Is The Random Walk Theory Accurate?

Is the Random Walk Theory accurate?

It’s an age old question in the markets…

Are stock price movements random?

Is market price action random?

Are prices just as likely to trade up as down next?  

If Stock A trades at $20 is it more likely to trade at $20.01 or $19.99 next? More importantly, what’s the next price after that? $20.02 or $19.98?

Those who adhere to the notion that market prices are random in nature, i.e. The Random Walk Theory would say no price is more likely than any other… 

The Random Theory itself is a pillar of traditional Wall Street.  And arguably has its roots in a bit of misinterpreted data.  

Burton G. Malkiel, an economics professor at Princeton University and writer of A Random Walk Down Wall Street, performed a test where his students were given a hypothetical stock that was initially worth fifty dollars. The closing stock price for each day was determined by a coin flip. If the result was heads, the price would close a half point higher, but if the result was tails, it would close a half point lower. Thus, each time, the price had a fifty-fifty chance of closing higher or lower than the previous day. Cycles or trends were determined from the tests. Malkiel then took the results in a chart and graph form to a chartist, a person who “seeks to predict future movements by seeking to interpret past patterns on the assumption that ‘history tends to repeat itself’”.  The chartist told Malkiel that they needed to immediately buy the stock. Since the coin flips were random, the fictitious stock had no overall trend. Malkiel argued that this indicates that the market and stocks could be just as random as flipping a coin.

–Investopedia, Random Walk Hypothesis

And from this as much as anything sprang a thesis based on an entirely false narrative… that stock price action is random.

Do you recognize the fallacy in Professor Malkiel’s argument? Ignoring for a moment the fact that trends can be easily found in “random” data (see below), it’s a pretty long stretch to suggest that stock price action is random because a chartist saw a trend in random data presented in chart form.   

At the risk of contradicting an esteemed academic (he with nary a bit of trading experience mind you), consider… just because the outcome of each discrete coin flip is random doesn’t mean the aggregate results are random.

I’ll say that again… Just because the outcome of a single coin flip is, by definition, random, that does not mean the result of 100 coin flips is random.  Notice, I’m not saying the outcome of 100 flips is predictable… just that the aggregate results are just as likely to be skewed as not.

It’s a bit like the molecules swirling around in a hurricane… the movement of each molecule is random… but there is definitely trend (direction) in a storm’s movement. 

Kinda kicks The Random Walk Theory in the teeth don’t you think?

The kernel behind my thesis is captured in an area called Chaos Theory [emphasis mine].

a branch of mathematics focused on the behavior of dynamical systems that are highly sensitive to initial conditions. ‘Chaos’ is an interdisciplinary theory stating that within the apparent randomness of chaotic complex systems, there are underlying patterns, constant feedback loops, repetition, self-similarity, fractals, self-organization

–Investopedia, Chaos Theory

A double rod pendulum animation showing chaotic behavior.

The Double Rod Pendulum illustrates Chaos Theory… it’s one of the simplest dynamical systems that has chaotic solutions.  Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. Further, applying a parameter such as gravity limits the possible touch points to below a certain level on the vertical scale.  Thus the results are chaotic (random) but within a range.

Trends “hide” inside chaos like this all the time.  

Think of the concept of inertia.  If an eighteen wheeler is moving down the road at even a moderate pace, inertia tells us that even if the breaks are applied, the truck will continue in the same direction for a time.  

The same can be said about freely traded securities.  And the Random Walk Theory fails to incorporate this.

If a stock is trading higher, it is most likely going to continue trading higher. Ditto if it’s trading lower.

This is called price persistence and it was discussed in the context of its use as an indicator by Gordon Gustafson in a January 2002 Stocks & Commodities Magazine article [emphasis mine].

Price persistency is the number of days that a market continues to close either up or down. It’s another term for a market run. As an indicator, price persistency is a measure of a very short-term trend based only on the history of the market’s movement, unfiltered by any complex calculation; all it involves is counting.

To be effective, any indicator must have at least a fairly consistent correlation with whatever market you’re going to trade. The advantage of price persistency is in its simplicity. The market is currently in a run or it isn’t. [As I tell my guys, either it is or it ain’t…] It’s either been down three days in a row or it hasn’t. Of course, this is an oversimplification that ignores the magnitude of the individual changes, which can be important. But for our purposes here — to form a trading system based on runs — let’s assume the magnitude of the changes doesn’t matter.

The usefulness of price persistency is based on the theory of runs. It is the idea that, given the market has moved in a particular direction for x days, the likelihood it will either continue to do so — or not — can be estimated and used in a profitable trading system.

–Gordon Gustafson, January 2002 Stocks & Commodities Magazine

All of this is a somewhat fancy way of saying things have a tendency to keep doing what they’ve been doing.

So how does it actually work?

Against The Random Walk Theory

Let’s say you decide to flip a coin 10 times.  Assuming a fair coin, each flip has a 50/50 chance of coming up head or tail.  Let’s also say you’ll add 1 each time it comes up head and subtract 1 each time it comes up tail.  Because the probability of each side on each flip is 50/50, you expect to end at or close to 0 at the end of 10 flips and all of the addition and subtraction.

You proceed to flip the coin 10 times and end up at -4… What gives?

It’s pretty simple actually… 

“Price” experienced at least 1 “run”… In other words, the tail side came up consecutively multiple times.

When that happens, “price” moves 3 steps in a given direction… In order to get back to the starting point, “price” must have the exact same number of consecutive steps right back in the direction from which it came… Here, 3 consecutive head results… Immediately.  Otherwise, the results have made a lower “low” and a lower “high”… and “price” has established a “trend” to the downside.

Here’s how it actually looks.

Price persistence

I know, I know… That was just 10 flips right? The probabilities didn’t have a chance to play themselves out right? Fair enough.

