Past Performance And The Unfair Coin

Investors like to believe they make rational decisions based on available data.  Do they really though?  We know from experience that humans are far from completely rational beings. People get emotional and make mistakes all the time.  There’s also a large number of cognitive biases we have to contend with.

Psychologists have been studying these issues for decades, and have discovered a long list of cognitive biases which affect human decision making.

I’ve written about a few of these cognitive biases in the past (most notably the Dunning-Kruger Effect), but I’d like to touch on one particular cognitive bias today — A variant of The Gamblers Fallacy.


The Gamblers Fallacy

Imagine for a moment you flip a coin seven times.  Each time the coin lands heads-up.  For most people, this would seem like a very unlikely outcome.  Based on the previous coin tosses, the flipper may believe that the next coin toss is far more likely to be ‘tails’.  This is what’s known as the Gamblers Fallacy.

In reality, the probability of a head or tails on the next coin toss is equally as likely on the first or seventh coin toss.

This is (of course) assuming a fair coin toss — one not biased to either outcome (heads or tails).  In this scenario the coin flipper believes it’s a fair coin.

At first glance this might not seem particularly relevant to investing, you’d be surprised how often I hear people say, “The stock market has been positive for 5 years in a row.  We’re due for a pullback soon.  Start taking some profits now.”

In other words, because we’ve seen [X] successive years of positive results from the stock market, investors believe we’re more likely to have negative performance the following year.

This is a classic example of the Gamblers Fallacy applied to the stock market.


The Unfair Coin

But what if the coin toss wasn’t fair?  Since we don’t know whether the coin is fair or not, after seven successive tosses the coin flipper may decide that the coin is weighted unfairly, and it will flip heads every time.  In other words, data from the previous flips directs us to believe the next toss will be heavily weighted towards ‘heads’.

This change in behavior happens when the flipper believes that the coin isn’t fair.

When it comes to the stock market, the probability of a stock rising or falling is completely unknown to us.  Essentially it’s an “unfair coin” to use terminology from the Gamblers Fallacy.

On any given day we don’t know the probability of whether a stock will rise or fall.  The outcome is essentially random for all intents and purposes.

In cases like these, our human brains begin to believe that past results can tell us what to expect in the future.  It’s a mental “rule of thumb” that human brains default to when we don’t have enough data to predict a future outcome.

Investors do this all the time.  We see past results and use it to predict a future outcome.  This may or may not be an accurate prediction of the future.

I’m sure you’ve heard the saying, “past performance is not indicative of future results.”  It’s written at the beginning of every mutual fund prospectus… yet we’ve all done it at some point.

Humans look at the data, see a pattern, and then extend that pattern out into the future.

Common real-world examples of this behavior:

  • Stock investors see a pattern of a hot stock rising, so they buy-in, believing the stock will continue to rise.
  • Bitcoin investors see gigantic gains in bitcoin price charts, so they believe they’ll see large gains in the future.
  • Real estate investors observe that a ‘house flipping’ is a successful strategy .  They believe this strategy will work well in the future.
  • Index investors have seen excellent results in recent years, so they believe the future will continue to have similar results.

Investing like this is incredibly dangerous, because Mr. Market provides essentially random outcomes in the short term.

A stock can continue to go ‘up’ for years despite earning very little money (Tesla anyone?).  Or, the stock could do nothing for a decade.  This non-performance can happen despite the fact a stock continues to grow earnings and shareholder value.

Microsoft stock is the perfect example of this in the real world:

msft stock
Microsoft stock did essentially nothing from 2001 to 2016. During this time the company continued to grow earnings and create value for shareholders.  Yet the stock went nowhere.

The lesson learned here should be:  Markets rarely create linear outcomes that can be easily predicted with past data.


Stop Looking At Past Results!

Looking at past results is a difficult habit to break.  Trust me, it’s taken me years to get to the point where I don’t even look at a stock chart to make buy/sell decisions.

Instead, I’ve learned instead to focus on other kinds of data that are not rearview mirror looking — like earnings yield, the business drivers, shared value economics, the ability of the CEO to compound capital, executive incentives, and so on.

Why are those metrics important?  They drive future value creation.  Just remember the classic investing maxim, “In the short-term the stock market is a voting machine.  In the long-run it’s a weighing machine”.

In the short-term the outcome of capital markets can be completely random, but in the long-term it’s the ability of that asset to build value that will drive the price.

This is exactly why purchase price matters.  If you buy a stock when it’s outrageously overvalued, it could be years or maybe even a decade until the underlying value of the stock catches up to it’s price.  Could you really hold onto a stock for a decade without seeing price gains?

For many novice investors (used to buying “at any price”), this concept can be difficult to grasp.  Price and value often seem like the same thing.  They are not.  It doesn’t matter if it’s a stock, bonds, index funds, real estate, or even a bitcoin — Don’t let past results trick you into believing the future will be just as rosy as that 5-year chart.


Final Thoughts

Cognitive biases can be tricky to overcome, but defeating them is just one more step on the path to becoming a truly rational investor.  This doesn’t mean you’ll no longer make cognitive mistakes (it’s still entirely possible).  The point is to reduce these errors in judgement.

We all make mistakes, but truly rational decision making will help you become a better investor (and less of a gambler).

It’s this distinction between investing and gambling that illustrates the point — Gamblers hope the price will go up.  Rational investors buy assets without “hoping” they’ll go up, they already know they will.

Even then, mistakes are still entirely possible.  Black swan events like COVID-19 can completely throw the world out of whack.  Lost decades do indeed happen.  A rational investor simply has more tools with which to protect him/herself from these unpleasant outcomes.

