Question on stock market "average" returns

[Noriko]

Hello! :) I was wondering if the stock market averages are TRUE averages.

Example:
Say I invest $1,000 and get a +20% gain that year, so I now have $1,200.
Then the market drops -20% the next year. I now have $960.

History will report that the market had a +20% year followed by a -20% year for a net gain of 0. But this can't be true as I LOST $40 total. Is there a word for that? How can I know what the true returns are for the market if they don't take this into account? Or do they?

Bear markets can be an average of -25% losses, but even if the market goes up by +25% the next year, I'm still at a loss as that's only +25% on the remaining 75% left from the previous year. It worries me to use the 7% market "averages" in my retirment calculations if this is before accounting for the true losses.

Can someone explain this? I'm confused!

[Cathy]

Whenever we talk about the "average" return of an investment, what that means is: "If you had put the money in a savings account instead of the investment, what interest rate would the savings account have needed to yield for you to end up with the same amount of money as you did from the investment?" This is also known as "compound annual growth rate", which would be a more precise term to use than "average".

So let's consider this example:

Say I invest $1,000 and get a +20% gain that year, so I now have $1,200.
Then the market drops -20% the next year. I now have $960.

You started with $1000 and two years later you ended up with $960. Assuming annual compounding (unlike most actual savings accounts), the equivalent savings account would have had an interest rate `r` satisfying `1000*(1+r)**2=960`. Solving for `r` gives you `r = (960/1000)**(1/2) - 1 ≈ -2%` (to one significant figure).

So we would say the average return of this investment was approximately -2%. In other words, you lost about 2% per year.

The way you have calculated average in your post is never used because it does not make sense.

[forummm]

Cathy's right. Also, what you really want to know is what your CAGR is after inflation. Historical CAGR for an asset class is not especially useful if you don't know how much of that is just due to higher prices for everything. In the 70's inflation was about 10% some years, so a 10% return wasn't very good back then. These days it's very good.

[Exflyboy]

Yes and of course this is where the 4% max Safe withdrawal rate came from.. I.e by the time you take into account inflation and huge swings in the stock market, 4% is the max you can withdraw to ensure you don't run out of money.

Now of course, its not impossible that a huge aberration will pull the stock market down for the next 10 years (there are a few 10 year periods in history where the market was a net loss over a decade).. So lets say next week is the start of a 50% correction and you have just retired today..

Well in that case a 4% SWR right now may not be appropriate and maybe a 3.5% WR might be required for a few years.

[beltim]

Whenever we talk about the "average" return of an investment, what that means is: "If you had put the money in a savings account instead of the investment, what interest rate would the savings account have needed to yield for you to end up with the same amount of money as you did from the investment?" This is also known as "compound annual growth rate", which would be a more precise term to use than "average".

This is also called the geometric average.

[hamildub]

I completely agree with cathy about how to calculate the return. However I have seen people use an average of periodic returns to describe performance, more commonly and appropriate though in calculating volatility.

I use CAGR as well as IRR to give me a little more context to my returns. I like CAGR for simplicity, whereas IRR tells me my returns adjusted for cash flows.