Here’s a look at how persistency might work… over 100 tries.  In the silent video below, starting at the Start Number, the “price” has 1 added or subtracted randomly for multiple iterations. Looking at the chart shows that even in action that is, by definition random, there are runs.  


This is one of the major keys to profitable trading.  

Interestingly, stock price movement is far less random than even this.  Because prices are driven by how the market (traders and investors) perceives the prospects of a company, sentiment is far less likely to change en masse from 1 trade to the next. As a result, prices that are rising tend to continue rising.  

The same can be said about prices that are falling.

All of this information can be used to create very simple, very profitable trading approaches.  

And I have. 

It’s how I called longs in FB below $20


and in ALGN… [very profitable, but required the most re-entries]


and in SWKS


and in IDTI

and in HDMore than once actually…

and also in… Well, you get the point.   

Stock Prices Are Random Right?

the random walk theory

Hopefully you’re clear now… Over any given timeframe, stock prices are NOT random. 

The inertia depicted in the example above (price moved from the bottom left toward the top right of the chart) alone is evidence of that, but feel free to look at any other extended timeframe you like… the result will likely be the same… prices tend to trend up (generally) or down over time despite assertions to the contrary by many “market professionals.”

The sticking point for most people (and constant argument by anti market timers) is the often maddening resistance of stock prices to prediction with any degree of certainty or consistency. 

It’s the foundation of that supposed market truism, “you can’t time the market.”  

That the market is “random.”

I suggest a slight modification to that principle.  Instead of you cant time the market at all, how about we change that to “you can’t time the market… perfectly.”  Further let’s add an extension… “you can’t time the market perfectly… but then you don’t need to time it perfectly to make a fortune.”

Wall Street’s Best

I know, I know… Wall Street’s best portfolio managers can’t manage to make double digit annual returns consistently (a fact of which they seldom fail to remind you… along with telling you that no one else can make double digit annual returns consistently either), so why should you think you can do any better?  

They even go so far as to say it’s impossible.  And if anyone tells you different it’s automatically a scam.

Now since you don’t have their expertise, information, size or market proximity advantages you’re inclined to believe them right?  After all, they ARE the professionals right?

The Reality

It’s true, you likely don’t have any of those things.

But then again, if theirs were such significant advantages, wouldn’t you think traditional portfolio managers far more capable of producing outsize returns?

Does it make sense to you that the average long term buy and holder spends 74% of their time in the market getting back to even?  Well that’s exactly what the well respected Ned Davis of Ned Davis Research found.  

“It’s a little-known but startling fact: The average buy-and-hold stock market investor spends 74% of his or her time recovering from cyclical downturns in the market (from 1900–May 2015).” (Ned Davis Research)

That’s according to well-respected Ned Davis Research, Inc… It raises a big question: How is it possible that investors spend three quarters of their time just getting back to the starting line?

The answer is explained by the unforgiving mathematics of loss: When investments lose ground, they must make up more ground, percentage-wise, just to get back to even.

Say you invest $10,000 and your account takes a 10% loss over six months. You’re down to a $9,000 balance. Because of your reduced capital base, you will have to earn 11% to recoup your losses. The steeper the losses, the higher the hurdle becomes for breaking even.

For example: Recovering a loss of 30% requires a 42.9% gain; a 50% loss requires a 100% gain. To recover from a loss of 75%, a 300% gain is required.

Getting back to even can eat up precious time. Take that 10% loss over six months. Earning a steady 4% annually after that, you will still need two and three-quarter years just to get back to where you started. That time would be much better spent accumulating new money. Remember, the idea is to grow your money, not just regain lost capital.

— Steve Blumenthal, The Merciless Math of Loss [All emphasis ours]

So What Are Your Advantages?

On this site, I write and teach about the so called advantages of the “professionals” and why they’re not nearly as significant as they would have you believe. I also showcase, emphasize and write more about YOUR advantages and how you’ve probably squandered (and likely continue to squander) them.

For example, despite what you’ve been taught, enormous size is not an advantage.  In fact, it’s the exact opposite.  As a result, what would appear to be a disadvantage to you [small size] is actually a tremendous advantage. 

An advantage you likely constantly give away…

Why?  Put simply, it’s much easier to move (grow) a $1,000,000 account than a $10,000,000,000 account.  It has to do with liquidity and opportunity, but that’s a lesson for a different day.

At any rate, these are the kinds of things I discuss and explain here.  I do this for folks on my email list. Don’t worry, registration and membership on the list  are free.  I also don’t bombard you with content or offers.  And I don’t do affiliate sales… Period.   

Is The Random Walk Theory Accurate? Let’s Go Back To The Charts

Have a look at the charts below.  They’re the exact same as that of the DJIA above except they’re broken into three distinct time ranges. 

Zooming in to multiple 6 month periods brings both trend and pivot (turning) points into sharper detail. 

Can you find 1 or more of the intermediate trends (trends lasting days to weeks) on each chart… all of which occurred within the context of the clear major uptrend between January 2013 and now (May 2014)?

January 2013 thru June 2013
the random walk theory

July 2013 thru January 2014
simple trading

January 2014 thru May 2014
simple trading

Did you find a few trends?

What’s really gonna freak you out is that the exact same thing happens on virtually every other timeframe… 4 Hour… 2 Hour… 5 Minute.  The only difference is a matter of degree.  It’s based on a principle called fractal geometry… again, that’s a topic for a different day.

Do you think you could find a few profitable trades in that action?

If your answer is yes, you’re right.  Stay tuned and I’ll show you some like that.

If your answer is no, you’re wrong, so stay tuned and I’ll show you some like that.

Until next time, may your trends be long and all of your losses small.


The Trader


Updated: 19 January 2018