The real world is, after-all, more than just a coin-flip.  Why not weight the odds in your favor?


[Image Credit: Flickr]

12 thoughts on “Past Performance And The Unfair Coin

    • May 23, 2021 at 2:30 PM

      Indeed this is exactly why I use a more conservative 3% or less. Many of the economic conditions that drove the returns for the 4% rule no longer exist — Population growth is lower, productivity growth is lower, interest rates are lower, inflation has been lower, etc.

      If the mathematics that drive stock market returns have changed, why wouldn’t the 4% rule need to change?

      • May 24, 2021 at 10:32 AM

        I’m probably down to using 2% and could even go lower if needed. But I’m confident in my strategy of indexing and not paying much attention to the market. My time is too valuable and better spent elsewhere
        Dave @ Accidental FIRE recently posted…T.G.I.F. Friday: Volume 43

    • May 24, 2021 at 10:10 PM

      Yeah the success rate of the 4% rule when just retiring when the CAPE is where it is now is concerning for sure. ERN did a good post on why ( I guess to that point the CAPE correlated to medium term total market returns does seem to be a case where data does seem to correlate to future returns of the total market? Interesting post and thanks Mr Tako 🙂

  • May 23, 2021 at 8:33 PM

    I think the most interesting part about Gambler’s Fallacy is that it shows how people don’t see where they are within a sequence of events. Using the coin flip analogy, it’s true to say:

    “There’s a near 3% chance of flipping five heads in a row!”

    This assumes you haven’t started flipping yet. However, once you flip the first head, there’s no longer a ~3% chance of getting four more heads. It’s about 6%. Just as there’d be a ~6% chance of getting four heads in a row if you started from scratch. Once you’ve got two heads in a row, it’s about a 13% chance of getting three more. And once you’ve got three heads in a row, it’s a 25% chance of getting two more.

    In fact, once you’ve got three heads in a row, there’s a 25% chance of you getting one more head and one tails. Or one tail and one head. Or two tails. That’s now accounted for all four possibilities. Hence, 25% chance. No pair of upcoming flips are any more likely than any other.

    And that last flip is an equal 50/50 shot. From the outset, you’re just as likely (~3%) of getting four heads and one tails as you are of getting five heads in a row. Or literally any of the possible permutations.

    To your point with the stock market, where chance applies, we’re bad at recognizing where we are within a sequence of events and thinking our “number has got to come up sometime!” in all manner of things. It’s part of why we throw good money after bad, get suckered into the sunk cost fallacy, and fail miserably at understanding the lottery.

    Fun thoughts Tako. Now I’ll have to figure out how to wedge it into my next post as I did with your recent inflation piece. 🙂 Cheers!
    Chris@TTL recently posted…Why You Don’t Need To Worry About Inflation (and the 4% Rule)

    • May 24, 2021 at 1:48 AM

      Nice picture of an old one pound coin. The writing around the edge reads ‘Decus et Tutamen’, a defence and an ornament. It was introduced by Isaac Newton when he was the head of the Royal Mint to guard against the practice of clipping the edges of coins, at a time when they were still made of silver. Alas, their bullion value these days is non existent.

  • May 24, 2021 at 4:21 AM

    I think there are two aspects to this. Actual revenue / earnings surprises and surprise changes in sentiment. A lot of the gains that we have seen have come from increased P/E expansions (sentiment is stronger) that far outweigh the bump seen in earnings and revenue. Eventually this comes back to Earth.

    Looking at the parameters of the business and trying to weigh this against the sentiment factor is probably the best tools we have to deal with the unknown outcome.

    This was a nice thought provoking post!

  • May 27, 2021 at 11:37 PM

    If interest rates are zero and thereby earrings yields can effectively be close to zero for a while. At what point does it unwind? With higher rates or higher inflation? A dangerous game to play and only buy growth stocks.

    If an investor were starting again today where would you look? I’m finding the US isn’t attractive on a macro level so back to individual shares? International?
    charlie @ recently posted…April 2021 numbers update

  • May 28, 2021 at 10:42 AM

    I like that reminder: Stop Looking At Past Results! We really aren’t as rational as we might think. So, going into the business fundamentals really is key. Whats, the economic moat, how will the business likely look in 10, 20, 30 years from now? How’s the earning quality? etc.
    With regard to the withdrawal rate, we are considering 3 % instead of 4 %, being more conservative.

  • June 4, 2021 at 12:33 PM

    This makes so much sense! Reading The Psychology of Money right now with the Afford Anything (Paula Pant’s) group. Have you read it?? 🙂

    • June 4, 2021 at 12:52 PM

      No, I haven’t. I’ll put it on my reading list.

  • November 5, 2021 at 1:25 PM

    Great post!

    Investing in an individual stock solely based on past results is equivalent to predicting the outcome of a coin toss (of which you don’t know whether is fair or not) — that is, impossible.

    But I think historical results can correlate to the future if an investor deems that the fundamentals for a particular company is good. As a popular example, Tesla back in the day didn’t have a lot of EV competitors. And now even that they do, their materials science and battery is much better than competitors’. Their car prices are also much lower than most competitors. Their main downside is that their cars have poor quality control. Their upside is that they’re always reinvesting into the future and scaling. Based on this information, if Tesla keeps being on track with their strategy and is beating earnings every quarter, then an investor could reasonably draw a rational conclusion that all things being equal, Tesla stock will rise based on some DFV analysis.

    That’s just an example though, I have no idea how well Tesla is priced considering it’s very expensive nowadays.


Leave a Reply

Your email address will not be published. Required fields are marked *

CommentLuv badge
Mr. Tako Escapes