25%?
« on: June 12, 2017, 03:34:29 PM »
Hey guys and gals, I was looking at this table and example, and am wondering why it feels... wrong, and if one of you could explain where I'm going wrong.

"In our example, Joe starts with \$10,000 and gets a 100% rate of return in year one, bouncing his balance up to \$20,000. The next year the market drops by 50% leaving him with \$10,000 again. In year three it goes up again by 100% to \$20,000. Then drops again in the fourth year by 50%, setting him right back at \$10,000.

In this case the market did average a 25% rate of return. But how much additional cash does Joe have left to show for his 25% average rate of return?
Zero."

excel:
year   market   starting balance   ending balance
1   100%    10,000     20,000
2   -50%    20,000     10,000
3   100%    10,000     20,000
4   -50%    20,000     10,000
average   25%    15,000     15,000

#### solon

• Handlebar Stache
• Posts: 1867
• Age: 1820
• Location: CO
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #1 on: June 12, 2017, 03:48:36 PM »
What it comes down to is, you can't average percentages like that.

If you wanted to find the average return over a four year period, you would take the change in value over the entire period and divide by the starting value.

#### kendallf

• Handlebar Stache
• Posts: 1064
• Age: 54
• Location: Jacksonville, FL
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #2 on: June 12, 2017, 03:55:10 PM »
The example is correct, but it shows why we don't talk about investment performance in terms of average annual return.  Instead, usually it's shown as CAGR, Compound Annual Growth Rate.  The CAGR of your example is 0%, much more indicative of the results than the annual average.

Definition and formula here:

http://www.investopedia.com/terms/c/cagr.asp

#### mjr

• Bristles
• Posts: 419
• Age: 54
• Location: Brisbane, Qld
• Retired at 52
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #3 on: June 12, 2017, 03:57:00 PM »
You need to research arithmetic versus geometric averages.  You're doing an arithmetic average, which assumes that each score is an independent event.   But with investment returns, the portfolio value isn't independent each year, rather the value depends as well on previous years.  This requires you to use geometric averages.

To use a simple example to illustrate why they're not independent, if you have any year where the portfolio lost 100%, the portfolio can never recover, regardless of how many positive years follow.

The geometric average is [(1 + 100%) x (1 + -50%) x (1 + 100%) x (1 + -50%)] ^ (1/4) = (2 x 0.5 x 2 x 0.5) ^ (1/4) = 1

« Last Edit: June 12, 2017, 04:13:04 PM by mjr »

#### fattest_foot

• Pencil Stache
• Posts: 845
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #4 on: June 12, 2017, 04:00:20 PM »
This is why CAGR is a thing.

#### extremedefense

• Posts: 63
• Location: DFW - Texas
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #5 on: June 12, 2017, 04:10:11 PM »
Thanks everyone!

I'm glad everyone agrees that it's because it's not the CAGR.

If anyone cares, I'm not actually dumb, I read it in this 'book' which is really just an advertisement for IUL's (Indexed universal life insurance) called Wealth Beyond Wall Street.

The faulty math in question is on page 49/52 of the attached pdf, or page 39 of the actual 'book'.

#### solon

• Handlebar Stache
• Posts: 1867
• Age: 1820
• Location: CO
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #6 on: June 12, 2017, 08:46:15 PM »
Wow, those guys are deliberately misleading people. I wonder if there is some law they broke?

#### marty998

• Walrus Stache
• Posts: 7039
• Location: Sydney, Oz
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #7 on: June 13, 2017, 05:21:57 AM »
To beat the dead horse further...

It would need to be rephrased as "given the following four independent annual % returns, the expected return in any given year is 25%"?

The logic just keeps breaking down.

FWIW, I bet there is a stock out there somewhere in the world where these 4 returns have happened in sequence. Wouldn't that be a rollercoaster to ride...

#### Lobo

• Posts: 40
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #8 on: June 15, 2017, 04:56:06 PM »
The example is correct, but it shows why we don't talk about investment performance in terms of average annual return.  Instead, usually it's shown as CAGR, Compound Annual Growth Rate.  The CAGR of your example is 0%, much more indicative of the results than the annual average.

Definition and formula here:

http://www.investopedia.com/terms/c/cagr.asp
Doesn't Vanguard advertise their fund's performance by Average Annual Returns?

#### mjr

• Bristles
• Posts: 419
• Age: 54
• Location: Brisbane, Qld
• Retired at 52
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #9 on: June 15, 2017, 05:43:51 PM »
"Average" is an overloaded term.  An arithmetic average can be one of a mean, median or mode.  Likewise an average needs to be qualified as to whether it's arithmetric or geometric unless clear from the context.

CAGR and geometric average are the same thing.

#### seattlecyclone

• Walrus Stache
• Posts: 5478
• Age: 36
• Location: Seattle, WA
##### Re: If you start with \$10k, and end with \$10k four years later, average return 25%?
« Reply #10 on: June 15, 2017, 05:44:17 PM »
The example is correct, but it shows why we don't talk about investment performance in terms of average annual return.  Instead, usually it's shown as CAGR, Compound Annual Growth Rate.  The CAGR of your example is 0%, much more indicative of the results than the annual average.

Definition and formula here:

http://www.investopedia.com/terms/c/cagr.asp
Doesn't Vanguard advertise their fund's performance by Average Annual Returns?

I believe Vanguard goes with an "annualized" return for multi-year periods. It's not the arithmetic average of the percentage returns (because that number is meaningless, as this example shows). Instead it's the percentage that the fund would have had to grow each year in order to get from its price N years ago to today if the growth rate were a constant over that period.