Investing Lesson Of Math Learned The Hard Way

Summary

• 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.

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 returns over the last decade. He quoted a snippet of an article by Ben Carlson.

To be fair, these losses need to be put into perspective. The gains leading up to this slaughter were gigantic. These are the annual returns for the Nasdaq since the Great Financial Crisis ended:"

• 2009: +45.3%
• 2010: +18.0%
• 2011: -0.8%
• 2012: +17.9%
• 2013: +40.9%
• 2014: +14.7%
• 2015: +7.0%
• 2016: +8.9%
• 2017: +29.6%
• 2018: -2.8%
• 2019: +36.7%
• 2020: +44.9%
• 2021: +22.2%

For those of you scoring at home, that's returns of more than 20% per year for 13 years!

Ben's math is correct. As such, the reader's email suggests the 2022 drawdown is nothing to be concerned with because of gargantuan percentage returns in previous years. To be exact:

Yes, I gave up 2021 gains, but I still have all the previous years in the bank."

Unfortunately, that isn't how math works; therein lies the investing lesson we must learn. As shown, corrections that seem small on a percentage basis can wipe out years of gains.

Author

Investing Lesson - How Math Works

The following chart proves my point, in the long-term; bear markets are harmless (and relatively small) as the chart indicates."

For data consistency, I recreated the "cumulative percentage return" chart that the reader provided from First Trust.

Robert Shiller; Chart by: Real Investment Advice

The problem is that your assumption is entirely wrong. The investing lesson buried in the chart above is the basic understanding of math. The chart uses percentage returns which is highly deceptive if you don't examine the issue beyond a cursory glance. Let's take a look at a quick example.

Let's assume that an index goes from 1000 to 8000.

• 1000 to 2000 = 100% return
• The index rises to 3000 = 200% return
• Going on to 4000 = 300% return
• And continues to 8000 = 700% return

Great, an investor bought the index and generated a 700% return on their money.

Why worry about a 50% correction in the market when you just gained 700%. Right?

Here is the problem with percentages.

A 50% correction does not leave you with a 650% gain.

A 50% correction subtracts 4000 points, reducing your 700% gain to just 300%.

St. Louis Federal Reserve; Chart by: Real Investment Advice

As shown in the example, the small drawdown seems innocuous until you realize it clipped 4000 points from the index. The problem now becomes the issue of regaining those 4000 lost points to break even.

Understanding the math of loss is incredibly important.

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.

The chart below reconstructs the percentage gain and loss chart above into actual point changes. In this form, we see that most of the advances in bull markets get subsequently destroyed in bear markets.

Robert Shiller; Chart: Real Investment Advice

The chart and table below show the point and percentage gain or loss for each market cycle to clarify that point. Again, the "math" is straightforward. Bear markets are devastating to financial outcomes.

Robert Shiller; Chart: Real Investment Advice

As is always the case, the "math of loss" matters over the long term. Such is why after 3-major bull market cycles since 1980, most Americans are woefully unprepared for retirement.

The investing lesson investors have yet to learn is that capital preservation matters most in achieving long-term financial goals.

Time Matters

If you have discovered the secret to eternal life, stop reading now.

For the rest of us, mere mortals, time matters.

Unfortunately, most investors remain woefully behind their promised financial plans. Given current valuations and the ongoing impact of "emotional decision making," the outcome will not likely improve over the next decade.

For investors, understanding potential returns from any given valuation point are crucial when considering putting their "savings" at risk. Risk is an important concept as it is a function of "loss." The more risk in a portfolio, the greater the destruction of capital when reversions occur.

However, the real damage that market declines inflict on investors is all too real and virtually impossible to recover from. When investors lose money in the market, it is possible to regain the lost principal given enough time. However, therein lies "the rub." We can never recover the "time" lost to reach our financial goals.

In the end, market corrections are very bad for your portfolio. However, before sticking your head in the sand and ignoring market risk based on an article touting "long-term investing always wins," ask yourself who benefits?

This time is "not different."

The clock on your retirement goals continues to tick... tick... tick.

Original Post

Editor's Note: The summary bullets for this article were chosen by Seeking Alpha editors.

Comments

[HoustonBrock]

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.

[UK Lawman]

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%.

[Derf]

And tech/crypto investors are learning a 90% loss requires +800% gain (give or take.)

[FrankVdK1]

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. 😏

[Fabien Hug]

And to that, you've all those who sell at the bottom.

[hawkeyec]

@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.

[jlipps75]

@hawkeyec very true! Luckily there's no negative impact from inflation over ten years to further erode returns....heavy sarcasm

[Charliedon'tsurf]

Thank you for the timely perspective. I learn a little bit every day.

[The hard realist]

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%.

[elba]

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]

@elba

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* (%)
3-month---$1,000.00--------------2.40%
6-month---$1,000.00-------------2.75%
9-month---$1,000.00-------------2.900%
1-year------$1,000.00-------------3.1%
18-month---$1,000.00------------3.15%
2-year--------$1,000.00-----------3.35%

[elba]

@LakeOZ boater Thanks.

[RZel]

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]

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]

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]

@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
#3---Sep-00------Feb-03---May-07----(-44%)---81---------30------------51
#4---Feb-73------Dec-74----Jul-80-----(-43%)---90--------- 23-----------67
#5---Oct-06-------Nov-07----Aug-09----(-38%)--35---------41-----------21

www.econ.yale.edu/...

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.

[Jack Reacher]

@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]

@Jack Reacher that's your opinion. I only argue facts.

[John R. Clark]

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.

[Derf]

I agree with you 200%

[DonPaul Olshove]

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]

@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.

[Jack Reacher]

@DonPaul Olshove

see my post above

[DonPaul Olshove]

@Jack Reacher @LakeOZ boater - Some people take everything literally.

[nestor7]

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.