Average yearly return

Ok, so I read in a lotta places that the average yearly return of the stock market was like 10%-11% for the past 75 years or so. How is that average calculated?

Consider the case where you have a $100 invested for two years. First year you lose 50% and second year gain 60%. This is a 10% average, but instead of having $121 you only have $80 which was actually a 20% decrease total.

If you gain 100% first year and lose 90% the second year, you only have $20 left...

If you gain 15% first year and gain 5% the second year, you have $120.75, etc...

The above cases had a 10% average yearly return but they didn't end up with $121 at the end of the two years. I hope this 10%-11% average was calculated in some other way than adding up all the yearly returns and dividing by the number of years.

EDIT: One more question. When someone says "If you had $x invested in ... 70 years ago it would have grown to $y now". Do they actually mean it or do they just see the average return over 70 years and plug the numbers in their calculators?

[edtost]

(price n yrs ago)*(1+r_average)^n = (price today)

i.e. it is calculated such that returns of r_average over n years would have taken the price n years ago to the price today if there were no variation of returns. this means that the scenario in your edit would involve someone who just plugs in the numbers AND who means it ... otherwise, the numbers would be worthless.

[hedgeyerbets]

When they say "average" they mean the geometric mean, not the arithmetic mean.

[Dazarath]

So if we let X being the starting amount, Y be the ending amount, Z be the average yearly return, and N be the number of years, then the calculation would be the following?

Z = (Y/X)^1/N - 1

[DesertCat]

[ QUOTE ]
So if we let X being the starting amount, Y be the ending amount, Z be the average yearly return, and N be the number of years, then the calculation would be the following?

Z = (Y/X)^1/N - 1

[/ QUOTE ]

If you are using the levels of stock indexes (i.e. the Dow) to estimate long term market returns, you also need to include dividends. Back in the fifties dividends added as much as 4% a year to the index.

[Bosox]

I've wondered these things a lot myself.
Any responses for the tougher questions up top and not the easy edit?

[Sniper]

which question do you think wasn't answered?

[lozen]

[ QUOTE ]
EDIT: One more question. When someone says "If you had $x invested in ... 70 years ago it would have grown to $y now". Do they actually mean it or do they just see the average return over 70 years and plug the numbers in their calculators?

[/ QUOTE ]

This is based on the overall S&P But does refect inflation or taxes.

[Dan Mezick]

One useful tool figuring this type of question out is: the rule of 72.

You take your return and put the value 72 over it. The result is a rough idea of how many years to double your bets.

Example: Stock market returns 11% a year for 70 years.

72/11 = 6.54 (years to double)

So if you are 22 and you have 20K figure:

160K of value in 26 years, (4 doubles,) at 48 years old, assuming 11% a year average return.

20, 40, 80, 160




If you earn 22% and not 11%, you get:

72/22 = 3.27 years to double. That's roughly 8 doubles in 26 years

20, 40 , 80, 160, 320, 640, 1280, 2560. Twice the doubles, 16 times the total return.


26 years and 20k.
Earn 11% and get 160K.
Earn 22% and get 2560K.

16 times more return over the same period of time.

Start young and be aggressive.

[BradleyT]

And don't stop after the initial 20K.