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If you haven't yet, I recommend reading How I Can Explain 96% Of Your Portfolio's Returns, Part 1 and How I Can Explain 96% Of Your Portfolio's Returns, Part 2, since they're crucial to most of the concepts discussed here.

I've covered a number of highly quantitative concepts in the first 2 parts of this series. Feedback has consistently indicated to me that there is simply not enough reason to expect that systematic risk factors like SMB and HML will be positive in the future. Still more refuse to consider the idea that there exist passive investing strategies that have outperformed for all of recorded history and will continue to outperform into perpetuity. When this breed of investor stares at a set of numbers or the raw output of a regression, all he/she sees is numbers. In most cases, the meaning of these numbers is understood, but they are only numbers at the end of the day. They are simply not a good enough reason to believe that past outperformance will continue. They need to see vats churning, pipelines pumping, satellites orbiting, and jeans selling before they can chalk up numbers to being anything more than "tortured data." I am not one of these people, but I will certainly try my best to provide a different lens to peer through.

Consider the following story about how a statistician for Target (NYSE:TGT) piqued a lot of consumers' interests. An article that appeared in the New York Times in February, 2012, entitled How Companies Learn Your Secrets by Charles Duhigg, details the drama that unfolded.

Data Is A Powerful Weapon

In the infancy of data analytics, many retailers initiated departments dedicated to using data to discover consumer insights. In one such department at Target, a statistician by the name of Andrew Pole sought to answer a valuable question: "How can we use available data to determine whether a customer is pregnant?" While it may seem like a strange question to ask, the reasoning was sound. New parents are extremely vulnerable to marketing campaigns that seek to shift their brand preferences. The first party to identify the consumer's pregnancy has the first shot at capturing a loyal customer. If Target could be the first to identify a pregnant couple, it could be the first to send specifically tailored coupons. What might start as a few baby products could easily snowball into food, furniture, silverware, and anything else you can think of. Chalk up another loyal customer to Target.

Pole examined Target's baby-shower registry, noting quantitative trends in which products the women tended to purchase, and at which points in their pregnancy they did so. Eventually, he identified 25 products that could be combined to produce a "pregnancy prediction" score for each shopper. Duhigg's article illustrates with the following example...

"Take a fictional Target shopper named Jenny Ward, who is 23, lives in Atlanta and in March bought cocoa-butter lotion, a purse large enough to double as a diaper bag, zinc and magnesium supplements and a bright blue rug. There's, say, an 87 percent chance that she's pregnant and that her delivery date is in August."

Using the individual shopper IDs of every female customer Target had in its system, Pole produced a list of thousands of women who were probably pregnant. Using his predictive model, Target began to implement the strategy. Knowing that pregnant women would react poorly to the company knowing about their unannounced pregnancy, Target designed coupon booklets with random products discreetly mixed with relevant baby coupons. The idea was to make the baby products seem "random."

About a year after the campaign was underway, a man approached the manager of a Target store in Minneapolis, angry about something. He went on to explain that his daughter had been sent coupons for baby clothes and cribs, despite being only high school age. He accused the manager of encouraging his daughter to get pregnant. The manager, obviously not in the loop about the baby coupon campaign, could only apologize. Days later, when the manager called to apologize again, the father promptly admitted that he had just found out his daughter was indeed pregnant, and offered the manager an apology instead.

The moral of the story is that there are indeed trends in human behavior that are not only unknown to the perpetrators of that behavior, but are also predictable by third parties through innocuous data. Target is not alone in its quest for data. You would be hard pressed to find a retailer that isn't employing data analytics to discover nuances in human behavior. The world of finance is no different. The stock market produces limitless data, simply waiting for the right analyst to crunch the numbers and uncover insights. At the very least, this example proves that simple data is more than capable of telling us things about ourselves that we may not even know.

Irrational Behavior

Expanding upon the same topic, there exist what marketers sometimes refer to as an "arsenal of weapons," or ways in which we can take advantage of when human beings act irrationally. We're wired to act instinctively like animals to certain situations, leading us to sometimes miss the whole picture. We all know how easy it is to take advantage of an animal's lapse in logic. Pretending to throw a stick for a dog to fetch, only to quickly hide it out of sight gives us the satisfaction of demonstrating how easily we can take advantage of the dog's irrationality. Human beings suffer from the same lapses in logic in predictable ways. The trick is to identify them.

