In August of 1913 something remarkable happened at the famed Monte Carlo Casino in Monaco. At the roulette table, a crowd began to form as the wheel was spun again and again, consistently landing black every time. Gamblers began placing greater bets on red, convinced that the wheel was due to break its streak. Those gamblers lost millions of francs. By the time the streak was over the ball had landed on black 26 times in a row.
Ultimately the behavior the gamblers exhibited that day would come to be known as the “Gambler’s Fallacy.” Each spin of the wheel is an independent random event – the prior result has no effect on subsequent results. But when humans see a continuous, increasingly unlikely pattern such as the one at Monte Carlo, they are wired to believe the odds of success have changed. Of course, they have not.
There are 37 slots on a European-style roulette wheel, 18 black, 18 red and one green. Assuming the wheel is not biased, that means the probability of the next spin coming up black is 18/37, or about 48.6%. The probability of the next two spins coming up black is (18/37)2, the probability of the next three spins coming up black is (18/37)3 etc. Thus, before the streak began, the probability it would occur was (18/37)26, which equals a minuscule 0.0000007%, or about 1 in 136,823,184. Yet it happened. Such a low probability confuses gamblers as well as investors. Although before the streak happened its likelihood was extremely low, at any point during the streak the likelihood of black remained 48.6%. This is an important distinction. Every spin was independent of the one before, so the odds never changed even as the highly improbable set of events unfolded.
What is random?
People often misunderstand randomness. Although flipping a coin involves a 50% probability of success, it does not follow that for any number of flips exactly 50% of flips should be heads. Consider a coin flipper who maintains a perfect 50% success rate by flipping a coin heads, then tails, then heads, then tails and so on. This is anything but random. In fact, it is an obvious pattern that would lead even a casual observer to conclude that something other than chance was driving the results. Instead, a truly random event will often have streaks that, although not predictable, are not surprising.
There is a lot of randomness in the stock market and one school of thought, led by Fama (1965), believes that stock returns themselves are largely random. Since that time, some finance professors have asserted that daily price changes are often completely consistent what would be expected from a mechanism as random as the flip of a coin. Nowadays, while most agree that stock price changes are not entirely random, randomness indubitably plays a big role in returns.
Yet biased interpretation continues...
In Burton Malkiel’s classic 1973 book A Random Walk Down Wall Street, the author recounts a story of a hypothetical stock chart he created by flipping a coin and recording a positive return for heads and a negative return for tails. Without revealing how the chart was created, he showed it to a technical stock analyst who immediately got very excited, pointing out that the stock was about to “break out on the upside.”
In the 45 years since the book was published a great deal of research has shown that sometimes such technical approaches can work. But only sometimes. And often they fail. This makes it important to consider the possibility that an apparent pattern is simply a mirage - a trick your mind is playing on you. And when faced with a pattern that is seemingly unbreakable, don’t bet that it will either continue or stop. Bet based on the true probability.
For all its popularity, the psychology of casino gambling was a field relatively unresearched by finance scholars until Barberis (2012) presented his model for casino behavior. In it, he addresses many of the seemingly illogical decision-making patterns of casino patrons. For instance, gamblers tend to mentally overweight the tails of the distribution, making large payoffs seem more likely than they really are. The roulette player, therefore, would not properly discount the payoff to account for the 48.6% odds of winning.
Meanwhile, the Barberis model assumes that all casino patrons enter the casino with a fairly rational plan, to continue gambling as long as they are winning and to stop once they begin losing. However, one subset of patrons is unable to stick with this plan and end up gambling too much when they are losing and stopping too early when they are winning. He argues that this so-called “naivete” makes people attracted to games such as blackjack and slot machines because of the extreme positive skewness of the payoffs that the gamblers perceive.
The foundation of the Barberis model is an adaptation of Tversky and Kahneman’s (1992) cumulative prospect theory (CPT), the dominant behavioral theory of risk taking. CPT incorporates many behavioral findings such as loss aversion and anchoring, but also allows for inconsistent weighting of very large payoffs or losses. That is, in a casino, a gambler will not necessarily overweight the most unlikely outcome, but rather the outcome with the largest payoff.
