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Investing Lesson Of Math Learned The Hard Way


  • When measuring markets in percentage terms, the math is very deceiving.
  • The investing lesson investors have yet to learn is that capital preservation matters most in achieving long-term financial goals.
  • In the end, market corrections are very bad for your portfolio.

Graphic Graphs against a wall

Jonathan Kitchen

Every investor must learn the one investing lesson in surviving the long game: how math works. I recently received an email from a reader suggesting that the 2022 decline in the market is "no big deal" because of the stellar

This article was written by

Lance Roberts profile picture

After having been in the investing world for more than 25 years from private banking and investment management to private and venture capital; I have pretty much "been there and done that" at one point or another. I am currently a partner at RIA Advisors in Houston, Texas.

The majority of my time is spent analyzing, researching and writing commentary about investing, investor psychology and macro-views of the markets and the economy. My thoughts are not generally mainstream and are often contrarian in nature but I try an use a common sense approach, clear explanations and my “real world” experience in the process.

I am a managing partner of RIA Pro, a weekly subscriber based-newsletter that is distributed to individual and professional investors nationwide. The newsletter covers economic, political and market topics as they relate to your money and life.

I also write a daily blog which is read by thousands nationwide from individuals to professionals at www.realinvestmentadvice.com.

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Comments (40)

HoustonBrock profile picture
Good summary. A point not well considered by most novices.
$100 + 10% = $110,
After 10% pullback = $99
Same outcome if the dip comes first:
100 - 10% = 90, + 10% = 99

For gains and losses of the same magnitude, in percentage terms, the drawdown is more impactful.
Running out of time to recover by retirement date: correct, of course. For this reason, before “retirement” (when I stopped paying in) I ‘dialled down Risk’ by holding more ‘cautious’ assets; and subsequently rebalanced after Equity gains.

Since the top (c. 01/01/22) my worst draw down was 13%: probably because non-Equity assets fell as well; and today 10% down. This means I need a further 11.1% from today to get ‘even’.

The point is a 50% fall needs a subsequent 100% gain; but 10% fall needs ‘only’ 11.1%.
And tech/crypto investors are learning a 90% loss requires +800% gain (give or take.)
FrankVdK1 profile picture
There is a typo in the line following this section header:
“The Math Can Be A Killer (Of Financial Goals)”

“When measuring markets in percentage terms, the math is very deceiving. Such is critical when you realize that a 100% gain and a 100% loss are the same.”

It should have read:
“a 100% gain and a 50% loss are the same.”

Great presentation! Enjoyed it. Will bookmark this one. 😏
And to that, you've all those who sell at the bottom.
hawkeyec profile picture
@Lance Roberts

Thank you, sir for an enlightening reminder of how this math works. One thing most people don't know about the sequence of returns is that over ten years, for example, it is only the beginning and ending index point that determine the average return realized per year. For example, if one invests $10,000 and in ten years the value of that investment is $25,000, the average annual compounded return is 9.6%/year. Nothing that happens in the market during the ten year period makes any difference in the average return. The market could go up 50% in one of the years, and down 80% in another. As long as you start with 10K and end up with 25k, your annual compound return is 9.6%! If you don't realize and gains or losses and just leave everything alone you erase the impact of intermediate ups and downs. People must remember that compound investment returns follow log math, not numeric averages.
@hawkeyec very true! Luckily there's no negative impact from inflation over ten years to further erode returns....heavy sarcasm
Thank you for the timely perspective. I learn a little bit every day.
Finally, someone puts pencil to paper and shows how the math works. It drives me crazy when financial advisers, mutual funds, etfs, etc. use "average" annual returns and then project that into the future. As some have already pointed out, if you lose 50% you need to gain 100% to break even. Think about losing 50% of a $100 investment 1 year, then the next year it gains 50%. These idiots will tell you the "average" annual return over these 2 years was 0%, but in actual dollars you are sitting at $75 and have lost 25%.
Oh, good, you've saved me from loss. Now I will put my money in a savings account, 1% if I am lucky, but no losses!
As if.
Lake OZ boater profile picture

In January of 2022, the S&P 500 hit an all-time closing high, and the Shiller P/E ratio was above 40.

Here are some long-term results starting from the last time when the Shiller P/E was in the 40s. From High-to-Low (Since Year 2000)...

+ 522.1% Gold
+ 346.4% Transports
+ 323.6% Oil
+ 250.3% Utilities
+ 160.4% Nasdaq
+ 170.5% Dow
+ 160.4% S&P 500
+ 65.0% Swiss Franc's
+ 52.0% 30yr Treasury Bonds

Yes, the S & P 500 index 500 stocks did OK. But investors who sought out what was on sale did a lot better.

If you might consider some profit harvesting and "Selling high" , check out what you can get a few short-term on brokered CDs. (FDIC insured).

