I had heard there had been some stock market research that suggested that after the market sold off for a few days, it was likely to trade flat or bounce a few days later.

I thought that was pretty cool except that for some reason I could never find the research to see it with my own eyes.

So I decided to do the research myself and this article outlines some of my findings. My full report which includes how to actual trade the results of this study was way too long for your typical
blog post so I wrapped it up in a free 43 page report. Sign up below and I'll send the the full PDF report to you titled **21 Year S&P 500 (SPY) Study Reveals High Probability Income
Trading System.**

### Random Walk, Brownian Motion, and Efficient Market Hypothesis

Before diving into the numbers of this 21 year study on the SPY, I think it's important to understand some of the underlying principles the related to the results of this research. In this section, I'm going to briefly explain how Random Walk, Brownian Motion, and Efficient Market Hypothesis are related. Chances are you've heard of at least one of these theories before and knowing this information will help explain why even though the SPY seems like it moves randomly on a day to day basis, that it is still moving in a Normal Distribution or Bell Curve fashion.

In 1900, French mathematician Louis Bachelier completed a doctoral thesis where he worked out a model on the variation of asset prices like stocks and bonds. Initially the thesis was well received after being published. However for the next 60 years his thesis was forgotten until economist Paul Samuelson and others realized that Bachelier had made a seminal contribution to the problem of understanding the fluctuations in asset prices. For any history buffs out there, this thesis is considered by many the founding document in quantitative finance.

Bachelier's key insight was that if asset prices showed any identifiable pattern, there would be an expectation that speculators (think traders) would find it and exploit it. And by doing so, eliminating it.

**Having flashbacks of all those failed trading patterns?** **You're not alone.**

For example, if you knew the weather was going to be dry next summer and affect the orange crops, you could exploit it with futures contracts expecting higher prices on a smaller crop. As more
people pile into this trade, the trade stops working. **Ever heard of a crowded trade?**

Here's where this starts to matter with our income trading strategy. After traders have incorporated all available knowledge into their trades, there should be en expectation of unpredictable fluctuations in stock prices independent of their past history.

The modern term for this is called a "random walk". The equations Bachelier obtained from this model correspond to what is known in physics as Brownian motion. More on that in a minute.

In the 1970s Black, Scholes, and Merton refined and systematized Bachelier's insights and solved the option pricing problem in finance. **(I told you this matters to our income strategy,
stay with me...)** In 1997 the Merton and Scholes won the Nobel Prize in 1997. Black had passed away by then but his name was still a part of the Black-Scholes model.

Their 1973 paper began by explaining that if options are correctly priced in the market, it should not be possible to make consistent profits by creating portfolios of long and short positions in options and their underlying stocks.

Such a model is based that all economically relevant information that could affect prices has in fact been incorporated by speculators, traders, retail investors, hedge funds, pension funds, and all other market participants into the prices themselves. This has been called Efficient Market Hypothesis.

In economics, an "efficient" outcome is one in which all gains from trades have been realized, so that everyone is as well off as they can be, without having to make someone else worse off. In this particular context, it means that speculators have found all possible gains that can be made from playing the market, so that what's left is a Brownian motion of the asset prices.

**Skeptical that all gains have been realized and that you have no chance of making money with a choppy market?** (ie Brownian Motion/Random Walk)

Here's what you should know. Every day new information comes out from around the world in our globally interconnected markets. This information is disseminated in a slow manner which can cause trends. Sometimes news comes out in a quick manner, such as an earning's report, that cause price spikes up or down. It's actually impossible for the stock market not to fidget around like a 3 year old because new information is constantly being released each and every minute.

Let me ask you, do you know how many iPhones Apple will sell next quarter? Me either, in fact neither does Apple. Once the numbers start to come out from various suppliers, think chip makers,
estimates start to be made by analysts. This can actually move the stock up or down until the real information or news is released. **Ever heard of "buy the rumor sell the news"?**

What I want you to walk away with from this section is that stock prices have an underlying fidgetiness (i just made that word up) about them. That there is a built in amount of chop and randomness that you can exploit to gain an edge in the markets. As you'll learn, even though the market seems random, it still falls into a normal distribution when looking at consecutive days of rallies and declines over the past 21 years.