In the context of the stock market, CPT might suggest that stocks with positively-skewed expected returns are also preferred over stocks with lower variance, lower skewness but reliably positive expected returns. However, the second component of the Barberis model – that gamblers will develop a rational plan but fail to adhere to it – is particularly important. Instead of selling only when losses begin to accumulate the trader will sell stocks that have gone up substantially. This implies that losing stocks are held too long and winning stocks are sold too early.
This tendency has not gone unnoticed in the finance literature. Eraker and Ready (2015) document that over-the-counter stocks, popular among retail investors, provide lottery-like returns. While many (25% of the sample) become worthless, and as a group they have extremely negative expected returns, a small subset has very large positive returns. So, in addition to overweighting the large positive returns, investors may also not weight the negative expected return appropriately. This makes over-the-counter stocks overpriced and generally bad investments.
The Gambler’s Portfolio
So what does the portfolio of a gambler look like? And how does it differ from a true investor? Subjectively, a gambler’s portfolio is likely made up of stocks chosen based on hunches and hope. This may be, at least in part, due to the “gamified” nature of gambling. Objectively, this might show itself in massive losses punctuated here and there by select successes. Not to be confused with volatility, these large variances are, in our opinion, evidence of the risk of human behavior at work. You see, we believe a true investor’s calling card is patience and the belief in probabilities. Investment successes are great, of course. But sometimes such investments are more the result of randomness and a cognitive bias to “win.” And, most importantly, such behavior goes hand-in-hand with steep losses which…you guessed it…is actually gambling rather investing.
Investors rely on skill. Gamblers rely on luck. The investor will not merely roll the dice and hope that they land favorably. Rather, the investor has some basis for making his or her decision. However, this decision must be made responsibly. The investor must be able to answer the question “Can I intentionally lose?” in the affirmative. If one cannot intentionally lose, they cannot intentionally win.
Investors understand what they own. Gamblers do not care. Nevertheless, many investors do not realize they are dealing with gambling outcomes, thereby exposing them to gambling risk even when they believe they are investing responsibly. This makes the mitigation of gambling risk paramount. The appropriate approach for an investor, therefore, will be to know the probability of investing in a loser.
What is a loser? A loser is a stock that fails to deliver the growth implied by its price. Measuring the probability of that happening allows the individual to truly behave like an investor.
In the end, one must ask themselves what they intend to be. In our opinion, gamblers rejoice in wins and conveniently ignore the losses while investors simply avoid the losers and reap greater returns as the result.
Which would you rather be?
New Age Alpha is a global leader in building actuarial based asset management solutions that aim to inure investor portfolios against an idiosyncratic risk caused by human behavior. Investors are unaware of this risk that leads to loss, cannot be diversified away, and don’t get rewarded for taking it. Unlike firm specific risk, that can often be diversified away, this risk affects stock prices specifically and we believe is caused by human behavior. Through our research we have identified a differentiated source of alpha that is uncorrelated with traditional risk factors and managers, and as the foundation to our investment approach, we have built a range of actuarial based asset management solutions that aim to mitigate and inure investors’ portfolios against this risk.
Barberis, Nicholas, 2012, “A Model of Casino Gambling,” Management Science 58, No. 1, 35-51.
Eraker, Bjorn and Mark Ready, 2015, “Do investors overpay for stocks with lottery-like payoffs? An examination of the returns of OTC stocks,” Journal of Financial Economics 115, Issue 3, 486-504.
Fama, Eugene, 1965, “Random Walks In Stock Market Prices". Financial Analysts Journal 22(5), 55–59.
Tversky, Amos and Daniel Kahneman, 1992, “Advances in prospect theory: Cumulative representation of uncertainty,” Journal of Risk and Uncertainty 5, 297-323.
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