I'm reminded of an example from the book Influence, The Psychology of Persuasion by Robert Cialdini. The author brings up the example of mother turkeys and their young. Mother turkeys are instinctively wired to react positively to the "cheep-cheep" calls of baby turkeys and respond aggressively to the approach of their natural predator, the polecat. A study was performed in which a stuffed polecat was introduced to a mother turkey. As expected, the mother turkey attacked ferociously. The experiment was repeated, but this time an authentic "cheep-cheep" sound emanated from the stuffed polecat. Upon hearing the sound, the mother turkey accepted the stuffed polecat and treated it as one of her own. Upon ceasing the "cheep-cheep" noises, the mother turkey promptly rejected the polecat and exhibited the same aggression as before. Mother turkeys react rationally to most stimuli, yet it seems this simple trigger can be used to induce a complex reaction.

Now, pretend that the average human investor is this mother turkey. If one could identify the "cheep-cheep" that induces irrational investing behavior, the identified behavior becomes highly predictable. This is the key to the success of both size and value as systematic risk factors. The irrational behavior that is induced by size and value traits causes investors to overcompensate in predictable ways. When this overcompensation is captured repeatedly, 2 powerful arbitrage strategies are born.

A comment I read recently sums up the value of these relationships quite nicely...

"...a lot of hedge funds are moving to factor based portfolio[s] (I research for a hedge fund). We started with the hypothesis that factors are building blocks of returns. The biggest puzzle for my research is... what is the source of return of these factors? Why [are they] not arbitraged away? Imagine, if I can just pick good stocks from bad stocks and keep investing in good ones. Taking it a bit further, if I can just pick good factors from bad ones... what will my return look like.. If I have an algorithm that tell[s] me that credit risk is under priced....I will immediately invest in long term bonds, high yield stocks, sell CDS and buy emerging market currencies. That will look quite diversified."

The Evidence

Divide the entirety of modern stock market history into monthly values for the market factor, SMB factor, HML factor, and an average of all three factors. Then, take a look at the 10 years that follow each (890 total 10 year intervals). For each of these 10 year intervals, compound the value of a given factor. In other words, we are left with a 10 year measure of performance if your strategy had been to perfectly track a given factor. Tracking the market factor closely mirrors a 10 year performance of the S&P 500, tracking the SMB factor reflects small cap outperformance, tracking the HML factor reflects value outperformance, and tracking an average of the three reflects an evenly weighted strategy. After doing this for every possible time of entry in history (890 instances) for each factor, we get a picture of how often each strategy would have paid off.

The results? Out of 890 possibly points of entry since 1929, the market turned a positive 10 year value 866 times (97% of entry points), SMB turned a positive 10 year value 612 times (69% of entry points, HML turned a positive 10 year value 877 times (99% of entry points), and an even combination of all three factors turned a positive 10 year value 890 times (100% of entry points).

What this means is that there are unquestionably forces that are compelling these factors to gravitate toward a positive value. We invest in the stock market because we believe its long-term value (such as a 10 year interval) will be positive from the growth of the United States economy and inflation. These are real reasons that drive our rationale for an investment in the broad market. They are obvious and don't need to be stated for most investors. However, the compelling forces behind the constant outperformance of size and value are a mystery to most.

What Causes Small Stocks To Outperform?

When you read the words "small-cap" or "micro-cap," there are preconceived notions that permeate your thoughts regardless of the context in which they are written. Indeed, Seeking Alpha requires a small disclosure for articles whose focus is a micro-cap. Our brains are wired to send up little red flags for these labels, yet I doubt most investors know specifically what is supposed to be scaring them. There is no question that there is more volatility due to burdens like illiquidity and penny-stock pricing that are borne by most small stocks, but we don't take the time to question whether these hiccups really matter. If we have compelling historical evidence that small companies have outperformed their large counterparts on average with great consistency, the ends justify the means. These real issues become irrelevant in a long-term investment.

From this apparent disconnect between real problems and perceived long-term risk, an arbitrage opportunity emerges. Most arbitrage opportunities are exactly what they sound like: individual opportunities. Once they are identified and executed, the gap is closed. However, this is an opportunity that resets itself constantly and on a large scale. As soon as one investor realizes he's made the irrational decision to avoid small caps because of perceived risk, another inexperienced investor is bound to enter the market that turns up his nose at small-caps. In this case, the words "small-cap" and "micro-cap" are the "cheep-cheep" sounds that investors have been conditioned to respond to, and in a very predictable way.