### 21 Years of Consecutive Day Rallies

So let's dive into some numbers and we'll start on a positive note, with rallies. (I'm really a closet bear)

This first chart shows the distribution of consecutive days of rallies on the SPY based on the daily closing price. A rally was defined as the closing price of the day being higher than the closing price of the previous day.

I love this chart because of the almost perfect normal or Gaussian distribution that is displayed. At least for half, as we are initially looking as just the rallies. We'll talk more in a minute about Random Walk and Brownian Motion but first let's make a couple insights into what we're seeing here.

The main takeaway for you is that the more consecutive days the SPY rallied (closed higher then the previous day) for the 21 year period, the less occurrences were present. **Another way to
say it is that for every day in a row the SPY rallies, the less likely it is to rally the following day.**

As you can see there were a whopping 2,948 days where the market rallied only 1 day in a row. This makes up about 53% of the total 5,537 trading days the past 21 years. Then if we look at 2 day rallies, the percentage starts to drop dramatically where only about 28% of the time the market would rally 2 days in row and so on.

### 21 Years of Consecutive Day Declines

So now let's take a look at a similar chart showing the distribution of consecutive days of declines on the SPY based on the daily closing price. A decline was defined as the closing price of the day being lower than the closing price of the previous day.

Now even though the charts look similar at first, I'd like to point out that the most consecutive declines on SPY during the 21 year period were 8 days and it only happened once. This is very
different from the previous rally chart in that stocks were able to rally much longer than the declines. **As we'll explore later, when it comes to exploiting these percentages for profit,
we will need to treat multi-day declines differently than multi-day rallies. **

For now though, the near perfect distribution on the declines is something to admire. I'd like to also note that after selling off 3 days in a row, the likelihood of getting 4 days in row of declines is much lower than getting 4 days of rallies. Only 3% where the latter was about 7%. You could then say that a 4 day rally is twice as likely to occur than a 4 day sell off.

### The Bell Curve

This chart includes both previous charts where the 1 day rally and 1 day decline are next to each other near the center. Then to the right you'll see # of occurrences of consecutive daily rallies. To the left, the consecutive daily declines. I've removed any bars with a value of zero to save space.

As I've mentioned before this is a beautiful representation of Gaussian Distribution in the real world. Also known as Normal Distribution or simply the Bell Curve. How it applies to the stock market is that when you have a large sample of random variables, the results tend to converge into this shape of distribution. In this case, we are talking about consecutive up or down days on the SPY. As you can see, 21 years of daily stock market data has been distributed normally over time.

### But What About Price Though?

Good question. Just because the market sells off 3 days in a row, doesn't mean it won't go lower after a 1 day dead cat bounce. This is absolutely true and the same goes for rallies. Just because you get a 5 day rally and then a rest day, the SPY could easily go higher and rally for several more days as the consecutive day rally count starts over.

So I am by no means recommending that you buy after a certain numbers of days down, or sell after a 5 day rally. I simply wanted to visually illustrate in this article the Gaussian or Normal Distribution, or Bell Curve is alive and well in the stock market and has been the past 21 years and will continue to in regards to consecutive rallies and declines in the SPY.

### So what's the trade?

Glad you asked. Being an options trader and knowing that volatility increases during sell offs, I couldn't help but do some backtesting for the 21 year period incorporating this study as well as the actual price of the SPY after a certain amount of consecutive days down.

So I've created a separate free report for those who want some insight on how they can use this in their trading. **In the report, I focused on 3, 4, and 5 days sell offs and where price
ends up 3, 4, and 5 days later.** The results were absolutely amazing and I'd love to share them with you for free.

Sign up in the form above and I'll send the PDF right over.

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