Term----- Minimum Deposit----Annual Percentage Yield* (%)
RZel profile picture
Yes, a math means a lot if you lose money. Many investors don't realize that if they have lost 50% of the asset(s), in order to get back to the same level, the asset(s) should earn 100%, not 50%. It's a painful discovery.
Bilbozark profile picture
Beautiful Baby!! This is why education is going to migrate to the web and zoomlike process globally. REALLY, education is ALL we have as a human edge! Let's let the real teachers, like YOU, teach instead of an uneducated school board with some other agenda. This is NOT political, but the ALTERNATE to a objective assessment.
ghrelin profile picture
Since 1928 the US stock market has only had 6 years of -20% or worse performances, and in the entire history of the market there have only been 3 periods (multiple year trends) of more than 50% declines. The total SP500 return since 1926 is 8,900,000%. If your point is crashes suck, but you should learn to just ride them out. I agree. But if you're implying investors should get better at TIMING the market, the "MATH" is NOT on your side. Especially since there's never been a single investor in the history of the world that figured out how to do that, and there never will be. There's a reason Warren Buffett has made more money than all hedge fund managers that try to time the market, because he actually knows the math. The best investors buy great companies and sit on their ass. period.
Lake OZ boater profile picture
@Chris Forza Everyone's situation is different, and your perpsective is often influenced by where you find yourself along the investing journey.

When making our financial plans, we all need to be cognizant of recency bias. Stocks have spent about half (1/2) of the last 91 years returning less than 3 month T-bills.

-2000-2012 (13 years)

Two other painful stretches when stocks returned less than three (3) month t-bills were...

17 Years: 1966-1982

15 Years: 1929-1943

Consider a typical retiree who is totally dependent on just Social Security and their nest egg. Would they have to possibly spend some of the money from their investment account during 13-17 year stretches? Of course they would!

Here's the Top 5 Deepest Drawdowns of the S & P 500. (monthly data).

#-----From------Trough----To---------Depth----Length---To Trough---Recovery
#1----Oct-29-----Jun-32----Sep-54---(-85%)---300-------33------------ 267
#2---Nov-07------Mar-09---Mar-13---(-51%)----65---------17------------ 48
#4---Feb-73------Dec-74----Jul-80-----(-43%)---90--------- 23-----------67


Lengthy recoveries like #1-4 are especially tough on retirees (and some pre-retirees) because they will need to make withdrawals from their investment accounts while waiting for the stocks index to recover.

Stocks are risky no matter what the time horizon. How confident are you that a 13-17 year stretch like those mentioned above aren't just around the corner?

I'd just make sure, whatever your situation, you can withstand a potential drawdown, and prolonged recovery time, like those found on the Top 5 list.
@Chris Forza

You've been programmed to believe this:

"Especially since there's never been a single investor in the history of the world that figured out how to do that, and there never will be."

And you need to be open to the possibility that maybe those who say this are jealous.
ghrelin profile picture
@Jack Reacher that's your opinion. I only argue facts.
John R. Clark profile picture
Mr. Roberts is correct. A 20% market drop this year means a loss on paper of one-fifth of all cumulated past gains.

On the bright side, every investor with a lick of sense knows that market losses are just a fact, having witnessed and read of many such times before.

That same lick of sense prompts us to THINK READY and KEEP READY for this, as simply perhaps as holding some cash in reserve. If it leaks value from inflation, so what? Everything has a cost. This is a small one to pay for leaving your depressed holdings intact.

Never mind if some wise alec always knows (too late) how you "could have" used your cash more gainfully. The point here is to preserve your assets for future growth.
I agree with you 200%
DonPaul Olshove profile picture
But, But, I'm sure I've heard, repeatedly, that you should never time the market. I hope you aren't saying that isn't true...
Lake OZ boater profile picture
@DonPaul Olshove For your consideration...

The market can be timed based on valuations.

-Ben Graham's track record proved it

-Dr. Shiller won a Nobel prize in finance for showing it as well.

Peter Lynch was a great portfolio manager back in his era, and here is one of his timeless quotes: "The real key to making money in stocks is not to get scared out of them."

Dr. Andrew Lo at MIT is the Director, Laboratory for Financial Engineering. His work reveals the majority of investors will abandon their investment plan when losses approach or exceed (-20%).

That is the essence of the problem for most small investors. Their portfolios are stock-heavy based on one-size fits all risk-tolerance surveys.

Small investors get scared out of stocks during big market drawdowns, and wait too long to get back in. Their long-term returns then fall way short of those of their ideal targeted allocation.
@DonPaul Olshove

see my post above
DonPaul Olshove profile picture
@Jack Reacher @LakeOZ boater - Some people take everything literally.
Measuring anything with percentages is extremely deceiving and misleading. Sure, as part of the regular cycles for everything, we may have a substantial giveback or retrenchment and many will lose their profits or capital. The real question becomes is if there will be a rebound anytime soon as there usually has been since the Civil War except for the 1930's depression. One of those purple swan things may be lurking in the shadows.
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