one of the most disingenuous things about financial advisers (and there are many) is their failure to teach their clients how to properly calculate returns. most people think in linear terms, in other words: y = ax + b, the graph of which will give you a straight line. in these terms, the average of 2 and 0, is 1.


but that's not how the financial world works.


in finance, everything is based on percentages. interest rates are based on percentages, fees are based on percentages, and returns are based on percentages.

when you are dealing with percentages, and compound interest, you can't think in linear terms. everything becomes an exponential function, in other words y = x^a.

when most people average their investment returns, they think "last year I made 8%, this year I made 8%."


so (8 + 8)/2 = (16)/2 = 8%.

^this is an arithmetic average. which is wrong.



the correct way to calculate the investment average is with a geometric average. you do that by multiplying the returns, then taking the root.

so in this example it would be (8 * 8)^(1/2) = (64)^(1/2) = 8%.



but what difference does it make if you get the same answer?



think about it this way: let's say you have a stock and it rises 50%, then it rises 50% again, then another 50%, then 50% again.

then you lose it all (a 100% loss).



you did pretty well, so if you do an arithmetic average of this, you get a 20% return:

(50+50+50+50-100)/5 = 20%.

obviously, this is wrong, because you lost everything.

so what happens when you do a geometric average?


(150% * 150% * 150% * 150% * 0.0%)^(1/5) = (0)^(1/4) = 0.


feel me?



so, why is this important?

if you lose 50% in the market one year, and make 50% back the next year, you are *not* back where you started. that is linear, arithmetic thinking.(i.e. you start with $100, then you have $50. a 50% return on $50 is $25. that gives you $75, not $100)

so if you lose 50% in one year, you would have to make a 100% return (i.e., double your money) next year just to break even. that's thinking geometrically.

losses and gains on investment funds are not symmetrical or linear; that is, a 10% loss is not simply the mirror image of a 10% gain. the loss has a *much* bigger effect on your portfolio than a gain will, due to these dynamics.

to quote warren buffet: "zero times any number is still zero."

this is why all financial advisors say you need bonds in your portfolio; the bonds are there to prevent 0% and -50% numbers (or -40% like the NASDAQ last year) from destroying your portfolio.

this is why you should ignore them when they say garbage like "you're young, you can make up the losses later." that is complete trash that is easily debunked with simple 6th grade math.

a stock can't fall below 0, but it can fall 99% every single day, forever.




this is why rich people invest in bonds; it is not to get rich, but to minimize losses.


these people understand that the average of 2 & 0 is not 1; it is zero.