The Random Walk and the Efficient Market Hypotheses

Early in the past century, statisticians noticed that changes in stock prices seem to follow a fair-game pattern. This has led to the random walk hypothesis, 1st espoused by French mathematician Louis Bachelier in 1900, which states that stock prices are random, like the steps taken by a drunk, and therefore, unpredictable. A few studies appeared in the 1930's, but the random walk hypothesis was studied — and debated — intensively in the 1960's. The current consensus is that the random walk is explained by the efficient market hypothesis, that the markets quickly and efficiently react to new information about stocks, so most of the fluctuations in prices are explained by the changes in the instantaneous demand and supply of any given stock, causing the random walk in prices.

The efficient market hypothesis (EMH) states that financial markets are efficient, that prices already reflect all known information concerning a stock or other security, and that prices rapidly adjust to any new information. Information includes not only what is currently known about a stock, but also any future expectations, such as earnings or dividend payments. It seeks to explain the random walk hypothesis by positing that only new information will move stock prices significantly, and since new information is presently unknown and occurs at random, future movements in stock prices are also unknown and, thus, move randomly. Hence, it is not possible to outperform the market by picking undervalued stocks, since the efficient market hypothesis posits that there are no undervalued or even overvalued stocks (otherwise, one could earn abnormal profits by selling short).

The basis of the efficient market hypothesis is that the market consists of many rational investors constantly reading the news and reacting quickly to any new significant information about a security. Similarly, many fund managers constantly read new reports and news, and use high-speed computers to constantly sift through financial data looking for mispriced securities. High-frequency traders, likewise, use high-speed computer systems located near exchanges to execute trades based on price discrepancies between securities on different exchanges or between related securities with interrelated prices, such as a stock and options based on the stock, or to front-run market orders.

To summarize, the efficient market hypothesis rests on the following predicates that:

The efficient market hypothesis has 3 forms differing in what information is considered:

  1. The weak form considers only past market trading information, such as stock prices, trading volume, and short interest. Hence, even the weak form of the EMH implies that technical analysis can't work, since technical analysis relies exclusively on past trading data to forecast future price movements.
  2. The semi-strong form extends the information to public information other than market data, such as news, accounting reports, company management, patents, products of the company, and analysts' recommendations.
  3. The strong form extends the information further to include not only public information, but also private information, typically held by corporate insiders, such as corporate officers and executives. Obviously, corporate insiders can make abnormal profits by trading their company's stock before a major corporate change is communicated to the public, which is why such insider trading is banned by the Securities and Exchange Commission (SEC). Corporate insiders can trade their stock, but only if the trade is not based on a major development few people know, such as a merger, a new product line, or significant key appointments within the company.

EMH posits that only information about the security affects its price. However, security prices also depend on how much money is invested in the markets and on how many investment opportunities are available. For instance, EMH does not account for the desirability of other investments, such as Bitcoin or gold. Another assumption of EMH is that information dispersal and reactions to that information are instant, which obviously is not the case. Professional traders will get the information sooner and react quicker, while retail investors will lag behind, if they react at all. Another tacit assumption is that investors know what price a security should be, based on the available information. But, obviously, investors will value the information differently, as people are wont to do.

Primary evidence that shows that information about a security is not the only thing affecting its price and that, in some cases, it may not even be a factor is the wild fluctuations of Bitcoin. As a cryptocurrency that has little practical value as money and does not even have fiat value, its true value cannot be anything other than 0, so there will never be fundamental information about Bitcoin that should change its price, yet prices for a single Bitcoin have exceeded $40,000, ranging over thousands of dollars just during January 2021, even though there is no fundamental news that would directly affect the price of Bitcoin, since its intrinsic value is always 0. (I discuss why cryptocurrencies have no practical value as money in my article Money: Commodity, Representative, Fiat, and Electronic Money, and why cryptocurrencies fluctuate in price.) That the price does change substantially every day causes people to invest in it simply to profit from those changes. This change of price results from changing demand while the supply is limited, but there is no fundamental reason why any cryptocurrency should be a certain price, so EMH can certainly not be applicable to the trading prices of cryptocurrencies. The trading of cryptocurrencies is pure speculation. The irony of Bitcoin is that its price is often determined by the investors themselves, who hype Bitcoin to increase its perceived value. For instance, if a famous celebrity hyped Bitcoin, then their followers may buy it up. Or if a major bank says that Bitcoin will reach a certain price, then the bank may increase demand simply by making that projection, even though such a projection cannot possibly have any foundation, since the intrinsic value of Bitcoin is always 0. Dogecoin is another example, a digital currency created in 2013 as a joke zoomed more than 1,500% between January 28 and February 8, 2021, during which time it was being mentioned on social media by celebrities Elon Musk, Snoop Dogg, and Gene Simmons.