The arbitrage opportunity itself is not difficult to execute or understand. A simple portfolio of small-caps is positioned to benefit. If each small-cap has a market cap of $100 million at the time of purchase, there is a high amount of perceived long-term risk per dollar of market cap. If over time, during the course of normal fundamental growth (such as revenue or earnings), the company sees great improvement, as most do, share price will increase and market cap will increase. If each of our picks sees fundamental growth and appreciates to $10 billion in market cap, this is obviously a positive result, but no different than what we might expect of a larger company's fundamental trajectory. However, since these $10 billion companies now carry the label "mid-cap" or "large-cap" there is less perceived long-term risk per dollar of market cap than before. Thus, while both small and large companies may see fundamental growth of equal magnitude, the small companies will benefit from the inflow of investors and funds that occurs when perceived long-term risk decreases simultaneously. The arbitrage opportunity for these few companies is closed, but nothing is stopping an investor from simply purchasing a fresh portfolio of $100 million stocks. Taking it one step farther, nothing is stopping an investor from identifying the window of market cap change in which perceived risk changes the most, purchasing positions at the beginning of that window and selling at the end. If history is any indication, that arbitrage window occurs when public stocks are as tiny as possible.

This begs the question, "Why do micro-cap ETFs not outperform?" They frequently do (iShares Russell Micro-Cap ETF (NYSEARCA:IWC) is up 37.7% TTM), yet not nearly as much as we would expect, given the above information. The reality is that most ETFs must be large to be viable, and their positions in micro-caps are significantly affected by liquidity issues. A retail investor quietly buying a few shares does not cause a ruckus, but a large ETF buying shares in a micro-cap that has only $5 million in market cap is bound to inflate the ETF position's cost basis disastrously. Thus, retail investors can capture much more of the arbitrage opportunity with their own small positions.

What Causes Value Stocks To Outperform?

Pretend that in front of you is an unmarked gold ring and next to it is a stack of unmarked gold bars. You are asked to value the two. As long as you have the price of gold, this doesn't seem too difficult. Your estimates of the gold ring probably won't be off by much on an absolute basis but the gold bars are another story. Since your measure is weight, you have much less confidence in the total value because weight is much more difficult to ascertain from a cursory inspection of a pile of gold bars than for a single ring. You have no frame of reference for a pile of gold bars... do they weigh 50 pounds? 100 pounds? It's hard to say.

The same problem occurs when we try to ascertain the future value of a business. If the future value is generally perceived to be large, there is a much greater chance that this perception is inaccurate because we have no frame of reference. Take Tesla Motors (NASDAQ:TSLA), for which the subject of future value has been hotly contested. The consensus is indeed that the company has enormous future value, but the question is whether current share prices have overestimated this future value. Tesla is the pile of gold bricks and we have no scale. Historical data tells us that, regardless of other fundamentals or real facts pertaining to the company, there is a high probability that the market has overestimated the company's future value because it sits in the most growth oriented 10% of all companies by P/B. Recall the historical reporting of each value/growth decile from Part 1 (and remember that Fama and French use "book/market" which is the inverse of P/B)...

Tesla may be "the most promising company you've ever seen," but everything has a price, even "the most promising company you've ever seen." More importantly, the company is without precedent. Thus, there is no reason a retail investor, let alone an industry professional, should be able to estimate enormous future growth with anything approaching accuracy.

Tesla isn't alone. Deciles 6-10 clearly show that the market sometimes estimates future growth correctly and sometimes estimates future growth incorrectly. Which of these two has occurred with Tesla is unknown for now, but it seems like a major gamble after observing the market's historical inaccuracy when it comes to growth stocks.

Thankfully, as soon as we stray into the value deciles (1-5), the market underestimates without exception, leaving yet another arbitrage opportunity. The 1st value decile contains stocks whose P/B value is below 1 in many cases (a single share owns more GAAP valued assets than its own price). For these stocks, there is little or no future value priced into the stock, and therefore no risk from the market overestimating future value. In fact, quite the contrary. The constant overvaluation of growth stocks means that value stocks are constantly undervalued. Returns from value stocks are essentially purchased at a discount. This is another perfect example of a natural flaw in human decision making that diverts funds in a predictable way.

Final Thoughts - "Just Be Faster Than The Guy Next To You"

There's a famous line that goes something like, "When running from a bear, you don't need to be faster than the bear... you just need to be faster than the guy next to you." The same advice is appropriate for investing. When there are only two choices, small versus large and value versus growth, there is only one winner in each case. As long as you're not on the losing end, you're on the winning end. It just so happens that there are subtle trends in human irrationality that are skewing success in favor of small and value, and these trends show no signs of erasing themselves from nature. For this reason, you can bet the last century of stock trading was no fluke: small and value superiority will continue. The information age is just recently allowing us to map this superiority and quantify exactly how much stands to be gained.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.