Although cryptocurrencies probably were not originally created as a scam, it is clear that they can be used as such. In my opinion, cryptocurrencies are the ultimate penny stock, the best pump-and-dump scheme, because their prices are mainly determined by hype! People with influence can buy Bitcoin, then hype it to increase its price, then sell for a fat profit! And because Bitcoin fluctuates wildly in price, even within a short time, people can continue doing this. But since this is unpredictable, the price of Bitcoin will also walk randomly, so EMH is not applicable, since Bitcoin is not based on a company or anything else that would provide it with real value, so no information could ever be provided that would determine its price.

The Random Walk of Prices is the Brownian Motion of Supply and Demand

In my opinion, the random walk is only partly explained by EMH in that information would make the walk less random, so if material information about the stock is quickly dispersed, than changes in price will seem random most of the time. But what causes this randomness? The random walk of stocks and other securities can best be explained by the same concept used to explain Brownian motion. Brownian motion, which is the random motion of small particles suspended in a fluid, was 1st observed by the botanist Robert Browning in 1827 as the random movement of pollen grains suspended in a liquid, and that this movement continued even for a liquid at equilibrium — in other words, the pollen grains continued to move randomly even though there was no evident force moving them. Albert Einstein provided a mathematical foundation to explain Brownian motion in 1905 as the result of the random molecular bombardment of the pollen grains — at any given time, the molecules bombarding the pollen grains on all sides are unbalanced, causing the grains to move one way, then another. Because this bombardment of molecules was random, so was the resultant motion.

So how does this apply to the stock market? Economists would say that stocks and other security prices result from the equilibrium of supply and demand — however, it is the instantaneous supply and demand that determines prices, and at any given time, supply and demand will differ simply due to chance.

For instance, suppose, on a particular day, that you have 100 investors who want to buy a particular stock and 100 investors who want to sell the same stock, and suppose further that they believe that the opening market price to be a fair price and they place market orders to effect their trades — and these traders are not aware of any news about the company during the course of the day. I think you will agree that there is little chance that these traders will all come to market at the same time, even on the same day, and if some of them do happen to trade at the same time, the number of buyers and sellers probably will not be equal at that time, and that whether there are more buyers than sellers or vice versa will differ throughout the day. Hence, at most times of the day, there will be an instantaneous imbalance of supply and demand for the stock, which will cause the stock price to move seemingly randomly throughout the day. I say seemingly, because even though the stock price is determined by the instantaneous supply and demand of the stock, no one can know what that equilibrium price will be ahead of time.

The proof of this explanation can be observed by the fact that even when there is no news about a particular company, its stock will walk randomly throughout the day because the instantaneous supply and demand will vary randomly throughout the day.

Nonetheless, news does move the markets, and news being mostly unpredictable, at least by most traders, means some randomness will be created by news events. But even when news about a particular company does move its stock price significantly, the response will still have some randomness, because different traders with different amounts of capital will learn about it at different times, and limit and stop-loss orders will be triggered as the stock price changes significantly, thereby causing the stock to zigzag up or down. But how much will the price move because of the news? Different traders will assess the news differently. Some traders will buy more on good news, believing that the good news will propel the stock price higher; others will sell because they believe the price has overshot its top, and these traders will trade at different times.

A good example of the fact that complete information about a security does not account for its total price is a closed-end mutual fund. A closed-end fund (CEF) is composed of certain securities that were initially selected when the fund was created. The fund is then closed with its security composition set, then the CEF shares trade like a stock on an exchange. The net asset value of the shares = the value of all the securities composing the fund divided by the number of fund shares. However, the market price of the shares often sell at a discount — sometimes, a steep discount — to the net asset value of the fund. This discrepancy exists because the supply and demand of the CEF shares depends on factors other than the intrinsic value of the shares, and these factors also vary randomly, thus partially explaining the random walk.

Is the Efficient Market Hypothesis True?

I have no reason to doubt some aspects of the efficient market hypothesis, but is there another reasonable explanation as to why it is difficult to outperform the market? After all, how does the efficient market hypothesis explain the stock market bubble of the latter half of the 1990's? If stock prices were simply the result of the total sum of all information about the companies and their stocks, then stock bubbles shouldn't happen — but they do happen. In the late 90's, it was evident that a bubble was forming because stock prices were growing much faster than the underlying companies — you don't have to be an economist or an analyst to know that this could not continue, and that stock prices would eventually decline significantly.

Some have argued that information only affects changes in prices, not their level. The problem that I have with this argument is that the old information should continually be telling investors that stock prices have already overshot their intrinsic value or their true pricing, and that investors should've been selling since even good news can't really overcome the fact that stock prices have soared much faster than the underlying businesses. But, alas, that isn't what happened.

What happened is that more and more people started piling into the stock market as it soared ever higher, thinking that it will go higher still — what Alan Greenspan has termed irrational exuberance. Indeed, the rest of the world joined in, buying stocks listed on the United States exchanges because they, too, expected the stock market to increase. I guess they thought they would be out of the market before it dropped. Some did get out at the top — that's why the market started dropping. But most investors suffered significant losses.

Another factor propelling stock market bubbles is the fear of missing out (FOMO). As a stock market ascends higher, people brag to their friends about how much money they are making, so people not yet invested in the stock market become envious and fear they are missing out, so they invest. Unfortunately, many of these people invest after the stock market has already ascended considerably, paying much higher bubble prices, only to suffer grievous losses after the market declines.

After the stock market bubble came the real estate bubble in 2005 through 2007, as people believed that real estate couldn't possibly decline in price — after all, they're not making any more of the stuff as Will Rogers once quipped. But maybe rational investors should've paused, thinking: "Can real estate prices really continue to rise much faster than people's incomes?" Or maybe these rational investors thought they would take advantage of the momentum and get out just before the market started falling. Some did get out before it fell, that's why it started falling, but most investors suffered horrendous losses.

Now some would argue that the smart money got out in time — the so-called rational investors posited in the efficient market hypothesis. And yet, it has come to light that the biggest banks, including investment banks, have suffered so many losses that they had to be bailed out by the United States government in late 2008 or be taken over by healthier banks; otherwise, they would have suffered the fate of Lehman Brothers — bankruptcy! Many of these investors working for these banks were making huge bonuses, supposedly because they were the smart money. Although these banks didn't directly buy real estate, they did invest in mortgage-backed securities and other derivatives based on mortgages, which they considered relatively safe. And yet, these were the very same banks that didn't worry too much about the creditworthiness of their borrowers, since they could pass on the credit default risk to the buyers of the securitized loans — many of whom turned out to be other banks! Where is the rationality here?

Then came the commodities bubble. A barrel of oil was priced above $147 in the summer of 2008, only to fall to less than $40 per barrel by December of the same year. Where is the efficiency here? And then the Bitcoin bubble in 2019, 2020, and 2021. I predict that the Bitcoin bubble will expand and contract continuously for the foreseeable future. It is simply 1 of the best scams ever devised! I don't believe it was devised as a scam, but it is becoming evident that its price can be easily manipulated, making it the ultimate penny stock of the 21st century! Although this is true of the other cryptocurrencies as well, it is currently Bitcoin that is receiving most of the hype, which is why it is fluctuating so wildly in price.


Although the efficient market hypothesis is a useful heuristic concept that may shed some light on trading and the markets, I believe that a more plausible reason to explain the inability of most investors to outperform the market, especially by active trading, is because there are so many factors affecting the prices of most investment products, that no one can know and quantify all these factors to arrive at what the future price of anything will be. This bounded rationality explains why many economic decisions are not rational or optimal. Moreover, it is reasonable to expect fluctuations over the short term will be more random than over the long term, but that fundamental values will be more determinative over the long term. Since many factors affect prices, not just information about companies or stocks, EMH explains some effects on prices, but EMH does not determine prices.